Abstract

Based on photon-phonon nonlinear interaction, a scheme of controllable photon-phonon converters is proposed at single-quantum level in a composed quadratically coupled optomechanical system. With the assistance of the mechanical oscillator, the Kerr nonlinear effect between photon and phonon is enhanced so that the single-photon state can be converted into the phonon state with high fidelity even under the current experimental condition that the single-photon coupling rate is much smaller than mechanical frequency (gωm). The state transfer protocols and their transfer fidelity are discussed analytically and numerically. A multi-path photon-phonon converter is designed by combining the optomechanical system with low frequency resonators, which can be controlled by experimentally adjustable parameters. This work provides us a potential platform for quantum state transfer and quantum information.

© 2017 Optical Society of America

1. Introduction

The radiation pressure in optomechanical system provides us nonlinear interaction between optical cavity mode and microcosmic or macroscopic mechanical mode [1–4]. In addition to some promising applications in fundamental physics research [5, 6], macroscopic mechanical oscillators cooling [7–9], weak force sensing [10–13] and quantum information processing [14–16], optomechanical interaction is naturally of the outstanding characteristic to transduce a state from high frequency object into another one with low frequency. It has been shown that the quantum-state can be converted from light to macroscopic oscillators [17, 18] via optomechanical systems in optical regime. In electro-opto-mechanical system, electrical and optical quantum states can be stored and transferred into mechanical resonators [19, 20], thus the system is able to serve as a microwave quantum-illumination device [21]. On the other hand, many proposal of convertors, transferring few photon state to different frequency electromagnetic wave state based on quantum nonlinearity [22–24], have been proposed, including four-wave mixing converter [24], single-photon frequency conversion in a Sagnac interferometer [23]. In order to employ the cavity optomechanical system in quantum information processing, single photon-phonon conversion is an important manipulation. There is a great challenge in converter when huge frequency difference exists between input state and output state such as optical mode and mechanical mode. Under current experimental parameters region, how to enhance the effective nonlinearity and how to employ their nonlinearity to perform quantum information processing deserve our investigation.

In this paper, we put forward a scheme to enhance the cross-Kerr nonlinearity in a quadratically coupled optomechanical system. Considering the realization, we use an auxiliary mechanical oscillators to enhance the quantum nonlinear effects in the system, and thus achieve an ultra-strong cross-Kerr nonlinearity (geffeff ≫ 1). By combining single bit operations in optical mode and mechanical mode, we can implement a photon-phonon converter at single-quantum level. Then we construct a multi-path photon-phonon converter by extending the dimension of system, which can be controlled by experimentally adjustable parameters.

2. Model

We consider an optomechanical system where a membrane in the middle of a Fabry-Pérot cavity is coupled with another mechanical oscillator, shown in Fig. 1. The membrane quadratically couples to the cavity field, and the interaction between two oscillators can be realized by a resonator interacting with a transmission line resonator through the medium of capacitance [25], or by using the geometrically interconnecting [26]. The Hamiltonian of the system is

H=Hsys+Hd
Hsys=ωcaagaa(b1+b1)2+j=1,2(ωmjbjbj+Vbjb3j),
Hd=ε(aeiωdt+aeiωdt),
where a(a), b1(b1) and b2(b2) are the creation (annihilation) operators of the F-P cavity, the mechanical membrane and the target mechanical oscillator, respectively. ωc, ωm1 and ωm2 are the resonant frequency of them. The second term in Hsys describes the quadratic optomechanical coupling between the cavity and the mechanical membrane with strength g. The last term in Hsys represent the free energy and the phonon tunneling coupling between two oscillators with strength V [27, 28]. Hd denotes that the cavity is driven by a laser with frequency ωd. By eliminating the rapid evolution mode b1 due to large frequency ωm1, we obtain the effective interaction between the optomechanical cavity and the oscillator mode b2, under the condition {ωm1, ωm2} ≫ {V, g} (Details are in Appendix). The effective Hamiltonian is
Heff=Δaa+ωeffb2b2+geffaab2b2,
where
Δ1=ωcωdg,
ωeff=ωm2V2(ωm1ωm2)|A|2,
geff=2gV2|A|2,
with
A=i(ωm1ωm2)+(γ1γ2)/2.
Δ′1 denotes the mechanically modulating detuning of the cavity with a driving frequency ωd. ωeff means the effective frequency of the mechanical oscillator, and geff represent nonlinear coupling strength. In the process of deriving effective Hamiltonian, we also obtain the effective and dampling rates γeff=γ2+V2(γ1γ2)2|A|2. We can clearly see the existence of the cross-Kerr nonlinear term between cavity mode and mechanical mode geffaab2b2 which can provide a way to preform manipulation between photons and phonons. The effective coefficient geff play the key factor in the quantum control schemes based on cross-Kerr nonlinearity [14, 29]. Usually, the cross-Kerr nonlinearity is very weak. Fortunately, in our scheme, the coefficients geff, Δ′ and ωeff are adjustable.

 figure: Fig. 1

Fig. 1 The quadratically coupled optomechanical system consists of a membrane in the middle of the cavity. The membrane is interacted to a low frequency resonator with the coupling strength V via a capacitance C.

Download Full Size | PPT Slide | PDF

As is shown in Fig. 2(a), within certain region of V, ωeff can be reduced, even approximation a minimal value zero, i.e., |ωeff| ≈ 0 at the specific value of Vωm1(ωm1ωm2). Meanwhile, the effective coupling rate geff increases with the mechanical coupling rate V raising, shown in Fig. 2(b). The ratio between the effective coupling rate and the effective mechanical frequency |geffeff| is shown in Fig. 2(c). There is a discontinuity point tending to infinity at a specific value of mechanical coupling rate Vωm1(ωm1ωm2). The coefficients ωeff, geff and γeff are affected by the frequency difference between two oscillators are shown in Fig. 3(d), 3(e) and 3(f). The modulated ωeff frequency also can be decreased by adjusting Δωm [shown in (d)], and geff decrease with increasing of Δωm [see (e)]. The ratio |geffeff| can be enlarged greatly at certain region, shown in (f). Although {g, V} ≪ {ωm1, ωm2}, the Δωm can be small so that effective Kerr nonlinearity is enlarged. For usual optomechanical system, the nonlinearity is g2/ωm1, while our modulated nonlinearity coefficient is geff (see Eq. (7)). Obviously, the nonlinearity is enlarged greatly, i.e., 2gV2|A|2g2/ωm1. Thus we can enlarge the ratio |geffeff| ≫ 1 by adjusting the coupling rate V and the frequency difference Δωm. So it is possible for us to achieve an ultra-strong cross-Kerr nonlinearity in the system.

 figure: Fig. 2

Fig. 2 The effective frequency of the mechanical oscillator ωeff, effective coupling strength geff, the ratio of |geffωeff| and effective damping rate γeff is a function of mechanical coupling strength V, corresponding to (a), (b) and (c), respectively. (d), (e) and (f) show these effective parameters changing with the frequency difference Δωm = ωm1ωm2 (. For (a), (b) and (c), the parameters are g/ωm1 = 10−4, ωm2/ωm1 = 0.998, γm1/ωm1 = 10−6, γm1/γm2 = 102, while for (d), (e) and (f), the parameters are g/ωm1 = 10−4, γm1/ωm1 = 10−6, V/ωm1 = 5 × 10−2, γm1/γm2 = 102.

Download Full Size | PPT Slide | PDF

 figure: Fig. 3

Fig. 3 (a) The comparison of analytical and numerical solution of fidelity Fcp. The mechanical coupling rate V/ωm1 = 3.16 × 10−2. The fidelity Fcp as a function of time t with different mechanical coupling strength V/ωm1 = 1.35 × 10−2, 2.58 × 10−2, 3.16 × 10−2, corresponding to (b), (c) and (d), respectively. The corresponding ratio |geffωeff|=0.01, 0.05, 0.1, and the maximal fidelity Fcpmax ≈ 0.83, 0.94, 0.97. For all of the figures, κ/g = 0.5, nth = 1, and the other parameters are the same with Fig. 2.

