Abstract

We report an experimental demonstration of storage of photonic polarization qubit (PPQ) protected by dynamical decoupling (DD). PPQ’s states are stored as a superposition of two spin waves by electromagnetically-induced-transparency (EIT). Carr-Purcell-Meiboom-Gill (CPMG) DD sequences are applied to the spin-wave superposition to suppress its decoherence. Thus, the quantum process fidelity remains better than 0.8 for up to 800μs storage time, which is 3.4-times longer than the corresponding storage time of ~180μs without the CPMG sequences. This work is a key step towards the storage of single-photon polarization qubit protected by the CPMG sequences.

© 2014 Optical Society of America

1. Introduction

Photons with their polarization states encoding in quantum information are good for transmitting quantum information. For realizing long-distance quantum communication [1] and scalable quantum computing [2], long-lived quantum memories for a photonic polarization qubit are crucial [35]. Many physical processes have been exploited to store quantum states of light. The absorptive electromagnetically-induced-transparency [6] and emissive spontaneous-Raman-emission processes [1] in atomic ensembles provide promising storage schemes. In both schemes, photonic states are stored as spin waves and then retrieved after a demand time. However, due to decoherence, the spin waves will decay with time and will be only effectively retrieved within storage lifetimes. There are several factors that limit the lifetimes of quantum memories in atomic ensembles. For the storages of a certain polarization state of light, only a single spin wave is required and the decoherence for such storages includes two main factors: atomic motion and inhomogeneous Zeeman broadening. For storages of photonic polarization qubit (PPQ), two spin waves (SWs) [7,8] are required. Thus, besides the above-mentioned two decoherence mechanisms, random phase between the two SWs caused by magnetic field fluctuations will degrade polarization fidelity and then lead to decoherence [9]. In the past several years, many studies on suppressions of spin-wave decoherence have been done and several methods have been proved to be effective. The decoherence resulting from atomic motion can be significantly suppressed by using cold atoms in magneto-optical traps [10] or ultra-cold atoms in optical lattice [11] as storage media and the decoherence caused by spatial gradient of magnetic fields and their temporal fluctuations can be obviously decreased by storing PPQ’s states as two magnetic-field-insensitive coherences [12,13] or two spatially distinct SWs [14] associated with the clock coherence. Another method to suppress the random phase in PPQ’s storages is to compensate the magnetic field noise by using an open-loop feed-forward technique [9]. In the past few years, a powerful strategy, known as dynamical decoupling (DD) technique, has been developed to protect qubit memories in single atoms [15,16], array of ions [17], spin ensembles [18], NV-center systems [19] and so on. In very recent years [2022], the optical quantum storages based on electromagnetically induced transparency (EIT) has also been introduced. By applying DD sequences to rotate the two states of a spin wave, the longest storage lifetimes for a fixed polarization light are 16 seconds in atoms confined in optical lattice [20] and 1 minute in solid-state ensembles [22]. However, the experiments of suppressing random phase between the two spin waves in the PPQ’s storages by DD have not been demonstrated.

In this paper, we experimentally demonstrate the PPQ’s storages protected by Carr-Purcell-Meiboom-Gill (CPMG) DD pulse sequences. Based on EIT effect in a cold atomic ensemble, the PPQ is stored as two spin waves, which are associated with the magnetic-field-insensitive and magnetic-field-sensitive coherences, respectively. The CPMG sequences containing multiple Raman π pulses are applied to suppress decoherence of the spin waves and thus the quantum process fidelity remains better than 0.8 for up to 800μs storage time.

2. Theoretical discussion for protecting PPQ’s storage by CPMG DD sequences

The involved levels of R87b atoms are shown in Fig. 1(a) and 1(b), where |a=|5S21/2,F=1, |b=|5S21/2,F=2 and |e=|5P21/2,F=1. All of the atoms are prepared in an incoherent mixture of the |amF=±1 states (mF denotes the magnetic quantum number) with equal population. The signal and writing/reading light fields propagate along z-axis, whose frequencies are tuned to transitions |a|e and |b|e, respectively, and their frequency difference equals to the frequency ωabof the transition |a|b. The writing/reading light field is left circular polarization and the input signal-light field is an arbitrary polarization state. The signal-light field can be written as

ε(t)=εR(t)+εL(t)=|ε(t)|(α|R+βeiφ|L),
where εR(t) and εL(t) denote the right-circularly (σ+) and left-circularly (σ) polarized components, respectively, |R and |L are their unit vectors, |ε(t)|=|εR(t)|2+|εL(t)|2, α=|εR(t)|/|ε(t)| and β=|εL(t)|/|ε(t)|. The Stokes parameters [9] of the input signal field can be written as:

 figure: Fig. 1

Fig. 1 The atomic level schemes of R87b for EIT storages (a) and Raman π rotations (b), respectively. σ+ and σ+ are the right- and left-circularly-polarized signal fields, respectively. W/R is the left-circularly-polarized writing/reading field. ΔR denotes the detuning of the Raman laser from the transition |a|e.

