We demonstrate a first-order interference between coherent light at 1580 nm and 795 nm by using a frequency-domain Mach-Zehnder interferometer (MZI). The MZI is implemented by two frequency-domain BSs based on a second-order nonlinear optical effect in a periodically-poled lithium niobate waveguide with a strong pump light. The observed visibility is over 0.99 at 50% conversion efficiencies of the BSs. Toward photonic quantum information processing, sufficiently small background photon rate is necessary. From measurement results with a superconducting single photon detector (SSPD), we discuss the feasibility of the frequency-domain MZI in a quantum regime. Our estimation shows that the single photon interference with the visibility above 0.9 is feasible with practical settings.
© 2017 Optical Society of America
Quantum frequency conversion (QFC)  enables a color change of light while preserving its quantum state. It has been actively studied for bridging gaps among physical systems and devices each of which prefers its own response frequency, such as upconversion single photon detectors [2–4] and photonic quantum memories connecting to a telecom optical fiber [5–13]. The QFC process is based on χ(2) or χ(3) nonlinear optical effect with strong pump lights. It is described by an effective Hamiltonian of a beamsplitter (BS) acting on two different frequency modes [1, 14]. Therefore QFC process is expected to work as a frequency-domain BS and plays an essential role for the universal quantum operation on the frequency degree of freedom, similarly to the conventional BS acting on spatial modes in linear optical quantum information processing (QIP) [15, 16]. One of the advantages of frequency domain QIP is easy access to the frequency multiplexed entangled photon sources [17–21]. Recently, to see the fundamental property of frequency-domain BS, Hong-Ou-Mandel interference between photons with different frequencies  which used a partial frequency converter based on χ(2) nonlinearity in a periodically-poled lithium niobate (PPLN) waveguide  has been observed. The first-order interference of a single photon in different frequencies with near 50% visibility has also been shown by using χ(3) nonlinear process in a 100 m fiber in a cryostat . On the other hand, the first-order interference by using the χ(2) nonlinear materials is expected to have a higher signal-to-noise ratio leading to a high visibility even in a room temperature.
In this paper, we construct the frequency-domain Mach-Zehnder interferometer (MZI) employing two frequency-domain BSs based on PPLN waveguides, which is used as the χ(2) nonlinear material. The first frequency-domain BS divides the input coherent light at 1580 nm into 795-nm and 1580-nm light. The second frequency-domain BS combines the two lights and shows the interference fringe at each output mode (795-nm and 1580-nm). When the conversion efficiency of both frequency-domain BSs is ∼ 0.5, the visibility is over 0.99. We also evaluate the performance of the interferometer at a single photon level. From the results, we show that the estimated visibilities at a single photon level will be over 0.9 by using commercially available bandpass filters.
2. Theory of QFC and frequency-domain Mach-Zehnder interferometer
We briefly review the dynamics of QFC process in a χ(2) nonlinear optical medium [1, 7]. We consider two signal modes at upper and lower angular frequencies ωU and ωL satisfying ωU = ωL + ωP, where ωP is the angular frequency of pump light. With an assumption of undepletion of the strong pump, the effective Hamiltonian of the three wave mixing process is described by
Eqs. (2) and (3) are regarded as dynamics of a BS with the transmittance T = |cos(|χ|τ)|2 and the reflectance R = |sin(|χ|τ)|2 on the two modes of âU and âL. They can be actively adjusted by changing the pump power.
The frequency-domain MZI consists of two frequency-domain BSs and a phase shifter as shown in Fig. 1. For simplicity, we deal with a lossless optical circuit. The phase shifter adds a phase shift ϕPS on the lower frequency mode as and , where ÛPS is a unitary operator of the phase shifter. The first (second) frequency-domain BS is represented by the unitary operator UBS1(2) which give the operations in Eqs. (2) and (3) with reflectance R1(2), transmittance T1(2) = 1 − R1(2) and phase ϕP,1(2) of the pump light. When the lower frequency light in state |ψ〉L is injected into the interferometer, average photon number of light in the upper and the lower modes is described byEqs. (2) and (3) and the transformation of the phase shifter, where ÛMZI ≡ ÛBS2ÛPSÛBS1 and δϕ ≡ ϕP,1 − ϕP,2 − ϕPS. pU and pL depend on the relative phase δϕ. This is a precise analogue to the first-order interference appearing in the conventional MZI. We define the interference visibility by V = (pmax − pmin)/(pmax + pmin), where pmax and pmin are the maximum and the minimum values of pU and pL, respectively. From Eqs. (4) and (5), the visibilities of the interference fringes VU and VL which are observed in the upper and the lower frequency modes, are described by
3.1. Experimental setup
The experimental setup is shown in Fig. 2. Two frequency-domain BSs of the MZI are composed of two PPLN waveguides  denoted by PPLN1 and PPLN2. The PPLN1 and PPLN2 are designed for the type-0 quasi-phase-matching for three wave mixing of 1600 nm, 1580 nm and 795 nm which are used as the pump, the lower and the upper frequencies, respectively. The pump light is a V-polarized cw laser amplified by the Erbium-doped fiber amplifier (EDFA). The seed laser is an external cavity diode laser (ECDL) with a full width at half maximum (FWHM) of 150 kHz. The coupled power P1 of the pump beam to PPLN1 is adjusted by a variable attenuator (VA) up to ∼ 400 mW. The pump beam is filtered by a Bragg grating (BGP) with FWHM of 120 GHz to reduce an amplified spontaneous emission noise from the EDFA. The lengths of PPLN1 and PPLN2 are 20 mm and 40 mm, respectively. These lengths determine their FWHM acceptance widths of PPLN1 and PPLN2 as 140 GHz and 70 GHz, respectively, for the conversion between 795 nm and 1580 nm.
