Abstract
Longlifetime quantum storages accessible to the telecom photonic infrastructure are essential to longdistance quantum communication. Atomic quantum storages have achieved subsecond storage time corresponding to 1000 km transmission time for a telecom photon through a quantum repeater algorithm. However, the telecom photon cannot be directly interfaced to typical atomic storages. Solidstate quantum frequency conversions fill this wavelength gap. Here we report on the experimental demonstration of a polarizationinsensitive solidstate quantum frequency conversion to a telecom photon from a shortwavelength photon entangled with an atomic ensemble. Atom–photon entanglement has been generated with a Rb atomic ensemble and the photon has been translated to telecom range while retaining the entanglement by our nonlinearcrystalbased frequency converter in a Sagnac interferometer.
Introduction
Quantum frequency conversion^{1} (QFC) based on nonlinear optical processes enables us to change the color of photons without destroying its quantum properties. This allows us to transfer quantum properties of a physical system to another one that has different accessible frequencies through a single photon^{2,3,4,5,6,7,8,9,10,11,12,13}. Besides that, one could use QFC for other purposes such as erasing distinguishability of photons^{14}, manipulating spectral and temporal modes of photons^{15,16,17,18,19,20,21,22,23}, and performing frequencydomain quantum information processing^{24,25,26} by tailoring of the pump light. Most of those abilities have been demonstrated with solidstate QFC devices because of its applicability to a wide frequency range, analogously to mirrors and beamsplitters (BSs) for the spatial manipulation of the photons.
The extension of the solidstate QFC for quantum storages has also been actively studied^{27,28,29}. For longdistance quantum communication with quantum repeater algorithms^{30,31,32}, a long lifetime quantum storage system that can be entangled with a telecom photon is necessary. The cold Rb atomic ensemble is one of the promising quantum storage systems that has a long lifetime and a high efficiency atom–photon entanglement generation^{3,33,34,35,36,37,38}. Recently, solidstate QFC of a single photon from a cold Rb atomic ensemble has been demonstrated^{28,29}, in which a nonclassical correlation between atoms and a telecom photon was reported^{28} and a single spin excitation of atoms heralded by a telecom photon detection was observed^{29}. But the quantum state preservation, which is an ability that cannot be mimicked by a classical memory, has never been shown yet.
In this paper, we report a polarizationinsensitive QFC (PIQFC), which converts the frequency (wavelength) of a photon while preserving the input polarization state. Our solidstate PIQFC device consists of a waveguided periodically poled lithium niobate (PPLN) crystal installed in a Sagnac interferometer. By using the QFC device, we converted a 780nm polarized photon entangled with a cold Rb atomic ensemble to a telecom wavelength of 1522 nm. Entanglement between the Rb atoms and the converted telecom photon has been clearly observed. The demonstration of interface between telecom photons and a good quantum storage is a key ingredient in the future quantum network technology.
Results
Polarizationinsensitive QFC
We first review the conventional QFC of a singlemode light with a specific polarization based on the secondorder nonlinear optical effect^{1,6}. When a pump light at angular frequency ω_{p} is sufficiently strong, the Hamiltonian of the process is described by H = \(i\hbar \xi ^ \ast a_{\mathrm{l}}^\dagger a_{\mathrm{u}} + {\mathrm{h}}{\mathrm{.c}}{\mathrm{.}}\), where h.c. represents the Hermitian conjugate of the first term, and a_{u} and a_{l} are annihilation operators of upper and lower frequency modes at angular frequencies ω_{u} and ω_{l}(=ω_{u} − ω_{p}), respectively. Coupling constant \(\xi = \left \xi \righte^{i\phi }\) is proportional to the complex amplitude of the pump light with its phase ϕ.