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(S0inS1inS2inS3in)=|ε(t)|2(12αβsinθα2β22αβcosθ)

The quantum axis defined by a bias magnetic field Bz is along z-direction, so, the σ±-polarized components of the signal field couple to |amF=1|emF=0 and |amF=1|emF=0 transitions, respectively, and the σ-polarized writing/reading light field couples |bmF=1|emF=0 transition. These couplings form two three-level Λ-type EIT systems: |amF=±1|emF=0|bmF=1. The spin waves S^+ and S^, which associate with the magnetic-field-insensitive coherence |amF=1|bmF=1 and magnetic-field-sensitive coherence |amF=1|bmF=1, respectively, are defined by [23],

S^±(z,t)=(Nz)1zjNz|amF=±1jjbmF=1|eiωabt,
where, Nz=Ndz/l is the number of atoms between z and z+dz, l is the length of the atomic ensemble. The conversion between the arbitrarily polarized signal-light fields and the two spin waves are described by the theory of two dark-state polaritons [24]. According to the theory, the σ+-and σ-polarized signal light fields will be converted into spin waves S^ and S^+, respectively, if the writing beam is turned off over a very short time interval [t0,t1]. Such conversion will create a superposition:
S(z,t1)=S^(z,t1)+S^+(z,t1)=|S(z,t1)|(αs++βeiφs).
where, |S(z,t1)|=|S+(z,t1)|2+|S(z,t1)|2, s+ and sare spin-wave unit vectors and defined by: s+=S^+(z,t1)/|S^+(z,t1)| and s=S^(z,t1)/|S^(z,t1)|. During the storage time, the spin waves S^+ and S^ will suffer from decoherence and undergo Larmor processes, respectively. For the presented storage scheme, the time interval t1t0 is close to zero, so we have t0t1. Assuming t0=0, the superposition at time t will evolve into:
S(z,t)=|S^(z,0)|et/2τdiωabt(αet/2τ+iΩ+ti0tω+(t)dt's++eiφβset/2τiΩti0tω(t)dt),
where, τd is the lifetime limited by atomic motions, τ± are the lifetimes for the magnetic-field-sensitive and magnetic-field-insensitive spin waves S^+ and S^, respectively, which are limited by inhomogeneous Zeeman broadening [11], Ω±=μBBz0(gb±ga) (ω±=μBδBz(gb±ga)) are the Larmor frequencies for the transitions |amF=±1|bmF=1, which are induced by the guiding magnetic field Bz0 (fluctuations of magnetic fieldδBz(t)) along z axis, ga0.5018, gb0.4998 are the Landé factors. If the reading beam is switched on at this time t, the spin-wave supposition will be transferred into the retrieved light field according to [24]:
εout(t)=RS(z,t)Ret/2τdiωabt(αet/2τ+|R+eiφβet/2τiΩti0tδω(t)dt|L),
where, R is the retrieval efficiency, Ω=(ΩΩ+)=2gaμBBz (δω(t)=(δω(t)δω+(t))=2gaμBδBz(t)) is the difference of Larmor frequency between the SWs S+ and S, which are induced by guiding magnetic field Bz (magnetic field noise δBz(t)). The calculated Stokes parameters for the retrieved light field are:
(S0outS1outS2outS3out)=Ret/τd(α2et/τ++β2et/τ2αβet(1/2τ++1/2τ)W(t)sin(Ωt+φ)α2et/τ+β2et/τ2αβet(1/2τ++1/2τ)W(t)cos(Ωt+φ)),
where, W(t)=exp[0tδω(t')dt']=exp[0dω2πS(ω)|f0(ω)|2] is the normalized coherence [25],S(ω)=dteiωtδω(t)δω(0) is noise spectrum, f0(t,ω)=0tdt'eiωt'. If t is large enough, we have
W(t)=et/T0,
where T0=1/S(0) is the coherence lifetime [26]. The quantum state fidelity is defined by
Fst=Tr(ρinρout).
where, ρin(out)=12i=03Siin(out)S0σ^i are the input (output) density matrices, σ^i are the Pauli spin operator. We calculate the quantum state fidelities for six input states based on the Eqs. (7)(9), the results are:
Fst(X)12+et(1/2τ++1/2τ)W(t)cosΩtet/τ++et/τ,
for |X=|H,|V,|A,|D and
Fst(X)=1,
for |X=|R,|L, where H,V,R,L,D and A denote horizontal, vertical, right circular, left circular, diagonal (45°), and antidiagonal (−45°) polarizations, respectively. The quantum process fidelity can be expressed as [26]:
Fp3Fst¯12,
where F¯st=(Fst(H)+Fst(V)+Fst(A)+Fst(D)+Fst(R)+Fst(L))/6 is the average quantum state fidelity. Based on Eqs. (10)(12), we calculate the quantum process fidelity, the result is:
Fst(X)12+et(1/2τ++1/2τ)W(t)cosΩtet/τ++et/τ,
where, θ=Ωt is the relative phase between the SWs S^+ and S^. According to the above equation, we may find that two factors cause decoherence of the qubit memory and make quantum process fidelity decrease with time. One factor is magnetic-field fluctuations, which causes a random phase between two spin waves and then makes the normalized coherence W(t) exponentially decay with the storage time. Another is difference between the lifetimes τ+ and τ, which also degrade the quantum process fidelity after a storage time t. The relative phase θ=Ωt changes with the storage time, which will lead to an oscillation of process fidelity Fp. However, it can be compensated by using linear optical elements or selecting the reading times at tj=jΔT (where j is an integer and ΔT=2π/Ω is the time interval) to make θ=2jπ. In this case, cosθ=1can be remained and the oscillation of process fidelity will be avoided. When the storage time is very long, W(t)0 and the quantum process fidelity Fp will be close to the boundary of 12. Such boundary corresponds to the case where the retrieval signal is unpolarized light when the input signal is a linearly-polarized light.