The input of the present MZI interferometer is a V-polarized lower frequency light (1580 nm) taken from a cw distributed feedback (DFB) laser with the linewidth of 10 MHz (FWHM) and the power of 10 mW. The input light is combined with the pump light by a dichroic mirror (DM1) and the two lights are coupled to PPLN1. The upper frequency light (795 nm) generated at PPLN1 is separated from the lower frequency and pump lights by DM2. The LCR adds approximately the same phase shifts to the lower-frequency and pump lights to sweep the relative phase δϕ in Eqs. (4) and (5). Then, three lights are recombined by DM3, and coupled to PPLN2.
Among the outputs from PPLN2, the upper frequency light (795 nm) is picked up by DM4 and BGU with the FWHM bandwidth of Δf,U ≡ 99 GHz. The lower frequency light (1580 nm) is separated from the pump beam at 1600 nm by bandpass filters (BPF1, BPF2). The total bandwidth of the set of two bandpass filters is Δf,L = 69 GHz. The upper and lower frequency lights extracted are coupled to the single mode fibers and measured by power meters PMU and PML.
3.2. Experimental results
We measured the dependencies of the interference visibility of the upper mode VU(P1) and the lower mode VL(P1) on the pump power P1 from the output power of the 795-nm and 1580-nm light by varying the relative phase through LCR. The result is shown in Fig. 3(a). The observed interference fringes at P1 = 140 mW are shown in Fig. 3(b). The interference fringes in the upper and the lower frequency modes are clearly seen. The observed interference visibilities take the same value of 0.99 in both modes at the pump power of 140 mW.
3.3. Theoretical analysis
The visibilities VU(P1) and VL(P1) depend not only on the pump power P1 but also on the losses inside the frequency-domain MZI. In Fig. 4, we show a theoretical model of a lossy frequency-domain MZI. In order to characterize the losses, we consider virtual loss media in front of and behind lossless frequency-domain BSs with conversion efficiencies R1(P1) = 1 − T1(P1) and R2(TPP1) = 1 − T2(TPP1). The ratios of transmittances of virtual loss media behind frequency-domain BSs in upper mode to that in lower mode are denoted by x1 for PPLN1 and x2 for PPLN2. The transmittances of PPLN1 for the 1580-nm light, when there is no pump light, is denoted by TL,in = TL,1T′L,1, where TL,1 and T′L,1 represent the transmittance of loss media in front of and behind lossless frequency-domain BSs. The transmittances from the end of PPLN1 to the end of unpumped PPLN2 are denoted by TU and TL for the 795-nm and 1580-nm light, respectively. For the pump light, we ignore the depletion resulting from the wavelength conversion and assume that the pump power for the PPLN2 to that for PPLN1 is given by a constant factor TP. We estimated the values of TL,in, TU, TL, and TP directly in our experiment. The result are TL,in ≈ 0.64, TU ≈ 0.63, TL ≈ 0.60, TP ≈ 0.54. The visibility of the lossy MZI for the output of the upper frequency mode is obtained by replacing T1, R1, T2 and R2 with T1(P1)TL,in, R1(P1)TL,inx1, T2(TPP1)TU and R2(TPP1)TLx2 in Eq. (6), respectively, asEq. (7), respectively, as
In order to calculate VU(P1) and VL(P1), we estimated the internal conversion efficiency R1(P1) = 1 − T1(P1) and the parameter x1 of PPLN1 in the same manner as in Ref. , by observing the output powers of 795-nm and 1580-nm light by power meters PMU and PML while varying the pump power P1. The temperature of PPLN2 was chosen to make its conversion efficiency negligible. Taking into account the values of TL and TU above, we determined x1 = 1.4 ± 0.1 and R1(P1) as shown in Fig. 5(a). The best fit to R1(P1) with gives A ≈ 0.94 and η ≈ 0.0042 /mW. From the result, R1(P1) ∼ 0.5 is achieved at 140-mW pump power. In a similar way, we determined x2 = 1.0 ± 0.1 and R2(TPP1) versus the pump power P1 as shown in Fig. 5(b). The best fit to R2(P) with gives A ≈ 0.58 and η ≈ 0.017 /mW.