Download Full Size | PPT Slide | PDF

3. Photon-phonon control phase-flip gate

Now we show that the composed optomechanical system can work as a photon-phonon control phase-flip gate (CPFG) analytically and numerically. We use the ground- (excited-) state of photon and phonon to denote the logical states |0〉 (|1〉) of signal mode and control mode, respectively. The unknown signal qubit inputs via the optical cavity. The arbitrary initial state of the system can be describes as

|ψ=α|0c|0m+β|0c|1m+γ|1c|0m+δ|1c|1m,
where |α|2 + |β|2 + |γ|2 + |δ|2 = 1. |0〉c (|1〉c) means no (one) photon in the cavity while |0〉m(|1〉m) stands for the ground state (the first excited state) of the oscillator. When we can accomplish the optomechanical CPFG, the target state should be
|Φ=α|0c|0m+β|0c|1m+γ|1c|0mδ|1c|1m.
If we use the effective Hamiltonian Eq. (4) and ignore the cavity’s decay and the mechanical damping, the finial state is |ψf〉 = eiHefft |ψ〉, which can be described as
|ψf=α|0c|0m+βeiθ01|0c|1m+γeiω10|1c|0m+δeiθ11|1c|1m,
where θ01 = ωefft, θ10 = Δ′t, θ11 = (ωeff + Δ′ − geff)t. We define the fidelity Fcp = |〈ψf |Φ〉| between the final state and the target state, thus
Fcp=|α2eiθ00+β2eiθ01+γ2eiθ10δ2eiθ11|,
If the conditions
θ01=ωefft=2n1π,θ10=Δt=2n2π,θ11=(ωeff+Δgeff)t=(2n3+1)π,ni(i=1,2,3),
are satisfied, we have Fcp = 1, which means the CPFG is realized. Then the ratio of the parameters should meet the relation ωeff : Δ′: geff = n1 : n2 : (n1 + n2n3 − 1/2).

Including the dissipation of the system, we can directly employ the master equation of the system to reconsider CPFG. The master equation is as

ρ˙=i[ρ,H]+κ𝒟[a]ρ+j=1,2γj(nthj+1)𝒟[bj]ρ+γjnthj𝒟[bj]ρ,
where H is the original Hamiltonian Eq. (1), κ, γj and nthj are the decay rates of the cavity, mechanical resonator and the thermal occupancy of the mechanical bath respectively. 𝒟[o]ρ = oρoo/2 − ρoo/2 is the Lindblad dissipation superoperator. Under this condition, Fcp=Φ|ρ|Φ.

We plot the fidelity in both analytical and numerical method in Fig. 3(a). One can observe that the CPFG can be realized in a specific time when the additional phase equals to (2n+1)π, n ∈ ℜ. Comparing the analytical and numerical solution, we find that the two lines almost coincide. Thus we can safely conclude that the effective Hamiltonian and the analytical solution are correct, except some point with low fidelity due to the approximation in analytical solution. The Kerr nonlinear term geffaab2b2 in Eq. (4) is the key point to realize the CPF gate. Choosing different values of V/ωm1 = 1.35 × 10−2, 2.58 × 10−2, 3.16 × 10−2, we plot the fidelity in (b),(c) and (d) respectively. The corresponding ratio |geffωeff|=0.01,0.05,0.1. The maximal fidelity with ratio are Fcpmax ≈ 0.83, 0.94, 0.97, respectively. It is clearly that the larger values of the ratio |geffωeff| the higher fidelity of the CPFG. In our scheme, with the assistance of mechanical oscillator we can enlarge the ratio |geffωeff|. Therefore, the current scheme provides a realizable method to perform controlled-phase gate between photons and phonons under weak coupling regime.

4. Single-quantum photon-phonon convertor

Employing optomechanical interaction, we can build a link between photons and phonons. Now, we show that our system can perform a photon-phonon convertor at the single-photon level using the cross-Kerr nonlinearity effect. As shown in Fig. 4, the quantum circuit denotes a basic process to realize photon-phonon convertor. The single-qubit code in photons can be realized by using a velocity-selected circular Rydberg atom in the cavity [30], pre-excited single atoms in the cavity [31] and parametric down-conversion in a distributed microcavity [32]. We can produce signal state directly in optomechanical system [30, 31] or introduce it into the system using low losing fiber [33], monochromatic waveguide [34]. And the single optical state can be easily operated by linear optical device [35]. The ground- and single- phonon state can be manipulated by film bulk acoustic resonator [26,36,37]. In Fig. 4, the c-phase gate is realized by the optomechanical system with fidelity Fmax = 0.97 which we have mentioned in section III. Here we code information as follows: |0〉1 means no photon in the cavity while |1〉1 means only one photon in the cavity. |0〉2 means that mechanical osillator is in its gound state and |1〉2 means in excited state. As shown in Fig. 4, to transfer an arbitrary optical state α|0〉1 + β|1〉1 to the mechanical oscillator through the convertor, we input the coded state into the cavity while the mechanical oscillator should be cooled into its ground state |0〉2. After a Hadamard gate operator manipulate in |0〉2, the state becomes 12(α|01+β|11)(|02+|12). The system undergoing a CPFG process, the quantum state becomes 12[α|01(|02+|12)+β|12(|02|12]. Then, ultimating two Hadamard gate operation on both photon and phonon state, we get the system state, 12[α(|01+|11)|02+β(|01|11)|12], which can be rewritten as

12|01(α|02+β|12)+|11(α|02β|12),
Then we detect the output photon from the the cavity. If the photon counting is zero, mechanical oscillator will collapse to the state α|0〉2 + β|1〉2. If the photon counting is one, the mechanical oscillator will collapse to the state α|0〉2β|1〉2, then we just need to performing a σz operation. Thus, finally, we can transfer optical state.

 figure: Fig. 4

Fig. 4 Quantum circuit of photon-phonon convertor. After performing single-qubit operation according to the measure result, we can obtain the state we want in mechanical mode.

Download Full Size | PPT Slide | PDF

In a recent experiment [38], single photon-phonon correlation using linearized optomechanical interaction G(ab + ab), can generate a single stokes scattering with probability p ≈ 3%. By using this scheme, a single photon is transfer into a single phonon with the efficiency that approximate equals to 3.7%. Differently, we aim to transfer a information encoded in a photon state (α|0〉 + β|1〉) into a phonon carrier. We employ an enhanced Kerr nonlinearity geffaabb. Theoretically speaking, our scheme, the phonon-to-photon information conversion might be achieved with a 100% efficiency and a high fidelity considering the dissipation.

5. Controllable multi-path photon-phonon converter

Now we expand our system to a more general model. As shown in Fig. 5, there is an array of quadratically coupled optomechanics, cavity-k (k > 1) coupled to the cavity-1 with strength Jk−1. Each membranae of the optomechanical cavity coupled to a low frequency oscillator with the strength Vj. The Hamiltonian of the system can be writte as

H=j=1nωjajaj+ωmjbjbj+ωAjbAjbAj+gjajaj(bj+bj)2+Vj(bjbAj+bjbAj)+s=1n1Js(a1as+1+a1as+1),
where aj and ωj denote the cavity photon operator and frequency, respectively. ωmj, bj and ωAj, bAj describe the membranae mode and target oscillator mode, respectively. The fourth term denotes the optomechanical interaction. The fifth and sixth term denote the interaction between the mechanical modes and optical modes, respectively.

 figure: Fig. 5

Fig. 5 Schematic diagram of multi-controlled phase gate and quantum circuit of photon-phonon conveter.

Download Full Size | PPT Slide | PDF

Using the same processing in section II, we get the effective Hamiltonian under the condition ωmj ≫ {gj, Vj, Jj}.

Heff=j=1nΔjajaj+ωejbAjbAj+gejajajbAjbAj+s=1n1Js(a1as+1+a1as+1),
where ωej=ωAjVj2(ωmjωAj)/|Aj|2, gej=2gjVj2/|Aj|2, Δj = ωjωjL, here Aj = i(ωmjωAj) + (γmjγAj)/2 and ωjL denotes the driving frequency of cavity-j.

If we set cavity-1 as an input port of the multi-path convert system, the input photon state can be transmitted from cavity-1 to cavity-k due to the Beam Splitter (BS) interaction. According to the analysis in former section, we can convert the single-photon state from optical mode to mechanical mode by using cross-Kerr nonlinearity. Thus, composing the two manipulations, we can convert the arbitrary input single-photon state from cavity-1 to any other target oscillator through cavity-k. According to the mode shows in Fig. 5, only when the CPFG is achieved and the optical state is transferred into cavity-j at the time, can we convert the input photon state to the j-th phonon state. In order to evaluate the quality of the conversion, we define the conversion fidelity which is defined as

FCj=FGjFSj=(ψf|ρj|ψfψ0|ρaj|ψ0)1/4,
where FGj denotes the fidelity of the CPFG between j-th optical mode and mechanical mode, ρj is the density operation of them. ψf is the final state after a perfect CPFG operator. FSj denotes the fidelity between input state ψ0 and the state in cavity-j ψ0.