For suppressing decoherence caused by the two factors, we can apply CPMG DD sequences to decouple the spin-wave superposition from environment noise. The CPMG sequences contains n instantaneous π pulses applied at times t1, t2, …, tn, with time delays: t1t0=T/2, tk+1tk=T (as shown in Fig. 2(a)), its frequency is Fdd=1T/2. Assuming that each π pulse is ideal (means that it doesn’t cause any spin-wave decay), it can swap spin waves in a superposition according to:

 figure: Fig. 2

Fig. 2 (a) CPMG π pulse sequence. (b) The illustration of function f(t') (n: even).

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αs+βeiφs+αs++βeiφs.

Such swapping can be viewed as a π rotation of the spin-wave superposition. Considering the case where the number of the π-pulses applied within the storage time t is even, i.e., n=2m(m is an integer), the evolution of the superposition S(z,t) for t[tn=2m,tn=2m+1] is:

S(z,t)=S^+(z,t)+S^(z,t)=|S(z,t0)|H(t)(αeδt2τ+s++eiφβW(τ)eδt2τiΩδtiττ+δtδω(t)dts),
where, H(t)=et/2τdi(ω0+δω+)τ(1/2τ++1/2τ)τ/2, δt=tτ with a range of [T2,T2], τ=t2m+T/2, the normalized coherence W(τ)=exp[0dω2πS(ω)|fn(ω,τ)|2], S(ω)=dteiωtΔ(t)Δ(0), fn(ω,τ)=dt'eiωt'f(t'), f(t') is given by:
f(t')=0fort'<0ort'>τ,f(t')=(1)lfortk<t'<tk+1,k=0,1,2,32m.
when τ, the normalized coherence W(τ)e2S(π/2T)π2τ [25]. Since the magnetic-field fluctuation δBz(t) is a typical 1/fα-type noise [27], so its power spectrum limωS(ω)0. If the DD period T is short enough, we have S(π/2T)0 and W(t)1. Also, the short period T leads to δt0 i.e., eδt2τ±1 and eiττ+δtδω(t)dt1. In this case, the two factors causing decoherence are eliminated and spin-wave superposition is changed into:
S(z,t)=|S(z,t0)|H(t)(αs+(z,t)+βeiφiΩδts(z,t)).
According to the Eq. (15), we derive the quantum process fidelity:
Fp1+cosϑ2.
where ϑ=Ωδt is the relative phase, which may cause an oscillation of quantum process fidelity with the time interval δt. Similar to the above discussion for θ, we may take cosϑ=1 by compensating the relative phase or selecting appropriate retrieval times. In this case, quantum process fidelity Fp1, which means that the CPMG DD sequences may effectively suppress the two decoherence factors.

If the number of the π-pulses applied within the storage time t is odd (n=2m1) and the period T is short enough, the time evolution of the superposition at time t[tn=2m1,tn=2m] can be written as:

S(z,t)=|S(z,t0)|H(t)(αs(z,t)+βeiφiϑs+(z,t)),
where τ=t2m1+T/2. Comparing with the superposition manipulated by 2m π pulses (See Eq. (15)), we find that this is a swapped superposition. For correcting this superposition, we have to apply an additional π-pulse to it after (2m-1)-th π-pulse and then it will be changed into the one that is the same with Eq. (15).