As shown in Fig. 1d, when two QFCs working for two different polarization modes are superposed, the interaction Hamiltonian can be described by H = iħ\(\left( {\xi _{\mathrm{H}}^ \ast a_{{\mathrm{l,H}}}^\dagger a_{{\mathrm{u,H}}} + \xi _{\mathrm{V}}^ \ast a_{{\mathrm{l,V}}}^\dagger a_{{\mathrm{u,V}}}} \right)\) + \({\mathrm{h}}{\mathrm{.c}}{\mathrm{.}}\), where a_{u(l),H} and a_{u(l),V} are annihilation operators of horizontally (H) polarized and vertically (V) polarized upper(lower) frequency modes, respectively. ξ_{H(V)} = \(\left {\xi _{{\mathrm{H}}({\mathrm{V}})}} \righte^{i\phi _{{\mathrm{H}}({\mathrm{V}})}}\) is proportional to the amplitudes of the H(V)polarized pump light with phase ϕ_{H(V)}. By using the Heisenberg representation, annihilation operators a_{u,H(V),out} and a_{l,H(V),out} of the upper and lower frequency modes coming from the nonlinear optical medium are represented by
and
where t_{H(V)} = \({\mathrm{cos}}\left( {\left {\xi _{{\mathrm{H}}({\mathrm{V}})}} \right\tau } \right)\) and r_{H(V)} = \(e^{i\phi _{{\mathrm{H}}({\mathrm{V}})}}{\mathrm{sin}}\left( {\left {\xi _{{\mathrm{H}}({\mathrm{V}})}} \right\tau } \right)\). τ is the traveling time of the light pulses through the medium. The transmittance T_{H(V)} ≡ \(\left {t_{{\mathrm{H}}({\mathrm{V}})}} \right^2\) and the reflectance R_{H(V)} ≡ \(\left {r_{{\mathrm{H}}({\mathrm{V}})}} \right^2\) for splitting into the two frequency modes propagating in the same direction can be changed by adjusting the amplitudes of the pump light. When T_{H} = T_{V} and R_{H} = R_{V} are satisfied, and a single photon converted event is postselected, the QFC process while preserving the input polarization state up to the constant phase shift of ϕ_{H} − ϕ_{V} is achieved. By compensating the constant phase, we thus achieve PIQFC, which we used in the experiments reported in this paper. On the other hand, we may also achieve other modes of operation depending on the choice of R_{H} and R_{V}. (I) For T_{H(V)} = R_{H(V)} = 1/2, it becomes a nonpolarizing frequencydomain half BS^{24,25,26,39} (see Fig. 1a). (II) For T_{H} = R_{V} = 1 and T_{V} = R_{H} = 0, it becomes a frequencydomain polarizing BS (PBS) (see Fig. 1b). (III) For T_{H} ≠ T_{V} and 0 < T_{H(V)} < 1, it becomes a frequencydomain partially polarizing BS (PPBS). PPBSs with proper settings of the transmittance and the reflectance can be used to perform frequencydomain quantum information protocols, such as entanglement distillation^{40,41}, probabilistic nonlinear optical gate^{42,43}, quantum state estimation^{44}, and manipulation of multipartite entangled states^{45,46}.
We explain the experimental detail of the PIQFC in Fig. 1d. The nonlinear optical medium for QFC is a type0 quasiphasematched PPLN waveguide (also see Methods section) that converts a Vpolarized input photon to a Vpolarized photon with the use of the Vpolarized pump light. The PPLN is installed in a Sagnac interferometer. In this demonstration, we prepare a polarized upper frequency photon at 780 nm entangled with a Rb atomic ensemble as an input signal to the converter that we explain in detail later. As shown in Fig. 1c, by using a strong pump light at 1600 nm with a linewidth of 150 kHz, the upper frequency photon at 780 nm is converted to the lower frequency photon at 1522 nm by difference frequency generation. In Fig. 1d, the polarization of the input photon is flipped from H (V) polarization to V (H) by a half wave plate (HWP). The photon is combined with the diagonally polarized strong pump light at 1600 nm at a dichroic mirror (DM1). At a PBS, the H and Vpolarized components of them are split into clockwise (CW) and anticlockwise (ACW) directions, respectively. For the CW direction, after flipping from H to V polarization at a HWP, the Vpolarized input photon and the pump light are coupled to the PPLN waveguide. After the conversion, the Vpolarized photons and pump light are reflected by the PBS. Then, only the converted photon is extracted from the reflection port of DM2, being separated from the pump light and the residual input photon by DM1 and DM2, respectively. On the other hand, for the ACW direction, the Vpolarized input photon and the pump light are coupled to the PPLN waveguide. After the conversion, the polarization is flipped from V to H by the HWP, and the photons and the pump light pass through the PBS. Finally, only the converted photon is extracted by DM1 and DM2. The conversion efficiencies of the QFC for CW and ACW directions are shown in Fig. 1e (see Methods section).
Experimental setup
In order to prepare a 780nm signal photon entangled with the Rb atoms, we construct an experimental setup as shown in Fig. 2a. We use Λtype energy levels of D_{2} line at 780 nm in ^{87}Rb atoms (5^{2}S_{1/2} ↔ 5^{2}P_{3/2}) as shown in Fig. 2b. We prepare the Rb atomic ensemble by a magnetooptical trap (MOT) in 20 ms (see Fig. 2c). After the trapping lasers and the magnetic field for the MOT are turned off, we perform the QFC experiment 990 times within 1 ms. A horizontally Hpolarized 200ns initialization pulse at the resonant frequency between a ground level g_{b} (F = 2) and an excited level (F′ = 2) initializes the atoms into another ground level g_{a} (F = 1). Then a vertically Vpolarized 70ns write pulse bluedetuned by Δ ~ 10 MHz from the resonant frequency between g_{a} and the excited level is injected to the atoms, causing the Raman transition from g_{a} to g_{b} with emission of antiStokes (AS) photons.