Take n = 2 as an example, we show the controllable photon-phonon conversion process using Heff. As shown in Fig. 6(a), we plot the conversion fidelity of the output port without dispassion. It shows that the photon-phonon conversion both for port 1 and 2 can be periodically realized at a specific time simultaneously. When the dissipation is included, the fidelity of the conversion for both ports decreased (see (b)). Although the parameters are the same for both of the subsystem, the fidelity FC2 is slightly lower than FC1 = 1, because the signal state is directly input from cavity 1, so it is directly conversed into port 1, while for port 2, it is needed firstly hopping from a1 into a2 and then conversed into port 2. Thus, it is reasonable to understand the slightly decrease of fidelity FC2. By individually adjusting V and ωmi (i = 1, 2) as we have discussed above, we can change the ratio geffeff. The conversion fidelity for individual different values geiei(i=1,2) are shown in Fig. 6(c) and 6(d). It is obvious that the periodic time is determined by the value of geiei. Thus, on the one hand, we can enlarge the the ratios geiei to compensate the dissipation of the system, on the other hand, we can control the time of the conversion reached.

 figure: Fig. 6

Fig. 6 The dynamic of the conversion fidelity with different effective coupling rate ge2. The blue line denotes the conversion fidelity of output port 1, the green line denotes the conversion fidelity of output port 2. Other parameters are ωe1 = ωe2, κ1 = κ2 = 0.1ωe1, J1/ωe1 = 0.1, γ1 = 10γ2 = 10−5ωe1, nth1 = nth2 = 5.

Download Full Size | PPT Slide | PDF

6. Discussion and conclusion

As we have shown, the FC of cavity-2 cannot reach 1 just like cavity-1 even without dispassion, because the rest systems can be seen as an environment, which introduces an effective dissipation rate to the sub-system (such as cavity-j) that we focus on. Thus, the number of output ports in the multi-path converter is limited to some extent if we require high fidelity of the converted state. To increase the fidelity of converter, on the one hand, we can enlarge the ratio of |geffeff| to accelerate the evolution, which will reduce the cumulative effects of system dissipation (shown in Fig. 3). On the other hand, we can directly improve the quality factor of cavity to reduce the effective dissipation rate. In our scheme, the optomechanical oscillator can be realized by a suspended film bulk acoustic resonator with frequency in the order of 109Hz [37]. The target oscillator can be realized by nanoobjects with frequency in the order of 106Hz [26, 39]. The interaction between them can be controlled by piezoelectric ceramics and LC circuits [25,37]. By changing the voltage V0 and capacitance C0 experimentally, we can control V because of VC0V0. A two-dimensional electron gas and Schottky-contacted gold electrodes can be used to output the phonon signal we need [40].

We propose a scheme to realize single photon-phonon converter by combining the single-bit operation with the cross-Kerr nonlinear effect between photons and phonons in quadratically coupled optomechanical system. Considering the realization, we use the weak coupling optomechanical oscillator coupled to a target oscillator to accelerate the evolution of system so as to improve the fidelity of CPFG, we can achieves Fcpmax ≈ 0.97 in consideration of dissipation, as is shown in Fig. 3. By controlling the adjustable parameters, we are able to achieve an ultra-strong cross-Kerr nonlinearity (geffeff ≫ 1), which makes sense for the realization of single quantum photon-phonon converter to a large extent. Moreover, we also extend the converter protocol to a controllable multiple outputs scheme through a dimension extension. By choosing the detection time of the output signal of cavity-1, we can transduce an unknown input single optical state into a mechanical state of an arbitrary output port we want with high fidelity. This protocol provides us with a possibility to perform photon-phonon multipath conversion and operation.

Appendix: derivation of the effective Hamiltonian

Under the weak diving condition, we tempt ignore the function of the Hamiltonian Hd so as to simplify the process of the deriving the effective Hamiltonian. Considering ωm1g, b12 and b12 can be ignored by rotating wave approximation, the Hamiltonian can be rewritten as

Hsys=ωcaagaa(b1b1+b1b1)+j=1,2(ωmjbjbj+Vbjb3j).
In a frame rotating at the frequency of optical drive, the nonlinear quantum Langevin equations are given by
a˙=(iΔ+κ/2)a+2igab1b1+κain,
b˙1=(iωm1+γ1/2)b1+2igb1a1a1iVb2+γ1bin,1,
b˙2=(iωm2+γ2/2)b2iVb1+γ2bin,2,
where Δ′1 = ωcωdg denotes the mechanically modulating detuning of the cavity with a driving frequency ωd. κ, γ1 and γ2 represent the decay rates of mode a, b1 and b2. The ain is the sum of coherent amplitudes āin and vacuum noise operator ξ. bin,1 and bin,2 are the noise operators associated with the mechanical dissipations. Defining photon number operator Na = aa and phtonon number operator Nb=b1b1, we can rewrite the nonlinear quantum Langevin equations as
a˙=(iΔ+κ/2)a+2igaNb+κain,
b˙1=(iωm1+γ1/2)b1+2igb1NaiVb2+γ1bin,1,
b˙2=(iωm2+γ2/2)b2iVb1+γ2bin,2,
N˙a=κ1Na,
These equations can be formally integrated as
a1(t)=a(0)e(iΔ+κ/2)te0tdτ2igNb(τ)+0tdτe(iΔ+κ/2)(tτ)eτtdτ2igNb(τ)κain(τ)],
b1(t)=b1(0)e(iωm1+γ1/2)te0tdτ2igNa(τ)+0tdτe(iωm1+γ1/2)(tτ)eτtdτ2igNa(τ)[iVb2(τ)+γ1bin,1(τ)],
b2(t)=b2(0)e(iωm2+γ2/2)t+0tdτe(iωm2+γ2/2)(tτ)[iVb1(τ)+γ2bin,2(τ)],
while (21d) denotes that the cavity field rapidly achieves its stead value because of its large frequency and dissipation rate κ1 so that we can treat Na as constant in integration (21b), in other words, when the dissipation rate of mechanical oscillators is weak enough and the dynamic time of the oscillators is much smaller than that for cavity field, we can regard Na as independent of time t in the phonon evolution period. Under the weak driving condition, the occupation number of the system is rather small. If ωm2 ≫ {g, V}, we can employ iteration method to solve (22c) and obtain the zero order solution (in terms of V) as
b2(0)(t)b2(0)e(iωm2+γ2/2)t+Bin,2(t),
where Bin,2(t)=0tdτe(iωm2+γ2/2)(tτ)γ2bin,2(τ) denote the noise terms. Substituting it into (22b), we have
b1(t)b1(0)e(iωm1+γ1/22igNat)+0tdτe(iωm1+γ1/22igNa)(tτ)×[iVb2(0)e(iωm2+γ2/2)τiVBin,2(τ)+γ1bin,1(τ)].
Under the condition γ1γ2 (the term containing eγ1t is a fast decaying term and can be neglected), we have
b1(t)iVb2(t)i(ωm1ωm2)+(γ1γ2)/22igNa+Bin,1
where the noise term is denoted by Bin,1(t)0tdτe(iωm1+γ1/2)(tτ)[iVBin,2(τ)+γ1bin,1(τ)]+iVBin,2/[A2igNa], where A = i(ωm1ωm2)+(γ1γ2)/2. When |ωm1ωm2| is much larger than 2gNa, we have
b1(t)iVb2(t)A[1+i(ωm1ωm2)+(γ1γ2/2)2igNa|A|2]+Bin,1(t)
Putting b1(t) back to (21a) and (21c), we finally obtain
a˙=(iΔ+κ/2)a+igeffab2b2+κain,
b˙2=(iωeff+γeff/2)b2+igeffb2aa+γeffBin,2,
where ωeff=ωm2V2|A|2(ωm1ωm2), geff=2gV2|A|2, γeff=γ2+V22|A|2(γ1γ2). Thus, the effective Hamiltonian is
Heff=Δaa+ωeffb2b2+geffaab2b2.

Funding

National Natural Science Foundation of China (NSFC) (11474044, 11547134).

Acknowledgments

We would like to thank Mr. Wen-Lin Li and Xun Li for helpful discussions.