3. Experimental set-up and results

The experimental setup is shown in Fig. 3 (a). A cold R87b atomic cloud in a magneto-optical trap serves as the memory medium. A polarization-insensitive beam-splitter (BS) is used to combine the input signal and writing/reading light beams. Before arriving BS, the signal beam goes through a quarter-wave plate (QWP1) and a half-wave plate (HWP1). By adjusting QWP1 and HWP1, the polarization state of the signal light can be arbitrarily set. For suppressing the dephasing effect resulting from atomic motion, we make the signal and writing/reading light beams collinearly go through the cold-atom cloud along z-direction. The powers (diameters) of the writing-reading and signal beam are 3mW (2mm) and 34μW (1mm), respectively. The horizontally-polarized Raman laser beam (with a ~4.5mm diameter) passes through the cold atoms with a deviation angle of ~0.2° from z^. It is tuned to the transitions |a|e with a blue detuning ΔR=90MHz (see Fig. 1 (b)). We use an analogue acousto-optic modulator (AOM) to modulate Raman laser amplitude and then obtain a rectangular pulse with a time length of 150ns. By carefully set the input power of the Raman laser beam, we realize a π-rotation between the SW S^+ and S^. As shown in Fig. 3(b), the σ-polarized pumping laser P1 and σ+-polarized pumping laser P2 collinearly propagate through the atoms with a deviation angle ~2° from z-direction, which drive the transitions |52S1/2,F=2,mF|52P1/2,F'=2,mF-1 and |52S1/2,F=2,mF|52P1/2,F'=1,mF+1, respectively. The π-polarized pumping laser P3 propagates through the atoms along x-direction, which drives the transition |5S1/2,F=1,mF=0|52P3/2,F'=0,mF=0. The powers and diameters of the lasers P1, P2 in the center of cold atoms are approximately equal, which are ~10 mW and ~7 mm, respectively, while that of the laser P3 is ~400 µW and ~8.8 mm, respectively. For each experimental circle, the durations for the preparation of the cold atoms and storage-retrieval experiments are ~98 ms and 2 ms, respectively. During the preparation stage, R87b atoms are loaded into magneto-optical trap (MOT) and then performed a Sisyphus cooling. The evaluated magneto-optical trap temperature is ~200 µK, the number of the atoms in the MOT na1×109, optical density is 4, size of the cloud V64mm3. After the Sisyphus cooling we apply a dc magnetic field B0=375mGsalong z^ to define the quantization axis. Then the pump P1, 2, 3 as well as the writing laser beams are switched on to prepare the atoms into the desired ground state |amF=1 or |amF=1 with the same population. After about 20μs, the pump P1, 2, 3 are turned off and the signal pulse (with a pulse length of 200ns) is injected into the atom ensemble. At the falling edge of the signal pulse (corresponding to t0=0), the writing laser beam is ramped to zero and thus the signal pulse is mapped into the spin-wave superposition S(z,t0). We then apply CPMG pulse sequences to manipulate the spin waves. By switching on the reading light beam, we retrieve optical signals from the spin waves. Since the reading and retrieval signal beams will propagate collinearly along z-axis, we have to block the reading beam by using a set of filters [13]. Then only the retrieved signals enter a polarization analyzing and measuring (PAM) system. The PAM system consists of a quarter-wave plate (QWP3), a half-wave plate (HWP3), a Glan-laser polarizer (GLP) and detectors D1,2 (Hamamatsu C5331). With QWP2 and HWP3, we can select the polarization basis HV,LR or DA in turn for the polarization analyzing and measuring.

 figure: Fig. 3

Fig. 3 (a) The experimental setup. HWP: half-wave plate; QWP: quarter-wave plate; PBS: polarizing beam splitter; BS: polarization-insensitive beam splitter; D1, 2: Photon detectors. (b) The involved atomic level scheme of R87b for optical pumping.

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We first measure the retrieval efficiencies as the function of time t. The square (black) and circle (red) dots in Fig. 4 are the measured results for (Ι) σ+-polarized and (ΙΙ) σ-polarized fields, respectively. The solid (black) and dash (red) curves are the fits to these data based on Ret/τ, yielding 1/e lifetimes of τ+=1.4ms for magnetic-field-insensitive SWS^+ and τ=0.47ms for the magnetic-field-sensitive SW S^.

 figure: Fig. 4

Fig. 4 The retrieval efficiencies as the function of the storage time. The square dots in curve (Ι) and circle dots in curve (ΙΙ) are the measured results for σ+-polarized and σ-polarized fields, respectively.