The momentum conservation guarantees that the wave vector k_{atom} of the collective spin excitation of the atoms satisfies k_{atom} = k_{W} − k_{AS}, where k_{W/AS} is the wave vector of the write/AS light. When we postselect a particular wave vector (path) of a single AS photon in a single mode whose quantum state is denoted by \(\left {{\mathrm{path}}_x} \right\rangle _{{\mathrm{AS}}}\), the wave vector of the atoms corresponding to the photonic state is decided by the momentum conservation. We denote the atomic state by \(\left {{\mathrm{k}}_x} \right\rangle _{{\mathrm{atom}}}\). As a result, when we postselect two different wave vectors of the AS photon corresponding to the states \(\left {{\mathrm{path}}_ + } \right\rangle _{{\mathrm{AS}}}\) and \(\left {{\mathrm{path}}_  } \right\rangle _{{\mathrm{AS}}}\), we obtain a quantum state of the atoms and the AS photon as
with \(\left \alpha \right^2 + \left \beta \right^2 = 1\). The subscripts + and − imply the upper and lower optical paths of the AS photons in Fig. 2a. By adjusting the excitation probabilities such that α = β is satisfied, we obtain a maximally entangled state. In our experiment, we select the Hpolarized AS photons emitted in two directions at small angles (~±3°) relative to the direction of the write pulse, whose emission probabilities are the same ideally. By using a HWP and a PBS (PBS_{as}), path information of AS photons is transformed to polarization information. After the operation, \(\left {{\mathrm{path}}_{ + /  }} \right\rangle _{{\mathrm{AS}}}\) in Eq. (3) is changed to the H/Vpolarized states denoted by \(\left {{\mathrm{H/V}}} \right\rangle _{{\mathrm{AS}}}\), and we obtain
In order to evaluate the quantum correlation between the atoms and the photons, we inject an Hpolarized 100ns read light at the resonant frequency between g_{b} and the excited level into the atoms. The read light provides the transition of the Rb atoms to g_{a} and generation of the Stokes (S) photons. In our experiment, we collect only the Vpolarized component of the S photons. Because of the momentum conservation, wave vector k_{S} of the S photons satisfies k_{S} = k_{atom} + k_{R}. The direction of the emitted S photons is decided by the wave vector of the atomic excitation. Because such a read operation does not access the AS photon, the operation never increase or newly create the entanglement between the atoms and the AS photon. Thus observation of an entangled state of the whichpath state of the S photon and the polarizing AS photon after the read operation is the evidence of the entanglement between the atoms and the AS photon before the read operation.
In the experiment, we inject the read pulse from the direction opposite to the write pulse. The wave vector k_{R} of the read pulse satisfies k_{R} ~ −k_{W}, leading to the relation k_{S} ~ −k_{AS} from the momentum conservation. This means the S photons are emitted in a direction at ~∓3° relative to the direction of the read pulse when the AS photons are emitted in a direction at ~±3° relative to that of the write pulse. By using a HWP and a PBS (PBS_{s}) shown in Fig. 2a, the path information of the Vpolarized S photons is transformed into the polarization. Finally, we can observe the entanglement between the atoms and the AS photons through the polarization entangled photon pair of the AS and the S photons.
After passing through a polarization analyzer composed of a QWP, a HWP, and a PBS for the quantum state tomography^{47}, S photon passes through a monolithic cavitycoated lens^{48} as a frequency filter with an observed bandwidth of 78 MHz and is coupled to a singlemode optical fiber. Then S photon is detected by a silicon avalanche photon detector (APD) denoted by D_{s} with a quantum efficiency of ~60%.
When we do not perform QFC, AS photon is detected by another APD (D_{as}) after passing through a polarization analyzer, a cavitycoated lens with an observed bandwidth of 61 MHz and a singlemode optical fiber. When we perform QFC, mirror M in Fig. 2a is flipped down in order to send the AS photon to the PIQFC depicted in Fig. 1d. We set the conversion efficiency from the front of the PPLN waveguide to the end of the QFC to 33% by using the pump power of 0.23 and 0.21 W for CW and ACW directions, respectively (see Fig. 1e). The telecom photon from the QFC passes through a polarization analyzer followed by an etalon with a bandwidth of 690 MHz and a pair of fiber Bragg gratings with a total bandwidth of ~0.9 GHz. Finally, the telecom photon is detected by a superconducting single photon detector (SSPD) denoted by D_{ast} with a quantum efficiency of ~60%^{49}.
We repeat the above measurement about 47,000 times per second. We use a trigger signal for starting each sequence as a start signal of a timetodigital converter (TDC). The photon countings measured by D_{s}, D_{as} and D_{ast} are used as stop signals of the TDC. We collect the coincidence events between the signals of modes S and AS in their time windows of 64 ns.
Experimental results
Without QFC, we performed the quantum state tomography between the S photon and the AS photon and reconstructed density operator ρ_{S,AS} by the use of the iterative maximum likelihood method^{50}. We estimated entanglement of formation (EoF)^{51} E and the purity defined by \(P = {\mathrm{tr}}\left( {\rho _{{\mathrm{S,AS}}}^2} \right)\) as E = 0.37 ± 0.11 and P = 0.61 ± 0.06, respectively. We also estimated a maximized fidelity to a maximally entangled state \(U_\theta \left {\phi ^ + } \right\rangle\) defined by \(F = {\mathrm{max}}_\theta \left\langle {\phi ^ + } \rightU_\theta ^\dagger \rho _{{\mathrm{S}},{\mathrm{AS}}}U_\theta \left {\phi ^ + } \right\rangle\), whose value was F = 0.78 ± 0.05 for θ = θ_{0} = −65°. Here \(\left {\phi ^ + } \right\rangle\) = \(\left( {\left {\mathrm{H}} \right\rangle _{{\mathrm{AS}}}\left {\mathrm{H}} \right\rangle _{\mathrm{S}} + \left {\mathrm{V}} \right\rangle _{{\mathrm{AS}}}\left {\mathrm{V}} \right\rangle _{\mathrm{S}}} \right){\mathrm{/}}\sqrt 2\) and U_{ θ } = exp(−iθZ/2) ⊗ I with \(Z = \left {\mathrm{H}} \right\rangle \left\langle {\mathrm{H}} \right  \left {\mathrm{V}} \right\rangle \left\langle {\mathrm{V}} \right\) and \(I = \left {\mathrm{H}} \right\rangle \left\langle {\mathrm{H}} \right + \left {\mathrm{V}} \right\rangle \left\langle {\mathrm{V}} \right\). The calculated values of the matrix elements of density operator \(U_{\theta _0}^\dagger \rho _{{\mathrm{S}},{\mathrm{AS}}}U_{\theta _0}\) and its visualization are shown in Table 1 and Fig. 3, respectively. These results show the entanglement between AS photon and the Rb atoms. The observed count rate of the twophoton state was about 0.08 Hz through the overall experiment time of 16 h including the load time of the atoms by MOT.