References and links

1. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014). [CrossRef]  

2. J.-Q. Liao and L. Tian, “Macroscopic quantum superposition in cavity optomechanics,” Phys. Rev. Lett. 116, 163602 (2016). [CrossRef]   [PubMed]  

3. H. Jing, D. S. Goldbaum, L. Buchmann, and P. Meystre, “Quantum Optomechanics of a Bose-Einstein Antiferromagnet”, Phys. Rev. Lett. 106, 223601 (2011). [CrossRef]   [PubMed]  

4. H. Jing, X. Zhao, and L. F. Buchmann, “Quantum optomechanics with a mixture of ultracold atoms”, Phys. Rev. A 86, 065801 (2012) [CrossRef]  

5. J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016). [CrossRef]   [PubMed]  

6. Q. Mu, X. Zhao, and T. Yu, “Memory-effect-induced macroscopic-microscopic entanglement,” Phys. Rev. A 94, 012334 (2016). [CrossRef]  

7. W.-Z. Zhang, J. Cheng, W.-D. Li, and L. Zhou, “Optomechanical cooling in the non-markovian regime,” Phys. Rev. A 93, 063853 (2016). [CrossRef]  

8. Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, and C. W. Wong, “Coupled cavities for motional ground-state cooling and strong optomechanical coupling,” Phys. Rev. A 91, 033818 (2015). [CrossRef]  

9. K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91, 063815 (2015). [CrossRef]  

10. K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015). [CrossRef]   [PubMed]  

11. Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014). [CrossRef]   [PubMed]  

12. O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006). [CrossRef]   [PubMed]  

13. S. Davuluri and Y. Li, “Absolute rotation detection by Coriolis force measurement using optomechanics,” New Journal of Physics 18, 103047 (2016). [CrossRef]  

14. W.-Z. Zhang, J. Cheng, and L. Zhou, “Quantum control gate in cavity optomechanical system,” Journal of Physics B: Atomic, Molecular and Optical Physics 48, 015502 (2015). [CrossRef]  

15. K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012). [CrossRef]   [PubMed]  

16. W. Li, C. Li, and H. Song, “Quantum synchronization in an optomechanical system based on lyapunov control,” Phys. Rev. E 93, 062221 (2016). [CrossRef]   [PubMed]  

17. J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68, 013808 (2003). [CrossRef]  

18. S. Singh, H. Jing, E. M. Wright, and P. Meystre, “Quantum-state transfer between a bose-einstein condensate and an optomechanical mirror,” Phys. Rev. A 86, 021801 (2012). [CrossRef]  

19. S. A. McGee, D. Meiser, C. A. Regal, K. W. Lehnert, and M. J. Holland, “Mechanical resonators for storage and transfer of electrical and optical quantum states,” Phys. Rev. A 87, 053818 (2013). [CrossRef]  

20. L. Tian, “Optoelectromechanical transducer: Reversible conversion between microwave and optical photons,” Annalen der Physik 527, 1–14 (2015). [CrossRef]  

21. S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015). [CrossRef]   [PubMed]  

22. Z. H. Wang, L. Zhou, Y. Li, and C. P. Sun, “Controllable single-photon frequency converter via a one-dimensional waveguide,” Phys. Rev. A 89, 053813 (2014). [CrossRef]  

23. W.-B. Yan, J.-F. Huang, and H. Fan, “Tunable single-photon frequency conversion in a Sagnac interferometer,” Sci. Rep. 3, 3555 (2013). [CrossRef]   [PubMed]  

24. A. Zhang and M. S. Demokan, “Broadband wavelength converter based on four-wave mixing in a highly nonlinear photonic crystal fiber,” Opt. Lett. 30, 2375–2377 (2005). [CrossRef]   [PubMed]  

25. L. Tian, M. S. Allman, and R. W. Simmonds, “Parametric coupling between macroscopic quantum resonators,” New Journal of Physics 10, 115001 (2008). [CrossRef]  

26. H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013). [CrossRef]  

27. A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, “Measures of quantum synchronization in continuous variable systems,” Phys. Rev. Lett. 111, 103605 (2013). [CrossRef]  

28. M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013). [CrossRef]   [PubMed]  

29. X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012). [CrossRef]  

30. P. Bertet et al.,“Direct Measurement of the Wigner Function of a One-Photon Fock State in a Cavity,” Phys. Rev. Lett. 89, 200402 (2002). [CrossRef]   [PubMed]  

31. M. Lee et al., “Three-dimensional imaging of cavity vacuum with single atoms localized by a nanohole array,” Nat. Commun. 5, 3441 (2014). [PubMed]  

32. M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005). [CrossRef]  

33. A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly Efficient Single-Pass Source of Pulsed Single-Mode Twin Beams of Light,” Phys. Rev. Lett. 106, 013603 (2011). [CrossRef]   [PubMed]  

34. X.-W. Xu and Y. Li, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a weakly nonlinear cavity,” Phys. Rev. A 90, 033832 (2014). [CrossRef]  

35. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000), Chap.7.

36. Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010). [CrossRef]  

37. A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010). [CrossRef]  

38. R. Riedinger et al.,“Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530, 313–316 (2016). [CrossRef]   [PubMed]  

39. J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008). [CrossRef]   [PubMed]  

40. I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, “Phonon lasing in an electromechanical resonator,” Phys. Rev. Lett. 110, 127202 (2013). [CrossRef]   [PubMed]  

References

  • View by:
  • |
  • |
  • |

  1. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
    [Crossref]
  2. J.-Q. Liao and L. Tian, “Macroscopic quantum superposition in cavity optomechanics,” Phys. Rev. Lett. 116, 163602 (2016).
    [Crossref] [PubMed]
  3. H. Jing, D. S. Goldbaum, L. Buchmann, and P. Meystre, “Quantum Optomechanics of a Bose-Einstein Antiferromagnet”, Phys. Rev. Lett. 106, 223601 (2011).
    [Crossref] [PubMed]
  4. H. Jing, X. Zhao, and L. F. Buchmann, “Quantum optomechanics with a mixture of ultracold atoms”, Phys. Rev. A 86, 065801 (2012)
    [Crossref]
  5. J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016).
    [Crossref] [PubMed]
  6. Q. Mu, X. Zhao, and T. Yu, “Memory-effect-induced macroscopic-microscopic entanglement,” Phys. Rev. A 94, 012334 (2016).
    [Crossref]
  7. W.-Z. Zhang, J. Cheng, W.-D. Li, and L. Zhou, “Optomechanical cooling in the non-markovian regime,” Phys. Rev. A 93, 063853 (2016).
    [Crossref]
  8. Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, and C. W. Wong, “Coupled cavities for motional ground-state cooling and strong optomechanical coupling,” Phys. Rev. A 91, 033818 (2015).
    [Crossref]
  9. K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91, 063815 (2015).
    [Crossref]
  10. K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
    [Crossref] [PubMed]
  11. Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
    [Crossref] [PubMed]
  12. O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
    [Crossref] [PubMed]
  13. S. Davuluri and Y. Li, “Absolute rotation detection by Coriolis force measurement using optomechanics,” New Journal of Physics 18, 103047 (2016).
    [Crossref]
  14. W.-Z. Zhang, J. Cheng, and L. Zhou, “Quantum control gate in cavity optomechanical system,” Journal of Physics B: Atomic, Molecular and Optical Physics 48, 015502 (2015).
    [Crossref]
  15. K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
    [Crossref] [PubMed]
  16. W. Li, C. Li, and H. Song, “Quantum synchronization in an optomechanical system based on lyapunov control,” Phys. Rev. E 93, 062221 (2016).
    [Crossref] [PubMed]
  17. J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68, 013808 (2003).
    [Crossref]
  18. S. Singh, H. Jing, E. M. Wright, and P. Meystre, “Quantum-state transfer between a bose-einstein condensate and an optomechanical mirror,” Phys. Rev. A 86, 021801 (2012).
    [Crossref]
  19. S. A. McGee, D. Meiser, C. A. Regal, K. W. Lehnert, and M. J. Holland, “Mechanical resonators for storage and transfer of electrical and optical quantum states,” Phys. Rev. A 87, 053818 (2013).
    [Crossref]
  20. L. Tian, “Optoelectromechanical transducer: Reversible conversion between microwave and optical photons,” Annalen der Physik 527, 1–14 (2015).
    [Crossref]
  21. S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
    [Crossref] [PubMed]
  22. Z. H. Wang, L. Zhou, Y. Li, and C. P. Sun, “Controllable single-photon frequency converter via a one-dimensional waveguide,” Phys. Rev. A 89, 053813 (2014).
    [Crossref]
  23. W.-B. Yan, J.-F. Huang, and H. Fan, “Tunable single-photon frequency conversion in a Sagnac interferometer,” Sci. Rep. 3, 3555 (2013).
    [Crossref] [PubMed]
  24. A. Zhang and M. S. Demokan, “Broadband wavelength converter based on four-wave mixing in a highly nonlinear photonic crystal fiber,” Opt. Lett. 30, 2375–2377 (2005).
    [Crossref] [PubMed]
  25. L. Tian, M. S. Allman, and R. W. Simmonds, “Parametric coupling between macroscopic quantum resonators,” New Journal of Physics 10, 115001 (2008).
    [Crossref]
  26. H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
    [Crossref]
  27. A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, “Measures of quantum synchronization in continuous variable systems,” Phys. Rev. Lett. 111, 103605 (2013).
    [Crossref]
  28. M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013).
    [Crossref] [PubMed]
  29. X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
    [Crossref]
  30. P. Bertet and et al.,“Direct Measurement of the Wigner Function of a One-Photon Fock State in a Cavity,” Phys. Rev. Lett. 89, 200402 (2002).
    [Crossref] [PubMed]
  31. M. Lee and et al., “Three-dimensional imaging of cavity vacuum with single atoms localized by a nanohole array,” Nat. Commun. 5, 3441 (2014).
    [PubMed]
  32. M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
    [Crossref]
  33. A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly Efficient Single-Pass Source of Pulsed Single-Mode Twin Beams of Light,” Phys. Rev. Lett. 106, 013603 (2011).
    [Crossref] [PubMed]
  34. X.-W. Xu and Y. Li, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a weakly nonlinear cavity,” Phys. Rev. A 90, 033832 (2014).
    [Crossref]
  35. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000), Chap.7.
  36. Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
    [Crossref]
  37. A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
    [Crossref]
  38. R. Riedinger and et al.,“Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530, 313–316 (2016).
    [Crossref] [PubMed]
  39. J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
    [Crossref] [PubMed]
  40. I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, “Phonon lasing in an electromechanical resonator,” Phys. Rev. Lett. 110, 127202 (2013).
    [Crossref] [PubMed]