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We next perform the storage and retrieval of|H, |V, |D and |R polarization light with and without CPMG pulse sequences, respectively. Figures 5(a) and 5(b) illustrate the π-pulse sequences for Fdd=5kHz and Fdd=10kHz, respectively. Based on the polarized analysis for the measured data of retrieval signals, we reconstruct the density matrix ρout and then obtain quantum process fidelities. Figure 5(c) shows the quantum process fidelities as the function of the storage time. According to the measured Larmor frequency difference Ω, we determine the time interval ΔT and then select reading at times of tj=jΔT (For details see Sec.2). In Fig. 5(c), the square dots correspond to the results when CPMG pulse sequence is not applied. It shows that the quantum process fidelity reduces to ~80% at 180μs. At t500μs, the quantum process fidelity reaches ~25%, which is less than the boundary of 1/2. We attribute this to inaccurate determination of the time interval ΔT. The circle and triangle dots are quantum process fidelities when CPMG pulse sequences with frequencies of Fdd=5kHz and Fdd=10kHz are applied, respectively. In the measurements for the two cases, if the stored optical signals are retrieved after (2m-1)-th π pulse, we apply an additional π-pulse to correct the spin-wave superposition before the retrieval of the optical signals. For Fdd=5kHz, two dips appear around t=200μs and t=600μs, respectively. While, for Fdd=10kHz, the quantum process fidelity keeps a monotonous decrease with the storage time. The reason for this is explained in the following. As discussed in Sec.2, the main decoherence factors in the presented storage system are the magnetic field fluctuationδBz and the difference between the lifetimes τ+ for the spin wave (SW) S^+ and τ for the SW S^. Both the two factors make the quantum process fidelity degrade with the storage time t. In the case where the CPMG pulse sequences are not applied, the quantum process fidelity keeps a monotonous decrease with the storage time t. However, at storage time t<100μs, the decrease of the quantum process fidelity caused by the two decoherence factors is not significantly since the time interval is short. While, the decrease of the quantum process fidelity will become significant at t200μs. In the case where a CPMG π-pulse sequence with Fdd=5kHz is applied, the first π-pulse is applied at t=200μs. Thus, after t=200μs the quantum process fidelity increases with t since the two spin waves have been swapped. At time t=400μs, it is the end of a spin-echo time interval, the quantum process fidelity recovers a larger value. At 400μs<t<800μs, the quantum process fidelity experiences an evolution process similar to that in 200μs<t<400μs. So, the two dips appear around t=200μs and t=600μs for Fdd=5kHz. In the case where a CPMG π-pulse sequence with Fdd=10kHz is applied, the first π-pulse is applied at t=100μs and the second π-pulse is applied at t=300μs, … . In this case, the CPMG π-pulse sequence can timely protect the qubit memory from decoherence and then the quantum process fidelity keeps a slow monotonous decrease with the storage time t. At 800μs, the quantum process fidelities reach ~80% for the cases of Fdd=5kHz and Fdd=10kHz. Figure 6 shows the quantum process fidelity at storage time of 800μs as the function of the π-pulse number n (lower) and the frequency Fdd(upper), respectively. The measured quantum process fidelity is better than 0.8 for n=4 and 0.77 for n=6.

 figure: Fig. 5

Fig. 5 (a) and (b) The applied CPMG sequences for Fdd=5kHz and Fdd=10kHz, respectively. πi (i=1,2,3,4) is the i-th π pulse. (c) The quantum process fidelities Fp as the function of the storage time. The square dots are the results without the CPMG sequence. The circle and triangle dots are the results with CPMG sequences of 5-kHz and 10-kHz frequencies, respectively. The horizontal dashed (red) line is the boundary of 1/2.

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 figure: Fig. 6

Fig. 6 Quantum process fidelity Fp at storage time of 800μs as the function of the number of π-pulses n (lower) and the frequency Fdd (upper).

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4. Discussions

We perform the polarization quantum memory with the classical signal-light pulses of different polarization. However, our storage scheme will also hold for the single-photon polarization states because the attenuation of the signal light in the storage process is linear [28] [29] [30]. In other words, the measured polarization fidelities for the single photons will be close to that for the classical light pulses. However, there might exist the background noise photons directed into the single-photon detectors, which will degrade the quantum fidelity of the single-photon polarization states. The background photons may come from the leakage photons from reading beam or spontaneous emissions from the atomic ensemble. For blocking the leakage photons from the reading beam, we may insert more number of optical filters before single-photon detectors. The reason for the generation of the spontaneous emissions is explained in the following. In the atomic ensemble, there may exist small number of atoms which are in the excited state |b but are not associated with the spin waves. When the reading beam is switched on to drive the transition|b|e, these atoms will be excited to |e and then generate spontaneous emissions. Many processes, for example, thermally excitations, etc., may induce incoherently transfer from the state |a into the state|b. In the presented scheme, the Raman π-rotations is one process which induce incoherently transfer from the state |a into |b [26]. By taking large enough detuning ΔR (Δ'R) of Raman laser from the transition |b|e (|b|5P1/2,F'=2, the number of the transferred atoms will be decreased [26] and then the background noise photons coming from such process may be significantly suppressed.