With QFC, we performed the quantum state tomography between S photon and the wavelengthconverted AS photon. The estimated EoF and purity of reconstructed density operator ρ_{S,ASt} were E = 0.25 ± 0.13 and P = 0.55 ± 0.07, respectively. The maximized fidelity to \(U_\theta \left {\phi ^ + } \right\rangle\) about θ was F = 0.69 ± 0.07 for θ = θ_{1} = 93°. The calculated values of the matrix elements of density operator \(U_{\theta _1}^\dagger \rho _{{\mathrm{S}},{\mathrm{ASt}}}U_{\theta _1}\) and its visualization are shown in Table 2 and Fig. 4, respectively. The EoF E is clearly >0, which shows that the state of the Rb atoms and the telecom photon has entanglement. From the result, we succeeded the creation of the entanglement between the Rb atoms and the telecom photon by using the PIQFC. The observed count rate of the twophoton state was about 0.0065 Hz through the experiment time of 83 h.
Discussion
First, let us discuss the reasons for the degradation of the fidelity of the reconstructed state due to QFC by comparing the cross correlation functions without QFC and those with QFC. We define the normalized cross correlation function without(with) QFC by \(g_{{\mathrm{S,AS}}mn}^{(2)}\left( {g_{{\mathrm{S,ASt}}mn}^{(2)}} \right)\) which is measured at D_{as(ast)} and D_{s} with m and n polarization, respectively, where m, n ∈ {H, V}. The cross correlations are calculated from the main experimental data of the coincidence counts used in the reconstruction of ρ_{S,AS} and ρ_{S,ASt}, and the single counts that were recorded in the same runs. We list the estimated values in Table 3. In order to discuss genuine effect of QFC, we should be careful about the effect of the strong laser light at 850 nm used for stabilizing the interferometer. The main cause of the degradation of the fidelity without QFC is the nonnegligible contamination from the 850nm light used for the stabilization of the interferometer by the mirror on PZT as mentioned in the caption of Fig. 2a. On the other hand, the fidelity with QFC does not suffer: the 850nm light is eliminated because it does not satisfy the phase matching of the PPLN crystal or the converted light cannot pass through the frequency filters even if the light is converted. For this reason, we ran additional experiments for measuring the intensity correlation \(g_{{\mathrm{S,AS}}mn}^{(2) \ast }\) without QFC while turning off the 850nm laser light, whose result is shown in Table 3. For (m, n) = (H, V) and (V, H), the cross correlation functions are around unity, which means the S photons (Rb atoms) and AS photons have no correlation. By using the values for (m, n) = (H, H) and (V, V), we will estimate the amount of the 850nm noise photons in the experiment without QFC, and will thereby estimate the amount of noise photons produced in the process of QFC. It is natural to assume the S photons and the noise photons are statistically independent. In this case the following equations are satisfied^{29}:
where ζ_{ n } and \(\zeta _n^\prime\) are the signaltonoise ratios, ζ_{ n } is ratio of the average photon number of the AS photons just before the QFC at mirror M and the equivalent input noise to the QFC device, and \(\zeta _n^\prime\) is ratio of that of the AS photons and the 850nm noise photons at mirror M. From the equations, we obtain ζ_{H} = 0.56 and ζ_{V} = 0.65 with QFC and \(\zeta _{\mathrm{H}}^\prime = 0.46\) and \(\zeta _{\mathrm{V}}^\prime = 0.44\) without QFC.