2016 (7)

J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016).
[Crossref] [PubMed]

Q. Mu, X. Zhao, and T. Yu, “Memory-effect-induced macroscopic-microscopic entanglement,” Phys. Rev. A 94, 012334 (2016).
[Crossref]

W.-Z. Zhang, J. Cheng, W.-D. Li, and L. Zhou, “Optomechanical cooling in the non-markovian regime,” Phys. Rev. A 93, 063853 (2016).
[Crossref]

J.-Q. Liao and L. Tian, “Macroscopic quantum superposition in cavity optomechanics,” Phys. Rev. Lett. 116, 163602 (2016).
[Crossref] [PubMed]

S. Davuluri and Y. Li, “Absolute rotation detection by Coriolis force measurement using optomechanics,” New Journal of Physics 18, 103047 (2016).
[Crossref]

W. Li, C. Li, and H. Song, “Quantum synchronization in an optomechanical system based on lyapunov control,” Phys. Rev. E 93, 062221 (2016).
[Crossref] [PubMed]

R. Riedinger and et al.,“Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530, 313–316 (2016).
[Crossref] [PubMed]

2015 (6)

W.-Z. Zhang, J. Cheng, and L. Zhou, “Quantum control gate in cavity optomechanical system,” Journal of Physics B: Atomic, Molecular and Optical Physics 48, 015502 (2015).
[Crossref]

Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, and C. W. Wong, “Coupled cavities for motional ground-state cooling and strong optomechanical coupling,” Phys. Rev. A 91, 033818 (2015).
[Crossref]

K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91, 063815 (2015).
[Crossref]

K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
[Crossref] [PubMed]

L. Tian, “Optoelectromechanical transducer: Reversible conversion between microwave and optical photons,” Annalen der Physik 527, 1–14 (2015).
[Crossref]

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

2014 (5)

Z. H. Wang, L. Zhou, Y. Li, and C. P. Sun, “Controllable single-photon frequency converter via a one-dimensional waveguide,” Phys. Rev. A 89, 053813 (2014).
[Crossref]

M. Lee and et al., “Three-dimensional imaging of cavity vacuum with single atoms localized by a nanohole array,” Nat. Commun. 5, 3441 (2014).
[PubMed]

X.-W. Xu and Y. Li, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a weakly nonlinear cavity,” Phys. Rev. A 90, 033832 (2014).
[Crossref]

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

2013 (6)

S. A. McGee, D. Meiser, C. A. Regal, K. W. Lehnert, and M. J. Holland, “Mechanical resonators for storage and transfer of electrical and optical quantum states,” Phys. Rev. A 87, 053818 (2013).
[Crossref]

W.-B. Yan, J.-F. Huang, and H. Fan, “Tunable single-photon frequency conversion in a Sagnac interferometer,” Sci. Rep. 3, 3555 (2013).
[Crossref] [PubMed]

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, “Measures of quantum synchronization in continuous variable systems,” Phys. Rev. Lett. 111, 103605 (2013).
[Crossref]

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013).
[Crossref] [PubMed]

I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, “Phonon lasing in an electromechanical resonator,” Phys. Rev. Lett. 110, 127202 (2013).
[Crossref] [PubMed]

2012 (4)

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[Crossref]

S. Singh, H. Jing, E. M. Wright, and P. Meystre, “Quantum-state transfer between a bose-einstein condensate and an optomechanical mirror,” Phys. Rev. A 86, 021801 (2012).
[Crossref]

H. Jing, X. Zhao, and L. F. Buchmann, “Quantum optomechanics with a mixture of ultracold atoms”, Phys. Rev. A 86, 065801 (2012)
[Crossref]

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

2011 (2)

H. Jing, D. S. Goldbaum, L. Buchmann, and P. Meystre, “Quantum Optomechanics of a Bose-Einstein Antiferromagnet”, Phys. Rev. Lett. 106, 223601 (2011).
[Crossref] [PubMed]

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly Efficient Single-Pass Source of Pulsed Single-Mode Twin Beams of Light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

2010 (2)

Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
[Crossref]

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

2008 (2)

L. Tian, M. S. Allman, and R. W. Simmonds, “Parametric coupling between macroscopic quantum resonators,” New Journal of Physics 10, 115001 (2008).
[Crossref]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

2006 (1)

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

2005 (2)

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[Crossref]

A. Zhang and M. S. Demokan, “Broadband wavelength converter based on four-wave mixing in a highly nonlinear photonic crystal fiber,” Opt. Lett. 30, 2375–2377 (2005).
[Crossref] [PubMed]

2003 (1)

J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68, 013808 (2003).
[Crossref]

2002 (1)

P. Bertet and et al.,“Direct Measurement of the Wigner Function of a One-Photon Fock State in a Cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[Crossref] [PubMed]

Agarwal, G. S.

K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91, 063815 (2015).
[Crossref]

Allman, M. S.

L. Tian, M. S. Allman, and R. W. Simmonds, “Parametric coupling between macroscopic quantum resonators,” New Journal of Physics 10, 115001 (2008).
[Crossref]

Ansmann, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Arcizet, O.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

Bajer, J. c. v.

Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
[Crossref]

Banaszek, K.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[Crossref]

Bariani, F.

K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
[Crossref] [PubMed]

Barzanjeh, S.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

Bennett, S. D.

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

Bertet, P.

P. Bertet and et al.,“Direct Measurement of the Wigner Function of a One-Photon Fock State in a Cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[Crossref] [PubMed]

Bialczak, R. C.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Blair, D. G.

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

Braunstein, S. L.

J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68, 013808 (2003).
[Crossref]

Briant, T.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

Buchmann, L.

H. Jing, D. S. Goldbaum, L. Buchmann, and P. Meystre, “Quantum Optomechanics of a Bose-Einstein Antiferromagnet”, Phys. Rev. Lett. 106, 223601 (2011).
[Crossref] [PubMed]

Buchmann, L. F.

H. Jing, X. Zhao, and L. F. Buchmann, “Quantum optomechanics with a mixture of ultracold atoms”, Phys. Rev. A 86, 065801 (2012)
[Crossref]

Chang, C.-Y.

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

Chang, E. Y.

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

Chen, Y.

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

Cheng, J.

J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016).
[Crossref] [PubMed]

W.-Z. Zhang, J. Cheng, W.-D. Li, and L. Zhou, “Optomechanical cooling in the non-markovian regime,” Phys. Rev. A 93, 063853 (2016).
[Crossref]

W.-Z. Zhang, J. Cheng, and L. Zhou, “Quantum control gate in cavity optomechanical system,” Journal of Physics B: Atomic, Molecular and Optical Physics 48, 015502 (2015).
[Crossref]

Christ, A.

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly Efficient Single-Pass Source of Pulsed Single-Mode Twin Beams of Light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000), Chap.7.

Cleland, a. N.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Cohadon, P.-F.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

Danilishin, S. L.

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

Davuluri, S.

S. Davuluri and Y. Li, “Absolute rotation detection by Coriolis force measurement using optomechanics,” New Journal of Physics 18, 103047 (2016).
[Crossref]

Demokan, M. S.

Didier, N.

A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, “Measures of quantum synchronization in continuous variable systems,” Phys. Rev. Lett. 111, 103605 (2013).
[Crossref]

Dong, Y.

K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
[Crossref] [PubMed]

Eckstein, A.

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly Efficient Single-Pass Source of Pulsed Single-Mode Twin Beams of Light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

Fan, H.

W.-B. Yan, J.-F. Huang, and H. Fan, “Tunable single-photon frequency conversion in a Sagnac interferometer,” Sci. Rep. 3, 3555 (2013).
[Crossref] [PubMed]

Farace, A.

A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, “Measures of quantum synchronization in continuous variable systems,” Phys. Rev. Lett. 111, 103605 (2013).
[Crossref]

Fazio, R.

A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, “Measures of quantum synchronization in continuous variable systems,” Phys. Rev. Lett. 111, 103605 (2013).
[Crossref]

Français, O.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

Fujiwara, A.