5. Conclusions

We demonstrate PPQ’s storages protected by CPMG DD sequences. The process fidelity better than 0.8 is measured for up to 800μs storage time with a 10kHz-frequency CPMG sequence being applied, while, it is measured for up to 180μs storage time without CPMG sequence. Compared with the previously reported PPQ’s storages [12,13], an advantage of the presented long-lived PPQ’s storage is that single-qubit operations can be easily implemented during storage. We believe that this advantage can be used to improve the success probability of the quantum teleportation based on atomic ensembles [31] and find more effective applications in quantum information processing.

Acknowledgments

We acknowledge funding support from the 973 Program (2010CB923103), the National Natural Science Foundation of China (No.10874106, 60821004).

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15. D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011). [CrossRef]  

16. S. Yu, P. Xu, X. He, M. Liu, J. Wang, and M. Zhan, “Suppressing phase decoherence of a single atom qubit with Carr-Purcell-Meiboom-Gill sequence,” Opt. Express 21(26), 32130–32140 (2013). [CrossRef]   [PubMed]  

17. G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010). [CrossRef]   [PubMed]  

18. J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009). [CrossRef]   [PubMed]  

19. F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004). [CrossRef]   [PubMed]  

20. Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013). [CrossRef]  

21. M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013). [CrossRef]   [PubMed]  

22. G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013). [CrossRef]   [PubMed]  

23. M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65(2), 022314 (2002). [CrossRef]  

24. Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013). [CrossRef]  

25. T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011). [CrossRef]   [PubMed]  

26. M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303(4), 249–252 (2002). [CrossRef]  

27. J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011). [CrossRef]  

28. Y. W. Cho and Y. H. Kim, “Atomic vapor quantum memory for a photonic polarization qubit,” Opt. Express 18(25), 25786–25793 (2010). [CrossRef]   [PubMed]  

29. D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012). [CrossRef]  

30. R. Loudon, The Quantum Theory of Light (Oxford University, 2004).

31. X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012). [CrossRef]   [PubMed]  

References

  • View by:

  1. L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
    [Crossref] [PubMed]
  2. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
    [Crossref]
  3. A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
    [Crossref]
  4. Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
    [Crossref]
  5. J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
    [Crossref]
  6. M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84(22), 5094–5097 (2000).
    [Crossref] [PubMed]
  7. T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
    [Crossref] [PubMed]
  8. L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
    [Crossref] [PubMed]
  9. S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
    [Crossref]
  10. B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
    [Crossref]
  11. R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
    [Crossref]
  12. Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
    [Crossref] [PubMed]
  13. Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
    [Crossref] [PubMed]
  14. Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
    [Crossref] [PubMed]
  15. D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
    [Crossref]
  16. S. Yu, P. Xu, X. He, M. Liu, J. Wang, and M. Zhan, “Suppressing phase decoherence of a single atom qubit with Carr-Purcell-Meiboom-Gill sequence,” Opt. Express 21(26), 32130–32140 (2013).
    [Crossref] [PubMed]
  17. G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
    [Crossref] [PubMed]
  18. J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
    [Crossref] [PubMed]
  19. F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
    [Crossref] [PubMed]
  20. Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
    [Crossref]
  21. M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
    [Crossref] [PubMed]
  22. G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
    [Crossref] [PubMed]
  23. M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65(2), 022314 (2002).
    [Crossref]
  24. Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
    [Crossref]
  25. T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011).
    [Crossref] [PubMed]
  26. M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303(4), 249–252 (2002).
    [Crossref]
  27. J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
    [Crossref]
  28. Y. W. Cho and Y. H. Kim, “Atomic vapor quantum memory for a photonic polarization qubit,” Opt. Express 18(25), 25786–25793 (2010).
    [Crossref] [PubMed]
  29. D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
    [Crossref]
  30. R. Loudon, The Quantum Theory of Light (Oxford University, 2004).
  31. X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
    [Crossref] [PubMed]

2013 (6)

