Quantum interface for telecom frequency conversion based on diamond-type atomic ensembles

In a fiber-based quantum network, the utilization of the telecom band is crucial for long-distance quantum information (QI) transmission between quantum nodes. However, the near-infrared wavelength is identified as optimal for storing and processing QI through alkaline atoms. Recognizing the challenge of efficiently bridging the frequency gap between atomic quantum devices and telecom fibers while maintaining the QI carried by photons, quantum frequency conversion (QFC) serves as a pivotal quantum interface. In this study, we explore an efficient telecom-band QFC mechanism based on diamond-type four-wave mixing (FWM) with rubidium energy levels. The mechanism enables the conversion of photons between the near-infrared wavelength of 795 nm and the telecom band of 1367 or 1529 nm. Using the Heisenberg-Langevin approach, we optimize conversion efficiency (CE) across varying optical depths while considering quantum noises and present corresponding experimental parameters. Unlike previous works neglecting the applied field absorption loss, our results are more relevant to practical scenarios. Moreover, by employing the reduced-density-operator theory to construct a theoretical framework, we demonstrate that this diamond-type FWM scheme can maintain the quantum characteristics of input photons with high fidelity, such as quadrature variances and photon statistics. Importantly, these properties remain unaffected by vacuum field noise, enabling the system to achieve high-purity QFC. Another significant contribution lies in examining how this scheme impacts QI encoded in photon-number, path, and polarization degrees of freedom. These encoded qubits exhibit remarkable entanglement retention under sufficiently high CE. In the case of perfect CE, the scheme can achieve unity fidelity. This comprehensive exploration establishes a theoretical foundation for the application of the diamond-type QFC scheme based on atomic ensembles in quantum networks, laying essential groundwork for advancing the scheme in distributed quantum computing and long-distance quantum communication.

Figure 1

Diamond-type atomic ensemble QFC system. (a) Energy-level diagram illustrating the QFC scheme and the corresponding transitions for the four participating fields. Note that no degenerate states of the energy levels are considered here. However, in Sec. 3b, we delve into the actual energy-level configurations. (b) Schematic diagram illustrating the propagation directions of the participating fields. All light fields propagate in the same direction, nullifying the phase mismatch in the system. The presented scenario involves frequency down-conversion, where the probe field is transformed into the signal field. Conversely, up-conversion proceeds in the opposite manner, converting the signal field back to the probe field.

Figure 2

Optimized CE is presented as a function of OD in the blue solid curve for both (a) telecom E-band QFC scheme and (b) telecom C-band QFC scheme. Here, OD is defined as ${\alpha }_p=n{\sigma }_{p}L\times \frac{1}{2}$, taking into account the transition coefficient of the selected transition scheme. The red solid circles represent the CE calculated using the Magnus expansion up to the second order. The black dotted curves show the CE curves for the model without considering the coupling field absorption loss. For the optimized five parameters and spontaneous emission rates of the two QFC schemes, please refer to Table 1.

Figure 3

Quadrature variances are analyzed as a function of CE for the input probe field in both (a) the single-photon Fock state and (b) the 6-dB squeezed coherent state. The red and blue curves represent the quadrature variances $X$ and $Y$ of the output signal field, respectively. In scenario (b), the phase of the signal field is nullified by a phase shifter, and the input field is squeezed with $\varphi =0$. Notably, the relative squeezing strength is defined as $P=-10{log}_{10}\frac{\sqrt{\mathrm{var}\left(X_i\right)}}{1/2}$, where $P$ measured in dB, and $\mathrm{var}\left(X_i\right)=\frac{1}{4}{e}^{-2r}$.

Figure 4

Fidelity between the input field and the converted field as a function of CE. The blue, red, and green lines correspond to the theoretical curves for the single-photon Fock, single-photon coherent, and 10-photon coherent input states, respectively. The phase of the converted field is eliminated by a phase shifter for both coherent input cases.

Figure 5

QFC scheme for path-encoded qubits integrated with the DLCZ protocol. (a) Schematic diagram depicting the frequency down-conversion of a path-encoded qubit. The conversion scheme comprises two spatially separated atomic ensembles. (b) Schematic diagram demonstrating the integration of the telecom-band QFC with the DLCZ protocol. The left and right rubidium atomic ensembles are illuminated by the writing beams (green arrows). The generated Stokes fields (blue wavy lines) are down-converted into the telecom band through the diamond-type QFC scheme after the writing beams are filtered. The converted fields (red wavy lines) are coupled to the telecom fibers for long-distance transmission. The transmitted fields interfere at a 50/50 beam splitter (BS) and are detected by two single-photon detectors, D1 and D2, respectively. The left and right ensembles are entangled if only one of the detectors is clicked.

Figure 6

QFC scheme for a polarization-encoded qubit. Here, ${\rho }_{\text{in}}$ and ${\rho }_{\text{out}}$ denote the input and converted polarization-encoded photons, respectively. The input photon initially passes through a PBS, separating the $|H\rangle$ and $|V\rangle$ components into distinct paths. Two QWPs in separate paths convert both fields to circular polarizations, aligning with the selected QFC schemes. Following the QFCs, another two QWPs, one in each path, revert the fields to horizontal (down) and vertical (up) polarization. Two phase shifters (PSs) are employed to eliminate the phases of $C_U\left(0\right)$ and $C_D\left(0\right)$, as well as the phase changes induced by the two PBSs. In the final step, the PBS recombines the distinct polarization components back into a single-polarization qubit.

Figure 7

(a) QFC scheme for a pair of polarization-entangled qubits $Q_1$ and $Q_2$. Following the similar setups as in Fig. 6 for both qubits, the qubits are converted into another wavelength with the fidelity determined by the four separate QFC setups. In the Bell test, the converted qubits $Q_1^{\prime }$ and $Q_2^{\prime }$ are sent to Alice and Bob, respectively. The selected local observables ${\widehat{A}}_0, {\widehat{A}}_1, {\widehat{B}}_0$, and ${\widehat{B}}_1$ are depicted in Eqs. (92, 93, 94, 95). (b) The postselected fidelity between the input $|{\mathrm{\Phi }}^{+}\rangle$ state and the converted state as a function of ${\overline{\eta }}_A$ and ${\overline{\eta }}_B$. The black plane represents the criteria of fidelity ($F=2^{-1/4}\approx 84.1\%$) for the CHSH inequality violation; nonlocality exists for the region with fidelity higher than the criteria. (c) The second converted density operator in Eq. (97) [the right-hand side intersecting line in panel (b)] with $F=2^{-1/4}$. The nonzero matrix elements are $-0.455$, 0.707, 0.293, and $-0.455$ using the Bell basis representation.