The above experimental results imply that the signaltonoise ratios are almost polarization independent. In the following discussion, we assume the signaltonoise ratios are ζ_{QFC} = 0.6 with QFC and ζ_{850} = 0.45 without QFC for any polarization. Here, we estimate an expected polarization correlation without QFC which would be obtained if we could remove the contamination from the 850nm laser without affecting the phase stability. Let us consider the three visibilities, V_{ z }(ρ) = tr(ρZZ), V_{ x }(ρ) = tr(ρXX) and V_{ y }(ρ) = tr(ρYY), where ρ is a density operator, \(X = \left {\mathrm{H}} \right\rangle \left\langle {\mathrm{V}} \right + \left {\mathrm{V}} \right\rangle \left\langle {\mathrm{H}} \right\) and \(Y =  i\left {\mathrm{H}} \right\rangle \left\langle {\mathrm{V}} \right + i\left {\mathrm{V}} \right\rangle \left\langle {\mathrm{H}} \right\). The fidelity of state ρ to the maximally entangled state \(\left {\phi ^ + } \right\rangle \left\langle {\phi ^ + } \right\) = \((1 + XX)(1 + ZZ){\mathrm{/}}4\) is then given by F(ρ) = (1 + V_{ z }(ρ) + V_{ x }(ρ) − V_{ y }(ρ))/4. For the reconstructed density operator \(U_{\theta _0}^\dagger \rho _{{\mathrm{S}},{\mathrm{AS}}}U_{\theta _0}\) without QFC, the visibilities are V_{ z } = 0.76, V_{ x } = 0.68, and V_{ y } = −0.69, respectively. By using these visibilities, \(g_{{\mathrm{S,AS}}mn}^{(2)^\ast }\) and ζ_{850}, the expected visibilities without QFC when we could remove the contamination of 850nm light are estimated as \(V_z^ \ast = 0.90\), \(V_x^ \ast = 0.81\), and \(V_y^ \ast =  0.82\). The corresponding fidelity is \(F^ \ast\) = \(\left( {1 + V_z^ \ast + V_x^ \ast  V_y^ \ast } \right){\mathrm{/}}4\) = \(0.88\). The details of the calculation are shown in Methods section.
Similarly to the above calculation, we can calculate expected degradation of the visibilities from \(V_i^ \ast\) for i = X, Y, Z associated with the noise photons produced in QFC, using the value of ζ_{QFC}. The estimated visibilities are \(V_z^{\mathrm{t}} = 0.76\), \(V_x^{\mathrm{t}} = 0.68\), and \(V_y^{\mathrm{t}} =  0.69\). On the other hand, the visibilities calculated from the density operator \(U_{\theta _1}^\dagger \rho _{{\mathrm{S}},{\mathrm{ASt}}}U_{\theta _1}\) reconstructed in the actual experiment with QFC are \(V_z^{{\mathrm{t}},{\mathrm{obs}}} = 0.79\), \(V_x^{{\mathrm{t,obs}}} = 0.50\), and \(V_y^{{\mathrm{t}},{\mathrm{obs}}} =  0.49\). We see that \(V_z^{{\mathrm{t,obs}}}\) is close to \(V_z^{\mathrm{t}}\), but \(V_{x(y)}^{{\mathrm{t,obs}}}\) is significantly lower than \(V_{x(y)}^{\mathrm{t}}\). This fact implies that we may ascribe the degradation of fidelity with QFC to the two causes, the noise photons induced from the strong pump for QFC and decoherence between the H and Vpolarized photons.
Based on the above analysis, we discuss possible improvements of the fidelity after QFC. As for the noise photons, the small value of ζ_{QFC} comes from the fact that the collection efficiency for the AS photons is <1% in the current experiment. If we could improve ζ_{QFC} 10 times enhancing it to around ~6 by increasing the collection efficiency of the AS photons (which could be done with stateoftheart technologies^{52}), we would expect \(V_z^{{\mathrm{t}},{\mathrm{exp}}} = 0.89\left( {\sim V_z^ \ast } \right)\), \(V_x^{{\mathrm{t}},{\mathrm{exp}}} = 0.56\), and \(V_y^{{\mathrm{t}},{\mathrm{exp}}} =  0.55\), resulting in an expected improvement of the fidelity to F = 0.75. In order to improve it further to approach F^{*}, it is necessary to mitigate the decoherence. We speculate that the cause of the decoherence is the phase fluctuations in the interferometers of the S and AS photons due to the fluctuation or drift of the wavelength of the 850nm laser, since the duration of the experimental run with QFC is much longer than the run without QFC. If this turned out to be the case, a possible solution could simply be a more stable laser.
In conclusion, we have shown entanglement between the wave vector of collective spin excitation of Rb atoms and a polarized telecom photon by using PIQFC composed by a PPLN waveguide installed in a Sagnac interferometer. Recent researches showed efficient and subsecond lifetime quantum memory^{38} and a multiplexed quantum memory^{53,54} by using Rb atomic ensembles. Combining such stateoftheart technologies with our experimental result will be useful for fiberbased quantum communication over long distance. Furthermore, the PIQFC is applicable to various conversion systems for matterbased quantum storages, such as trapped ions^{55,56}, diamond color centers^{39}, and quantum dots^{10}, which are useful for measurementbased quantum computation^{57,58,59}. The potential of our QFC is not limited by the use of the PIQFC. The proposed dualpolarizationmode QFC has additional features as a nonpolarizing frequencydomain half BS, a frequencydomain PBS, and a frequencydomain PPBS. The devices will provide various kinds of tasks developed in the linear optical quantum information processing.
During preparation of our paper, we found a related work^{60} in which polarization entanglement between a trapped calcium ion and a telecom Oband photon with QFC was demonstrated.
Methods
PPLN waveguide
The PPLN waveguide used in our experiment is a ridged type with 8μm wide. The length is 40 mm. The temperature is controlled to be about 20 °C for the best conversion efficiency.