S. Yu, P. Xu, X. He, M. Liu, J. Wang, and M. Zhan, “Suppressing phase decoherence of a single atom qubit with Carr-Purcell-Meiboom-Gill sequence,” Opt. Express 21(26), 32130–32140 (2013).
[Crossref] [PubMed]

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
[Crossref]

M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
[Crossref] [PubMed]

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
[Crossref] [PubMed]

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
[Crossref]

2012 (4)

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

2011 (3)

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
[Crossref]

T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011).
[Crossref] [PubMed]

2010 (3)

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

Y. W. Cho and Y. H. Kim, “Atomic vapor quantum memory for a photonic polarization qubit,” Opt. Express 18(25), 25786–25793 (2010).
[Crossref] [PubMed]

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

2009 (5)

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
[Crossref]

2008 (1)

L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
[Crossref] [PubMed]

2007 (2)

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

2005 (1)

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
[Crossref] [PubMed]

2004 (1)

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

2002 (2)

M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303(4), 249–252 (2002).
[Crossref]

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65(2), 022314 (2002).
[Crossref]

2001 (1)

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

2000 (1)

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84(22), 5094–5097 (2000).
[Crossref] [PubMed]

Bao, X. H.

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Baur, S.

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

Blumoff, J. Z.

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

Bylander, J.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Campbell, C. J.

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

Champion, T. F. M.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Chanelière, T.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
[Crossref] [PubMed]

Chen, L.

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Chen, S.

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Chen, Y. A.

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
[Crossref]

Chen, Z. B.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
[Crossref]

Cho, Y. W.

Chuu, C. S.

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Cirac, J. I.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

Cory, D. G.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

de Lange, G.

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

Dobrovitski, V. V.

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

Domhan, M.

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

Dowling, J. P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

Du, J.

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

Duan, L. M.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

Dudin, Y. O.

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
[Crossref]

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
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S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
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M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
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J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
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M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65(2), 022314 (2002).
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M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84(22), 5094–5097 (2000).
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M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
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J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
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F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
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Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
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T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
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D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
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B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
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L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
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Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
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R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
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Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
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P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
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D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
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Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
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Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
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Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
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T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
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Lan, S. Y.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
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D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
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D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
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S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
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X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
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Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
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Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
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Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
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Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
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Liu, R. B.

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
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M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
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J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
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X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
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D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
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M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65(2), 022314 (2002).
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L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
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M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84(22), 5094–5097 (2000).
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A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
[Crossref]

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R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
[Crossref] [PubMed]

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D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
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P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
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P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
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J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
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P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
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J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
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J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
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Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
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Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

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F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

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Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

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P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
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D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

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S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

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S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
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G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

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J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

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A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
[Crossref]

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T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011).
[Crossref] [PubMed]

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B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
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Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
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D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
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D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
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B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
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M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
[Crossref] [PubMed]

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D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
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Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

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A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
[Crossref]

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J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

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L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
[Crossref] [PubMed]

Vo, C.

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

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D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
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Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Wang, J.

Wang, Y.

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

Wang, Z. H.

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

Webster, S. C.

D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
[Crossref]

Weinfurter, H.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

Weitz, M.

L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
[Crossref] [PubMed]

Wrachtrup, J.

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

Wu, Y.

Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
[Crossref]

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Xie, C.

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Xu, P.

Xu, X. F.

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

Xu, Z.

Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
[Crossref]

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Yan, F.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Yan, Z.

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Yang, J.

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

Yoshihara, F.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Yu, S.

Yuan, Z. S.

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
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B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
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Yuge, T.

T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011).
[Crossref] [PubMed]

Zeilinger, A.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

Zhan, M.

Zhang, Z.

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Zhao, B.

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
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Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
[Crossref]

Zhao, N.

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

Zhao, R.

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
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R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
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Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
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L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
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Zukowski, M.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

J. Phys. At. Mol. Opt. Phys. (2)

D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
[Crossref]

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
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Nat. Photon. (1)

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
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Nat. Phys. (3)

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Nature (3)

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
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T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
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Opt. Express (2)

Phys. Lett. A (1)

M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303(4), 249–252 (2002).
[Crossref]

Phys. Rev. A (5)

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
[Crossref]

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65(2), 022314 (2002).
[Crossref]

Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
[Crossref]

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
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Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
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Phys. Rev. Lett. (9)

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84(22), 5094–5097 (2000).
[Crossref] [PubMed]

L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011).
[Crossref] [PubMed]

M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
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G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
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Proc. Natl. Acad. Sci. U.S.A. (1)

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

Rev. Mod. Phys. (2)

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

Science (1)

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

Other (1)

R. Loudon, The Quantum Theory of Light (Oxford University, 2004).

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Figures (6)