I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, “Phonon lasing in an electromechanical resonator,” Phys. Rev. Lett. 110, 127202 (2013).
[Crossref] [PubMed]

Gao, Y. B.

Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
[Crossref]

Giovannetti, V.

A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, “Measures of quantum synchronization in continuous variable systems,” Phys. Rev. Lett. 111, 103605 (2013).
[Crossref]

Girvin, S. M.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

Goldbaum, D. S.

H. Jing, D. S. Goldbaum, L. Buchmann, and P. Meystre, “Quantum Optomechanics of a Bose-Einstein Antiferromagnet”, Phys. Rev. Lett. 106, 223601 (2011).
[Crossref] [PubMed]

Gong, Q.

Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, and C. W. Wong, “Coupled cavities for motional ground-state cooling and strong optomechanical coupling,” Phys. Rev. A 91, 033818 (2015).
[Crossref]

Gourgout, A.

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

Guha, S.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

Habraken, S. J. M.

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

Harris, J. G. E.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

Heidmann, A.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

Hofheinz, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Holland, M. J.

S. A. McGee, D. Meiser, C. A. Regal, K. W. Lehnert, and M. J. Holland, “Mechanical resonators for storage and transfer of electrical and optical quantum states,” Phys. Rev. A 87, 053818 (2013).
[Crossref]

Huang, J.-F.

W.-B. Yan, J.-F. Huang, and H. Fan, “Tunable single-photon frequency conversion in a Sagnac interferometer,” Sci. Rep. 3, 3555 (2013).
[Crossref] [PubMed]

Jayich, A. M.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

Jing, H.

S. Singh, H. Jing, E. M. Wright, and P. Meystre, “Quantum-state transfer between a bose-einstein condensate and an optomechanical mirror,” Phys. Rev. A 86, 021801 (2012).
[Crossref]

H. Jing, X. Zhao, and L. F. Buchmann, “Quantum optomechanics with a mixture of ultracold atoms”, Phys. Rev. A 86, 065801 (2012)
[Crossref]

H. Jing, D. S. Goldbaum, L. Buchmann, and P. Meystre, “Quantum Optomechanics of a Bose-Einstein Antiferromagnet”, Phys. Rev. Lett. 106, 223601 (2011).
[Crossref] [PubMed]

Kippenberg, T. J.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

Komar, P.

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

Korth, W. Z.

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

Kuang, L.-M.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[Crossref]

Lee, M.

M. Lee and et al., “Three-dimensional imaging of cavity vacuum with single atoms localized by a nanohole array,” Nat. Commun. 5, 3441 (2014).
[PubMed]

Lehnert, K. W.

S. A. McGee, D. Meiser, C. A. Regal, K. W. Lehnert, and M. J. Holland, “Mechanical resonators for storage and transfer of electrical and optical quantum states,” Phys. Rev. A 87, 053818 (2013).
[Crossref]

Lenander, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Li, C.

W. Li, C. Li, and H. Song, “Quantum synchronization in an optomechanical system based on lyapunov control,” Phys. Rev. E 93, 062221 (2016).
[Crossref] [PubMed]

Li, W.

W. Li, C. Li, and H. Song, “Quantum synchronization in an optomechanical system based on lyapunov control,” Phys. Rev. E 93, 062221 (2016).
[Crossref] [PubMed]

Li, W.-D.

W.-Z. Zhang, J. Cheng, W.-D. Li, and L. Zhou, “Optomechanical cooling in the non-markovian regime,” Phys. Rev. A 93, 063853 (2016).
[Crossref]

Li, Y.

S. Davuluri and Y. Li, “Absolute rotation detection by Coriolis force measurement using optomechanics,” New Journal of Physics 18, 103047 (2016).
[Crossref]

Z. H. Wang, L. Zhou, Y. Li, and C. P. Sun, “Controllable single-photon frequency converter via a one-dimensional waveguide,” Phys. Rev. A 89, 053813 (2014).
[Crossref]

X.-W. Xu and Y. Li, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a weakly nonlinear cavity,” Phys. Rev. A 90, 033832 (2014).
[Crossref]

Liao, J.-Q.

J.-Q. Liao and L. Tian, “Macroscopic quantum superposition in cavity optomechanics,” Phys. Rev. Lett. 116, 163602 (2016).
[Crossref] [PubMed]

Liu, Y.-C.

Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, and C. W. Wong, “Coupled cavities for motional ground-state cooling and strong optomechanical coupling,” Phys. Rev. A 91, 033818 (2015).
[Crossref]

Liu, Y.-x.

Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
[Crossref]

Luan, X.

Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, and C. W. Wong, “Coupled cavities for motional ground-state cooling and strong optomechanical coupling,” Phys. Rev. A 91, 033818 (2015).
[Crossref]

Lucero, E.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Ludwig, M.

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013).
[Crossref] [PubMed]

Lukin, M. D.

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

Ma, Y.

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

Mackowski, J.-M.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

Mahboob, I.

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, “Phonon lasing in an electromechanical resonator,” Phys. Rev. Lett. 110, 127202 (2013).
[Crossref] [PubMed]

Mari, A.

A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, “Measures of quantum synchronization in continuous variable systems,” Phys. Rev. Lett. 111, 103605 (2013).
[Crossref]

Marquardt, F.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013).
[Crossref] [PubMed]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

Martinis, J. M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

McGee, S. A.

S. A. McGee, D. Meiser, C. A. Regal, K. W. Lehnert, and M. J. Holland, “Mechanical resonators for storage and transfer of electrical and optical quantum states,” Phys. Rev. A 87, 053818 (2013).
[Crossref]

Meiser, D.

S. A. McGee, D. Meiser, C. A. Regal, K. W. Lehnert, and M. J. Holland, “Mechanical resonators for storage and transfer of electrical and optical quantum states,” Phys. Rev. A 87, 053818 (2013).
[Crossref]

Meystre, P.

K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
[Crossref] [PubMed]

S. Singh, H. Jing, E. M. Wright, and P. Meystre, “Quantum-state transfer between a bose-einstein condensate and an optomechanical mirror,” Phys. Rev. A 86, 021801 (2012).
[Crossref]

H. Jing, D. S. Goldbaum, L. Buchmann, and P. Meystre, “Quantum Optomechanics of a Bose-Einstein Antiferromagnet”, Phys. Rev. Lett. 106, 223601 (2011).
[Crossref] [PubMed]

Miao, H.

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

Michel, C.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

Miranowicz, A.

Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
[Crossref]

Mosley, P. J.

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly Efficient Single-Pass Source of Pulsed Single-Mode Twin Beams of Light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

Mu, Q.

Q. Mu, X. Zhao, and T. Yu, “Memory-effect-induced macroscopic-microscopic entanglement,” Phys. Rev. A 94, 012334 (2016).
[Crossref]

Neeley, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000), Chap.7.

Nishiguchi, K.

I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, “Phonon lasing in an electromechanical resonator,” Phys. Rev. Lett. 110, 127202 (2013).
[Crossref] [PubMed]

Noh, J.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[Crossref]

Nori, F.

Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
[Crossref]

O’Connell, A. D.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Okamoto, H.

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

Onomitsu, K.

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

Peng, K.

J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68, 013808 (2003).
[Crossref]

Pinard, L.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

Pinard, M.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

Pirandola, S.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

Qu, K.

K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91, 063815 (2015).
[Crossref]

Rabl, P.

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

Raymer, M. G.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[Crossref]

Regal, C. A.

S. A. McGee, D. Meiser, C. A. Regal, K. W. Lehnert, and M. J. Holland, “Mechanical resonators for storage and transfer of electrical and optical quantum states,” Phys. Rev. A 87, 053818 (2013).
[Crossref]

Riedinger, R.

R. Riedinger and et al.,“Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530, 313–316 (2016).
[Crossref] [PubMed]

Rousseau, L.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

Sank, D.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Shapiro, J. H.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

Silberhorn, C.

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly Efficient Single-Pass Source of Pulsed Single-Mode Twin Beams of Light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

Simmonds, R. W.

L. Tian, M. S. Allman, and R. W. Simmonds, “Parametric coupling between macroscopic quantum resonators,” New Journal of Physics 10, 115001 (2008).
[Crossref]

Singh, S.

S. Singh, H. Jing, E. M. Wright, and P. Meystre, “Quantum-state transfer between a bose-einstein condensate and an optomechanical mirror,” Phys. Rev. A 86, 021801 (2012).
[Crossref]

Song, H.

W. Li, C. Li, and H. Song, “Quantum synchronization in an optomechanical system based on lyapunov control,” Phys. Rev. E 93, 062221 (2016).
[Crossref] [PubMed]

Stannigel, K.

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

Sun, C. P.