The dependencies of the conversion efficiencies on the pump power for CW and ACW directions shown in Fig. 1e are measured by using laser light, which propagates along the same spatial path as the AS photon. The conversion efficiency was calculated by measuring the power of the 780nm light in front of the QFC and the 1522nm light at end of the QFC before the fiber coupling. The maximum conversion efficiency is not unity. One of the reasons is the nonunit coupling efficiencies of the signal light, which are 0.83 and 0.65 for CW and ACW directions, respectively. Another reason may be mode mismatching of the signal and the pump light propagating in the PPLN waveguide. We aligned the QFC circuit to achieve the same maximum conversion efficiency in total for CW and ACW directions.
We estimated the amount of the noises at QFC by measuring the photon counts without the input of the signal photons. The count rates were 3.1 × 10^{−6} counts/pulse and 3.5 × 10^{−6} counts/pulse for H and V polarization, respectively. By considering the quantum efficiency 60% of the SSPD and transmittances 50 and 17% of the frequency filters (the etalon and the fiber Bragg gratings (FBGs)), the noise photons just after the QFC are estimated to be 6.1 × 10^{−5} and 7.0 × 10^{−5} counts/pulse for H and V polarization, respectively, in the bandwidth of 540 MHz that are calculated by using the bandwidths 690 MHz and 0.9 GHz of the frequency filters. Since the total conversion efficiency used in our experiment is 0.33 for both H and V polarization, the signaltonoise ratios for a deterministic single photon input are 5400 and 4700, respectively.
Transmittance of the optical components
Below we list the transmittance of the optical components for the signal photons in our experiment. For 780 nm, the transmittances of DM1 and DM2 in the QFC circuit are both 0.99. The transmittances of the monolithic cavitycoated lenses for the S and AS photons are both 0.2 including the fiber coupling efficiency.
For 1522 nm, the transmittance of DM1 is over 0.98 and the reflectances of DM2 are about 1.0 and 0.88 for H and Vpolarized photons, respectively, which are included in the efficiency of the QFC shown in Fig. 1e. The transmittance of the etalon is 0.5 inclusive of the fiber coupling efficiency. The transmittance of a pair of FBGs is 0.17.
Estimation of visibilities and fidelity
As is the common situation in quantum information experiments using single photons, we assume that \(\left\langle {mn\left \rho \rightmn} \right\rangle\) is measured by coincidence probability P_{ mn } of the m and n polarized two photons^{47}. In this case, the visibility V_{ z } is written as V_{ z } = (P_{ HH } + P_{ VV } − P_{ HV } − P_{ VH })/(P_{ HH } + P_{ VV } + P_{ HV } + P_{ VH }). When the single counts are independent of the measurement polarization, the visibilities are calculated by using the cross correlation functions for m and n polarization. For example, \(V_z^ \ast\) is given by
From Eq. (6), we have
with
From \(g_{{\mathrm{S,AS}}HH}^{(2) \ast }\) = 29.0, \(g_{{\mathrm{S,AS}}VV}^{(2) \ast }\) = 15.7 and \(g_{{\mathrm{S}},{\mathrm{AS}}HV}^{(2) \ast }\) = \(g_{{\mathrm{S}},{\mathrm{AS}}VH}^{(2) \ast }\) = 1, we obtain \(\mathop {\sum}\nolimits_{m,n \in \{ H,V\} } {\kern 1pt} g_{{\mathrm{S}},{\mathrm{AS}}mn}^{(2) \ast }\) = 46.7, and this is basis independent due to the property of the trace. Together with our assumption that ζ_{850} is polarization independent, we also have V_{x(y)} = \(V_{x(y)}^ \ast \gamma ^ \ast \left( {\zeta _{{\mathrm{8}}50}} \right)\). Using the values of V_{ z } = 0.76, V_{ x } = 0.68, and V_{ y } = −0.69, we obtain \(V_z^ \ast\) = 0.90, \(V_x^ \ast\) = 0.81, and \(V_y^ \ast\) = −0.82. In a similar manner, we also obtain \(V_z^{\mathrm{t}} = V_z^ \ast \gamma ^ \ast \left( {\zeta _{{\mathrm{QFC}}}} \right)\) = 0.76, \(V_x^{\mathrm{t}} = V_x^ \ast \gamma ^ \ast \left( {\zeta _{{\mathrm{QFC}}}} \right)\) = 0.68, and \(V_y^{\mathrm{t}} = V_y^ \ast \gamma ^ \ast \left( {\zeta _{{\mathrm{QFC}}}} \right)\) = −0.69.
Data availability
The data that support the findings of this study are available from the corresponding author on reasonable request.
References
Kumar, P. Quantum frequency conversion. Opt. Lett. 15, 1476–1478 (1990).
Tanzilli, S. et al. A photonic quantum information interface. Nature 437, 116–120 (2005).
Dudin, Y. et al. Entanglement of lightshift compensated atomic spin waves with telecom light. Phys. Rev. Lett. 105, 260502 (2010).