Fig. 1
Fig. 1 The atomic level schemes of R 87 b for EIT storages (a) and Raman π rotations (b), respectively. σ + and σ + are the right- and left-circularly-polarized signal fields, respectively. W / R is the left-circularly-polarized writing/reading field. Δ R denotes the detuning of the Raman laser from the transition | a | e .
Fig. 2
Fig. 2 (a) CPMG π pulse sequence. (b) The illustration of function f ( t ' ) (n: even).
Fig. 3
Fig. 3 (a) The experimental setup. HWP: half-wave plate; QWP: quarter-wave plate; PBS: polarizing beam splitter; BS: polarization-insensitive beam splitter; D1, 2: Photon detectors. (b) The involved atomic level scheme of R 87 b for optical pumping.
Fig. 4
Fig. 4 The retrieval efficiencies as the function of the storage time. The square dots in curve ( Ι ) and circle dots in curve ( Ι Ι ) are the measured results for σ + -polarized and σ -polarized fields, respectively.
Fig. 5
Fig. 5 (a) and (b) The applied CPMG sequences for F d d = 5 k H z and F d d = 10 k H z , respectively. π i ( i = 1 , 2 , 3 , 4 ) is the i-th π pulse. (c) The quantum process fidelities F p as the function of the storage time. The square dots are the results without the CPMG sequence. The circle and triangle dots are the results with CPMG sequences of 5- k H z and 10- k H z frequencies, respectively. The horizontal dashed (red) line is the boundary of 1/2.
Fig. 6
Fig. 6 Quantum process fidelity F p at storage time of 800μs as the function of the number of π-pulses n (lower) and the frequency F d d (upper).

Equations (19)

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

ε ( t ) = ε R ( t ) + ε L ( t ) = | ε ( t ) | ( α | R + β e i φ | L ) ,
( S 0 i n S 1 i n S 2 i n S 3 i n ) = | ε ( t ) | 2 ( 1 2 α β sin θ α 2 β 2 2 α β cos θ )
S ^ ± ( z , t ) = ( N z ) 1 z j N z | a m F = ± 1 j j b m F = 1 | e i ω a b t ,
S ( z , t 1 ) = S ^ ( z , t 1 ) + S ^ + ( z , t 1 ) = | S ( z , t 1 ) | ( α s + + β e i φ s ) .
S ( z , t ) = | S ^ ( z , 0 ) | e t / 2 τ d i ω a b t ( α e t / 2 τ + i Ω + t i 0 t ω + ( t ) d t ' s + + e i φ β s e t / 2 τ i Ω t i 0 t ω ( t ) d t ) ,
ε o u t ( t ) = R S ( z , t ) R e t / 2 τ d i ω a b t ( α e t / 2 τ + | R + e i φ β e t / 2 τ i Ω t i 0 t δ ω ( t ) d t | L ) ,
( S 0 o u t S 1 o u t S 2 o u t S 3 o u t ) = R e t / τ d ( α 2 e t / τ + + β 2 e t / τ 2 α β e t ( 1 / 2 τ + + 1 / 2 τ ) W ( t ) sin ( Ω t + φ ) α 2 e t / τ + β 2 e t / τ 2 α β e t ( 1 / 2 τ + + 1 / 2 τ ) W ( t ) cos ( Ω t + φ ) ) ,
W ( t ) = e t / T 0 ,
F s t = T r ( ρ i n ρ o u t ) .
F s t ( X ) 1 2 + e t ( 1 / 2 τ + + 1 / 2 τ ) W ( t ) cos Ω t e t / τ + + e t / τ ,
F s t ( X ) = 1 ,
F p 3 F st ¯ 1 2 ,
F s t ( X ) 1 2 + e t ( 1 / 2 τ + + 1 / 2 τ ) W ( t ) cos Ω t e t / τ + + e t / τ ,
α s + β e i φ s + α s + + β e i φ s .
S ( z , t ) = S ^ + ( z , t ) + S ^ ( z , t ) = | S ( z , t 0 ) | H ( t ) ( α e δ t 2 τ + s + + e i φ β W ( τ ) e δ t 2 τ i Ω δ t i τ τ + δ t δ ω ( t ) d t s ) ,
f ( t ' ) = 0 f o r t ' < 0 o r t ' > τ , f ( t ' ) = ( 1 ) l f o r t k < t ' < t k + 1 , k = 0 , 1 , 2 , 3 2 m .
S ( z , t ) = | S ( z , t 0 ) | H ( t ) ( α s + ( z , t ) + β e i φ i Ω δ t s ( z , t ) ) .
F p 1 + cos ϑ 2 .
S ( z , t ) = | S ( z , t 0 ) | H ( t ) ( α s ( z , t ) + β e i φ i ϑ s + ( z , t ) ) ,

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