By using observed values, we calculated VU(P1) and VL(P1) in Eqs. (8) and (9) as shown with dashed curves in Fig. 3(a). These are in good agreement with the experimental data around the pump power of 140 mW. In our lossy interferometer, the transmittances TU and TL for the upper and lower frequency modes have similar values, and thus the maximum visibilities of VU and VL are simultaneously achieved at 140-mW pump power corresponding to R1(P1) ∼ 0.5 and R2(TPP1) ∼ 0.5, similarly to the lossless case.
In this section, we discuss the performance of the frequency-domain MZI expected in the case where the input comes from a typical single photon source. We first measured background photon count rates by replacing the power meters with superconducting single-photon detectors (SSPDs) . The quantum efficiencies are 0.3 and 0.6 for the 795-nm and 1580-nm light, respectively. For measuring the background photon count rate dU1 at 795 nm induced by PPLN1, we dumped the 1580-nm and 1600-nm light after PPLN1 and injected only the 795-nm light to PPLN2. For measuring the background photon count rate dU2 at 795 nm induced by PPLN2, we dumped the 795-nm light after PPLN1 and injected the 1580-nm and 1600-nm light to PPLN2. For background photons at 1580 nm, we cannot separately measure the noise photons induced by pump light at PPLN1 and PPLN2. Therefore we measured only the sum of the background photon count rates dL induced by pump light at PPLN1 and PPLN2. The experimental result is shown in Fig. 6. The result shows nonlinear and linear dependencies for 795-nm and 1580-nm light, which is the same tendency reported in Ref. . It means the background photons are mainly originated from Raman scattering of the strong pump light.
By using the observed background photon count rates, we estimate the expected interference visibility when we use the typical single photon source and filters. We assume that the spectral bandwidth of the input light is a transform-limited pulse of a Gaussian with its FWHM bandwidth of Δin and the measurement time window is set to 4 ln 2/πΔin which corresponds to the twice of FWHM pulse length of the input light, which leads to 98% collection efficiency. The background-photon reduction of the output light is performed by the filters with the bandwidth of Δ̃f,U and Δ̃f,L for the upper light and the lower light, where Δ̃f,U, Δ̃f,L > Δin. We assume that the spectral shapes of the filters are Gaussian with the peak value of unity and the transmittances T̃U,out and T̃L,out from PPLN2 to the single mode fibers are estimated by using Δin, Δ̃f,U, Δ̃f,L and the observed values TU,out ≈ 0.71 and TL,out ≈ 0.13. It is reasonable to assume the numbers of the background photons are proportional to the measurement time window and the bandwidth. Under this assumption, the numbers of the background photons in the measurement time window are derived as functions of P1, Δ̃f,U/Δin and Δ̃f,L/Δin, as follows;Fig. 7 by using TL,in ≈ 0.64. We see that the bandpass filters with the bandwidth of 1.4 × Δin is sufficient for achieving high visibilities over 0.9 when the input light has the average photon number above 0.1. For example, in the case of a single photon with a bandwidth of 9.6 MHz borrowed from Ref. , a visibility of > 0.9 will be obtained by using filters with a bandwidth of < 13 MHz. If we use a single photon with a bandwidth of 1.2 GHz reported in Ref. , the high visibility will be obtained by using filters with a bandwidth of < 1.6 GHz. Such frequency filters are achieved by commonly-used etalons, cavities and fiber Bragg gratings.
In conclusion, we have demonstrated the first-order interference between 1580-nm and 795-nm light by constructing the frequency-domain MZI composed of two partial frequency converters using PPLN waveguide and the pump light at 1600 nm as the frequency-domain BSs. The observed visibilities for both output modes (1580 nm and 795 nm) are 0.99 when the conversion efficiency is set to be ∼ 0.5. The background noise estimation of our interferometer shows that if the transform-limited light pulse with the average photon number over 0.1 and sufficiently narrow filters are used, the visibility will be still over 0.9. Such a condition can be realized by the current single photon sources and usual filtering techniques. We believe that the interferometer will be useful tool for large-scale frequency-encoded photonic quantum information processing.
Core Research for Evolutional Science and Technology, Japan Science and Technology Agency (CREST, JST) (JPMJCR1671); Ministry of Education, Culture, Sports, Science, and Technology (MEXT); Japan Society for the Promotion of Science (JSPS) (JP25247068, JP15H03704, JP16H02214, JP16K17772); JSPS Grant-in-Aid for JSPS Fellows (JP14J04677).
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