McGuinness, H. J., Raymer, M. G., McKinstrie, C. J. & Radic, S. Quantum frequency translation of singlephoton states in a photonic crystal fiber. Phys. Rev. Lett. 105, 093604 (2010).
Rakher, M. T., Ma, L., Slattery, O., Tang, X. & Srinivasan, K. Quantum transduction of telecommunicationsband single photons from a quantum dot by frequency upconversion. Nat. Photonics 4, 786–791 (2010).
Ikuta, R. et al. Wideband quantum interface for visibletotelecommunication wavelength conversion. Nat. Commun. 2, 1544 (2011).
Ramelow, S., Fedrizzi, A., Poppe, A., Langford, N. K. & Zeilinger, A. Polarizationentanglementconserving frequency conversion of photons. Phys. Rev. A 85, 013845 (2012).
Zaske, S. et al. Visibletotelecom quantum frequency conversion of light from a single quantum emitter. Phys. Rev. Lett. 109, 147404 (2012).
Ates, S. et al. Twophoton interference using backgroundfree quantum frequency conversion of single photons emitted by an inas quantum dot. Phys. Rev. Lett. 109, 147405 (2012).
De Greve, K. et al. Quantumdot spinphoton entanglement via frequency downconversion to telecom wavelength. Nature 491, 421–425 (2012).
Ikuta, R. et al. Highfidelity conversion of photonic quantum information to telecommunication wavelength with superconducting singlephoton detectors. Phys. Rev. A 87, 010301(R) (2013).
Rütz, H., Luo, K.H., Suche, H. & Silberhorn, C. Quantum frequency conversion between infrared and ultraviolet. Phys. Rev. Appl. 7, 024021 (2017).
Liu, S.L. et al. Coherent frequency bridge between visible and telecommunications band for vortex light. Opt. Express 25, 24290–24298 (2017).
Takesue, H. Erasing distinguishability using quantum frequency upconversion. Phys. Rev. Lett. 101, 173901 (2008).
Kielpinski, D., Corney, J. F. & Wiseman, H. M. Quantum optical waveform conversion. Phys. Rev. Lett. 106, 130501 (2011).
Brecht, B., Eckstein, A., Christ, A., Suche, H. & Silberhorn, C. From quantum pulse gate to quantum pulse shaperengineered frequency conversion in nonlinear optical waveguides. New J. Phys. 13, 065029 (2011).
Lavoie, J., Donohue, J. M., Wright, L. G., Fedrizzi, A. & Resch, K. J. Spectral compression of single photons. Nat. Photonics 7, 363–366 (2013).
Fisher, K. A. et al. Frequency and bandwidth conversion of single photons in a roomtemperature diamond quantum memory. Nat. Commun. 7, 11200 (2016).
Matsuda, N. Deterministic reshaping of singlephoton spectra using crossphase modulation. Sci. Adv. 2, e1501223 (2016).
Manurkar, P. et al. Multidimensional modeseparable frequency conversion for highspeed quantum communication. Optica 3, 1300–1307 (2016).
Kroh, T., Ahlrichs, A., Sprenger, B. & Benson, O. Heralded wave packet manipulation and storage of a frequencyconverted pair photon at telecom wavelength. Quantum Sci. Technol. 2, 034007 (2017).
Allgaier, M. et al. Highly efficient frequency conversion with bandwidth compression of quantum light. Nat. Commun. 8, 14288 (2017).
Allgaier, M. et al. Fast timedomain measurements on telecom single photons. Quantum Sci. Technol. 2, 034012 (2017).
Kobayashi, T. et al. Frequencydomain HongOuMandel interference. Nat. Photonics 10, 441–444 (2016).
Clemmen, S., Farsi, A., Ramelow, S. & Gaeta, A. L. Ramsey interference with single photons. Phys. Rev. Lett. 117, 223601 (2016).
Kobayashi, T. et al. Machzehnder interferometer using frequencydomain beamsplitter. Opt. Express 25, 12052–12060 (2017).
FernandezGonzalvo, X. et al. Quantum frequency conversion of quantum memory compatible photons to telecommunication wavelengths. Opt. Express 21, 19473–19487 (2013).
Farrera, P., Maring, N., Albrecht, B., Heinze, G. & de Riedmatten, H. Nonclassical correlations between a cband telecom photon and a stored spinwave. Optica 3, 1019–1024 (2016).
Ikuta, R. et al. Heralded single excitation of atomic ensemble via solidstatebased telecom photon detection. Optica 3, 1279–1284 (2016).
Briegel, H.J., Dür, W., Cirac, J. I. & Zoller, P. Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932–5935 (1998).
Duan, L.M., Lukin, M., Cirac, J. I. & Zoller, P. Longdistance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001).
Sangouard, N., Simon, C., De Riedmatten, H. & Gisin, N. Quantum repeaters based on atomic ensembles and linear optics. Rev. Mod. Phys. 83, 33 (2011).
Yuan, Z.S. et al. Experimental demonstration of a bdcz quantum repeater node. Nature 454, 1098–1101 (2008).
Zhao, R. et al. Longlived quantum memory. Nat. Phys. 5, 100–104 (2009).
Ritter, S. et al. An elementary quantum network of single atoms in optical cavities. Nature 484, 195–200 (2012).