Z. H. Wang, L. Zhou, Y. Li, and C. P. Sun, “Controllable single-photon frequency converter via a one-dimensional waveguide,” Phys. Rev. A 89, 053813 (2014).
[Crossref]

Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
[Crossref]

Tang, S.-Q.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[Crossref]

Thompson, J. D.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

Tian, L.

J.-Q. Liao and L. Tian, “Macroscopic quantum superposition in cavity optomechanics,” Phys. Rev. Lett. 116, 163602 (2016).
[Crossref] [PubMed]

L. Tian, “Optoelectromechanical transducer: Reversible conversion between microwave and optical photons,” Annalen der Physik 527, 1–14 (2015).
[Crossref]

L. Tian, M. S. Allman, and R. W. Simmonds, “Parametric coupling between macroscopic quantum resonators,” New Journal of Physics 10, 115001 (2008).
[Crossref]

Vitali, D.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

Walmsley, I. A.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[Crossref]

Wang, H.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Wang, X.-W.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[Crossref]

Wang, Z. H.

Z. H. Wang, L. Zhou, Y. Li, and C. P. Sun, “Controllable single-photon frequency converter via a one-dimensional waveguide,” Phys. Rev. A 89, 053813 (2014).
[Crossref]

Wang, Z.-Y.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[Crossref]

Ward, R. L.

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

Weedbrook, C.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

Weides, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Wenner, J.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Wong, C. W.

Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, and C. W. Wong, “Coupled cavities for motional ground-state cooling and strong optomechanical coupling,” Phys. Rev. A 91, 033818 (2015).
[Crossref]

Wright, E. M.

S. Singh, H. Jing, E. M. Wright, and P. Meystre, “Quantum-state transfer between a bose-einstein condensate and an optomechanical mirror,” Phys. Rev. A 86, 021801 (2012).
[Crossref]

Xiao, Y.-F.

Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, and C. W. Wong, “Coupled cavities for motional ground-state cooling and strong optomechanical coupling,” Phys. Rev. A 91, 033818 (2015).
[Crossref]

Xie, L.-J.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[Crossref]

Xu, X.-W.

X.-W. Xu and Y. Li, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a weakly nonlinear cavity,” Phys. Rev. A 90, 033832 (2014).
[Crossref]

Yamaguchi, H.

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, “Phonon lasing in an electromechanical resonator,” Phys. Rev. Lett. 110, 127202 (2013).
[Crossref] [PubMed]

Yan, W.-B.

W.-B. Yan, J.-F. Huang, and H. Fan, “Tunable single-photon frequency conversion in a Sagnac interferometer,” Sci. Rep. 3, 3555 (2013).
[Crossref] [PubMed]

Yu, T.

Q. Mu, X. Zhao, and T. Yu, “Memory-effect-induced macroscopic-microscopic entanglement,” Phys. Rev. A 94, 012334 (2016).
[Crossref]

Zhang, A.

Zhang, D.-Y.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[Crossref]

Zhang, J.

J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68, 013808 (2003).
[Crossref]

Zhang, K.

K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
[Crossref] [PubMed]

Zhang, W.

J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016).
[Crossref] [PubMed]

K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
[Crossref] [PubMed]

Zhang, W.-Z.

W.-Z. Zhang, J. Cheng, W.-D. Li, and L. Zhou, “Optomechanical cooling in the non-markovian regime,” Phys. Rev. A 93, 063853 (2016).
[Crossref]

J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016).
[Crossref] [PubMed]

W.-Z. Zhang, J. Cheng, and L. Zhou, “Quantum control gate in cavity optomechanical system,” Journal of Physics B: Atomic, Molecular and Optical Physics 48, 015502 (2015).
[Crossref]

Zhao, C.

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

Zhao, X.

Q. Mu, X. Zhao, and T. Yu, “Memory-effect-induced macroscopic-microscopic entanglement,” Phys. Rev. A 94, 012334 (2016).
[Crossref]

H. Jing, X. Zhao, and L. F. Buchmann, “Quantum optomechanics with a mixture of ultracold atoms”, Phys. Rev. A 86, 065801 (2012)
[Crossref]

Zhou, L.

J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016).
[Crossref] [PubMed]

W.-Z. Zhang, J. Cheng, W.-D. Li, and L. Zhou, “Optomechanical cooling in the non-markovian regime,” Phys. Rev. A 93, 063853 (2016).
[Crossref]

W.-Z. Zhang, J. Cheng, and L. Zhou, “Quantum control gate in cavity optomechanical system,” Journal of Physics B: Atomic, Molecular and Optical Physics 48, 015502 (2015).
[Crossref]

Z. H. Wang, L. Zhou, Y. Li, and C. P. Sun, “Controllable single-photon frequency converter via a one-dimensional waveguide,” Phys. Rev. A 89, 053813 (2014).
[Crossref]

Zoller, P.

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

Zwickl, B. M.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

Annalen der Physik (1)

L. Tian, “Optoelectromechanical transducer: Reversible conversion between microwave and optical photons,” Annalen der Physik 527, 1–14 (2015).
[Crossref]

Journal of Physics B: Atomic, Molecular and Optical Physics (1)

W.-Z. Zhang, J. Cheng, and L. Zhou, “Quantum control gate in cavity optomechanical system,” Journal of Physics B: Atomic, Molecular and Optical Physics 48, 015502 (2015).
[Crossref]

Nat. Commun. (1)

M. Lee and et al., “Three-dimensional imaging of cavity vacuum with single atoms localized by a nanohole array,” Nat. Commun. 5, 3441 (2014).
[PubMed]

Nature (3)

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

R. Riedinger and et al.,“Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530, 313–316 (2016).
[Crossref] [PubMed]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

Nature Phys. (1)

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

New Journal of Physics (2)

S. Davuluri and Y. Li, “Absolute rotation detection by Coriolis force measurement using optomechanics,” New Journal of Physics 18, 103047 (2016).
[Crossref]

L. Tian, M. S. Allman, and R. W. Simmonds, “Parametric coupling between macroscopic quantum resonators,” New Journal of Physics 10, 115001 (2008).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (13)

Z. H. Wang, L. Zhou, Y. Li, and C. P. Sun, “Controllable single-photon frequency converter via a one-dimensional waveguide,” Phys. Rev. A 89, 053813 (2014).
[Crossref]

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[Crossref]

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[Crossref]

X.-W. Xu and Y. Li, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a weakly nonlinear cavity,” Phys. Rev. A 90, 033832 (2014).
[Crossref]

J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68, 013808 (2003).
[Crossref]

S. Singh, H. Jing, E. M. Wright, and P. Meystre, “Quantum-state transfer between a bose-einstein condensate and an optomechanical mirror,” Phys. Rev. A 86, 021801 (2012).
[Crossref]

S. A. McGee, D. Meiser, C. A. Regal, K. W. Lehnert, and M. J. Holland, “Mechanical resonators for storage and transfer of electrical and optical quantum states,” Phys. Rev. A 87, 053818 (2013).
[Crossref]

H. Jing, X. Zhao, and L. F. Buchmann, “Quantum optomechanics with a mixture of ultracold atoms”, Phys. Rev. A 86, 065801 (2012)
[Crossref]

Q. Mu, X. Zhao, and T. Yu, “Memory-effect-induced macroscopic-microscopic entanglement,” Phys. Rev. A 94, 012334 (2016).
[Crossref]

W.-Z. Zhang, J. Cheng, W.-D. Li, and L. Zhou, “Optomechanical cooling in the non-markovian regime,” Phys. Rev. A 93, 063853 (2016).
[Crossref]

Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, and C. W. Wong, “Coupled cavities for motional ground-state cooling and strong optomechanical coupling,” Phys. Rev. A 91, 033818 (2015).
[Crossref]

K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91, 063815 (2015).
[Crossref]

Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
[Crossref]

Phys. Rev. E (1)

W. Li, C. Li, and H. Song, “Quantum synchronization in an optomechanical system based on lyapunov control,” Phys. Rev. E 93, 062221 (2016).
[Crossref] [PubMed]

Phys. Rev. Lett. (12)

P. Bertet and et al.,“Direct Measurement of the Wigner Function of a One-Photon Fock State in a Cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[Crossref] [PubMed]

A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, “Measures of quantum synchronization in continuous variable systems,” Phys. Rev. Lett. 111, 103605 (2013).
[Crossref]

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013).
[Crossref] [PubMed]

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly Efficient Single-Pass Source of Pulsed Single-Mode Twin Beams of Light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, “Phonon lasing in an electromechanical resonator,” Phys. Rev. Lett. 110, 127202 (2013).
[Crossref] [PubMed]

K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
[Crossref] [PubMed]

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref] [PubMed]

J.-Q. Liao and L. Tian, “Macroscopic quantum superposition in cavity optomechanics,” Phys. Rev. Lett. 116, 163602 (2016).
[Crossref] [PubMed]