Bao, X.H. et al. Efficient and longlived quantum memory with cold atoms inside a ring cavity. Nat. Phys. 8, 517–521 (2012).
Hofmann, J. et al. Heralded entanglement between widely separated atoms. Science 337, 72–75 (2012).
Yang, S.J., Wang, X.J., Bao, X.H. & Pan, J.W. An efficient quantum lightmatter interface with subsecond lifetime. Nat. Photonics 10, 381–384 (2016).
Ikuta, R. et al. Frequency downconversion of 637 nm light to the telecommunication band for nonclassical light emitted from nv centers in diamond. Opt. Express 22, 11205–11214 (2014).
Bennett, C. H., Bernstein, H. J., Popescu, S. & Schumacher, B. Concentrating partial entanglement by local operations. Phys. Rev. A. 53, 2046–2052 (1996).
Kwiat, P. G., BarrazaLopez, S., Stefanov, A. & Gisin, N. Experimental entanglement distillation and ‘hidden’ nonlocality. Nature 409, 1014–1017 (2001).
Knill, E., Laflamme, R. & Milburn, G. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2000).
Okamoto, R., O’Brien, J. L., Hofmann, H. F. & Takeuchi, S. Realization of a KnillLaflammeMilburn controlledNOT photonic quantum circuit combining effective optical nonlinearities. Proc. Natl. Acad. Sci. 108, 10067–10071 (2011).
Ling, A., Soh, K. P., LamasLinares, A. & Kurtsiefer, C. Experimental polarization state tomography using optimal polarimeters. Phys. Rev. A 74, 022309 (2006).
Tashima, T. et al. Local transformation of two EinsteinPodolskyRosen photon pairs into a threephoton W state. Phys. Rev. Lett. 102, 130502 (2009).
Ikuta, R., Tashima, T., Yamamoto, T., Koashi, M. & Imoto, N. Optimal local expansion of W states using linear optics and Fock states. Phys. Rev. A 83, 012314 (2011).
James, D. F. V., Kwiat, P. G., Munro, W. J. & White, A. G. Measurement of qubits. Phys. Rev. A 64, 052312 (2001).
Palittapongarnpim, P., MacRae, A. & Lvovsky, A. Note: A monolithic filter cavity for experiments in quantum optics. Rev. Sci. Instrum. 83, 066101 (2012).
Miki, S., Yabuno, M., Yamashita, T. & Terai, H. Stable, highperformance operation of a fibercoupled superconducting nanowire avalanche photon detector. Opt. Express 25, 6796–6804 (2017).
Řeháček, J., Hradil, Z., Knill, E. & Lvovsky, A. I. Diluted maximumlikelihood algorithm for quantum tomography. Phys. Rev. A. 75, 042108 (2007).
Wootters, W. K. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998).
Chen, S. et al. Demonstration of a stable atomphoton entanglement source for quantum repeaters. Phys. Rev. Lett. 99, 180505 (2007).
Pu, Y. et al. Experimental realization of a multiplexed quantum memory with 225 individually accessible memory cells. Nat. Commun. 8, 15359 (2017).
Pu, Y.F. et al. Experimental entanglement of 25 individually accessible atomic quantum interfaces. Sci. Adv. 4, eaar3931 (2018).
Lenhard, A., Brito, J., Bock, M., Becher, C. & Eschner, J. Coherence and entanglement preservation of frequencyconverted heralded single photons. Opt. Express 25, 11187–11199 (2017).
Krutyanskiy, V., Meraner, M., Schupp, J. & Lanyon, B. Polarisationpreserving photon frequency conversion from a trappedioncompatible wavelength to the telecom cband. Appl. Phys. B 123, 228 (2017).
Briegel, H., Browne, D., Dur, W., Raussendorf, R. & Van den Nest, M. Measurementbased quantum computation. Nat. Phys. 5, 19–26 (2009).
Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).
Buluta, I., Ashhab, S. & Nori, F. Natural and artificial atoms for quantum computation. Rep. Progress. Phys. 74, 104401 (2011).
Bock, M. et al. Highfidelity entanglement between a trapped ion and a telecom photon via quantum frequency conversion. Nat. Commun. (https://doi.org/10.1038/s41467018043412 (2018).
Acknowledgements
We thank Yoshiaki Tsujimoto and Motoki Asano for helpful discussions about QFC. This work was supported by CREST, JST JPMJCR1671 and MEXT/JSPS KAKENHI Grant Numbers JP26286068, JP15H03704, JP16H02214, and JP16K17772.
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R.I., T.K., T.Y., and T.M. designed the experiment. R.I., T.K., and T.K. carried out the experiments under supervision of T.Y., M.K., T.M., and N.I. S.M., M.Y., T.Y., and H.T. developed the system of the superconducting singlephoton detectors. All authors analyzed the experimental results, contributed to the discussions and interpretations. R.I. wrote the manuscript, with inputs from all coauthors.
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Ikuta, R., Kobayashi, T., Kawakami, T. et al. Polarization insensitive frequency conversion for an atomphoton entanglement distribution via a telecom network. Nat Commun 9, 1997 (2018). https://doi.org/10.1038/s4146701804338x
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DOI: https://doi.org/10.1038/s4146701804338x
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