H. Jing, D. S. Goldbaum, L. Buchmann, and P. Meystre, “Quantum Optomechanics of a Bose-Einstein Antiferromagnet”, Phys. Rev. Lett. 106, 223601 (2011).
[Crossref] [PubMed]

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

Sci. Rep. (2)

J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016).
[Crossref] [PubMed]

W.-B. Yan, J.-F. Huang, and H. Fan, “Tunable single-photon frequency conversion in a Sagnac interferometer,” Sci. Rep. 3, 3555 (2013).
[Crossref] [PubMed]

Other (1)

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000), Chap.7.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 The quadratically coupled optomechanical system consists of a membrane in the middle of the cavity. The membrane is interacted to a low frequency resonator with the coupling strength V via a capacitance C.
Fig. 2
Fig. 2 The effective frequency of the mechanical oscillator ωeff, effective coupling strength geff, the ratio of | g eff ω eff | and effective damping rate γeff is a function of mechanical coupling strength V, corresponding to (a), (b) and (c), respectively. (d), (e) and (f) show these effective parameters changing with the frequency difference Δωm = ωm1ωm2 (. For (a), (b) and (c), the parameters are g/ωm1 = 10−4, ωm2/ωm1 = 0.998, γm1/ωm1 = 10−6, γm1/γm2 = 102, while for (d), (e) and (f), the parameters are g/ωm1 = 10−4, γm1/ωm1 = 10−6, V/ωm1 = 5 × 10−2, γm1/γm2 = 102.
Fig. 3
Fig. 3 (a) The comparison of analytical and numerical solution of fidelity Fcp. The mechanical coupling rate V/ωm1 = 3.16 × 10−2. The fidelity Fcp as a function of time t with different mechanical coupling strength V/ωm1 = 1.35 × 10−2, 2.58 × 10−2, 3.16 × 10−2, corresponding to (b), (c) and (d), respectively. The corresponding ratio | g eff ω eff | = 0.01, 0.05, 0.1, and the maximal fidelity Fcpmax ≈ 0.83, 0.94, 0.97. For all of the figures, κ/g = 0.5, nth = 1, and the other parameters are the same with Fig. 2.
Fig. 4
Fig. 4 Quantum circuit of photon-phonon convertor. After performing single-qubit operation according to the measure result, we can obtain the state we want in mechanical mode.
Fig. 5
Fig. 5 Schematic diagram of multi-controlled phase gate and quantum circuit of photon-phonon conveter.
Fig. 6
Fig. 6 The dynamic of the conversion fidelity with different effective coupling rate ge2. The blue line denotes the conversion fidelity of output port 1, the green line denotes the conversion fidelity of output port 2. Other parameters are ωe1 = ωe2, κ1 = κ2 = 0.1ωe1, J1/ωe1 = 0.1, γ1 = 10γ2 = 10−5ωe1, nth1 = nth2 = 5.

Equations (36)

Equations on this page are rendered with MathJax. Learn more.

H = H sys + H d
H sys = ω c a a g a a ( b 1 + b 1 ) 2 + j = 1 , 2 ( ω m j b j b j + V b j b 3 j ) ,
H d = ε ( a e i ω d t + a e i ω d t ) ,
H eff = Δ a a + ω eff b 2 b 2 + g eff a a b 2 b 2 ,
Δ 1 = ω c ω d g ,
ω eff = ω m 2 V 2 ( ω m 1 ω m 2 ) | A | 2 ,
g eff = 2 g V 2 | A | 2 ,
A = i ( ω m 1 ω m 2 ) + ( γ 1 γ 2 ) / 2 .
| ψ = α | 0 c | 0 m + β | 0 c | 1 m + γ | 1 c | 0 m + δ | 1 c | 1 m ,
| Φ = α | 0 c | 0 m + β | 0 c | 1 m + γ | 1 c | 0 m δ | 1 c | 1 m .
| ψ f = α | 0 c | 0 m + β e i θ 01 | 0 c | 1 m + γ e i ω 10 | 1 c | 0 m + δ e i θ 11 | 1 c | 1 m ,
F c p = | α 2 e i θ 00 + β 2 e i θ 01 + γ 2 e i θ 10 δ 2 e i θ 11 | ,
θ 01 = ω eff t = 2 n 1 π , θ 10 = Δ t = 2 n 2 π , θ 11 = ( ω eff + Δ g eff ) t = ( 2 n 3 + 1 ) π , n i ( i = 1 , 2 , 3 ) ,
ρ ˙ = i [ ρ , H ] + κ 𝒟 [ a ] ρ + j = 1 , 2 γ j ( n t h j + 1 ) 𝒟 [ b j ] ρ + γ j n t h j 𝒟 [ b j ] ρ ,
1 2 | 0 1 ( α | 0 2 + β | 1 2 ) + | 1 1 ( α | 0 2 β | 1 2 ) ,
H = j = 1 n ω j a j a j + ω m j b j b j + ω A j b A j b A j + g j a j a j ( b j + b j ) 2 + V j ( b j b A j + b j b A j ) + s = 1 n 1 J s ( a 1 a s + 1 + a 1 a s + 1 ) ,
H eff = j = 1 n Δ j a j a j + ω e j b A j b A j + g e j a j a j b A j b A j + s = 1 n 1 J s ( a 1 a s + 1 + a 1 a s + 1 ) ,
F Cj = F Gj F Sj = ( ψ f | ρ j | ψ f ψ 0 | ρ a j | ψ 0 ) 1 / 4 ,
H sys = ω c a a g a a ( b 1 b 1 + b 1 b 1 ) + j = 1 , 2 ( ω m j b j b j + V b j b 3 j ) .
a ˙ = ( i Δ + κ / 2 ) a + 2 i g a b 1 b 1 + κ a in ,
b ˙ 1 = ( i ω m 1 + γ 1 / 2 ) b 1 + 2 i g b 1 a 1 a 1 i V b 2 + γ 1 b in , 1 ,
b ˙ 2 = ( i ω m 2 + γ 2 / 2 ) b 2 i V b 1 + γ 2 b in , 2 ,
a ˙ = ( i Δ + κ / 2 ) a + 2 i g a N b + κ a in ,
b ˙ 1 = ( i ω m 1 + γ 1 / 2 ) b 1 + 2 i g b 1 N a i V b 2 + γ 1 b in , 1 ,
b ˙ 2 = ( i ω m 2 + γ 2 / 2 ) b 2 i V b 1 + γ 2 b in , 2 ,
N ˙ a = κ 1 N a ,
a 1 ( t ) = a ( 0 ) e ( i Δ + κ / 2 ) t e 0 t d τ 2 i g N b ( τ ) + 0 t d τ e ( i Δ + κ / 2 ) ( t τ ) e τ t d τ 2 i g N b ( τ ) κ a in ( τ ) ] ,
b 1 ( t ) = b 1 ( 0 ) e ( i ω m 1 + γ 1 / 2 ) t e 0 t d τ 2 i g N a ( τ ) + 0 t d τ e ( i ω m 1 + γ 1 / 2 ) ( t τ ) e τ t d τ 2 i g N a ( τ ) [ i V b 2 ( τ ) + γ 1 b in , 1 ( τ ) ] ,
b 2 ( t ) = b 2 ( 0 ) e ( i ω m 2 + γ 2 / 2 ) t + 0 t d τ e ( i ω m 2 + γ 2 / 2 ) ( t τ ) [ i V b 1 ( τ ) + γ 2 b in , 2 ( τ ) ] ,
b 2 ( 0 ) ( t ) b 2 ( 0 ) e ( i ω m 2 + γ 2 / 2 ) t + B in , 2 ( t ) ,
b 1 ( t ) b 1 ( 0 ) e ( i ω m 1 + γ 1 / 2 2 i g N a t ) + 0 t d τ e ( i ω m 1 + γ 1 / 2 2 i g N a ) ( t τ ) × [ i V b 2 ( 0 ) e ( i ω m 2 + γ 2 / 2 ) τ i V B in , 2 ( τ ) + γ 1 b in , 1 ( τ ) ] .
b 1 ( t ) i V b 2 ( t ) i ( ω m 1 ω m 2 ) + ( γ 1 γ 2 ) / 2 2 i g N a + B in , 1
b 1 ( t ) i V b 2 ( t ) A [ 1 + i ( ω m 1 ω m 2 ) + ( γ 1 γ 2 / 2 ) 2 i g N a | A | 2 ] + B in , 1 ( t )
a ˙ = ( i Δ + κ / 2 ) a + i g eff a b 2 b 2 + κ a in ,
b ˙ 2 = ( i ω eff + γ eff / 2 ) b 2 + i g eff b 2 a a + γ eff B in , 2 ,
H eff = Δ a a + ω eff b 2 b 2 + g eff a a b 2 b 2 .

Metrics