Topological Quantum Transducers in a Hybrid Rydberg Atom System

Abstract

We propose a topological transport platform for microwave-to-optical conversion at the single-photon level in a Rydberg atom-cavity setting. This setting leverages a hybrid dual-mode Jaynes-Cummings (JC) configuration, where a microwave resonator couples an optical cavity mediated by a Rydberg atom ensemble. Our scheme uniquely enables the formation of Fock-state lattices (FSLs), where photon hopping rates depend on photon numbers in individual sites. We identify an inherent zero-energy mode corresponding to the dark state of the dual-mode JC model. This enables to build a high-efficiency single-photon transducer, which realizes topologically protected photon transport between the microwave and optical modes. Crucially, we show analytically that the FSL features continuous variations of the winding number. Our work establishes a robust mechanism for efficient quantum transduction in synthetic dimensions and opens avenues for exploring topological physics with continuous winding numbers in the atom-cavity system.

Figures (4)

• Figure 1: Topological quantum transducer with continuous winding number. (a) Scheme of Rydberg-superatom quantum transducer based on 4WM, where atoms in the superatom are coupled simultaneously to an optical cavity (${\hat{a}}^\dagger$, ${\hat{a}}$) and a MW resonator (${\hat{b}}^\dagger$, ${\hat{b}}$), assisted by two counterpropagating 297 nm- (Rabi frequency $\Omega_1$) and 481 nm-wavelength (Rabi frequency $\Omega_2$) lasers; $G_m$ ($G_o$) is the coupling strength between the superatom spin and the MW (optical) mode. Topological pumping based on (b) FSL and (c) SSH model. The winding number changes continuously and discretely in (b) and (c), respectively. This is implemented when the ratio $G_m/G_0$ is modulated continuously from 0 to $\infty$. Winding number data with different excitation numbers $N$ are obtained by numerically measuring the time-averaged chiral displacements. See text for details.
• Figure 2: Topological pumping for MTO photon conversion. (a) Energy spectrum versus time and population evolution of eigenstates when considering the initial state $|5_m,G,0_o\rangle$ and $T=8.2~{\rm \mu s}$. (b) Temporary evolution of ${\overline N}_o(t)$ with $T=5.26~{\rm \mu s}$, $8.2~{\rm \mu s}$, and $18.18~{\rm \mu s}$, corresponding to effective pulse area $A=2\pi$, $4\pi$, and $10\pi$, respectively. Photon number $N_{\phi_0}(A)$ and $N_{s}(A)$ are calculated based on the zero-mode state $|\phi_0(t)\rangle$ and density operator of the syste,, respectively. (c) Population distribution on the eleven sites with $T=8.2~{\rm \mu s}$.
• Figure 3: (a) Final average optical photon number ${\overline N}_o(T)$ versus topological pumping duration $T_N$ with different $N_m$. The green arrows indicate the critical transfer time $T_m$ for different initial $N_m$. They take place at the first peak of the transmission fidelity. The number shows the final photon number. For $N_m=5$, we obtain $T_m=8.2 ~\mu s$, which has been used as the example discussed in the main text. (b) Dimensionless time $gT_m$ versus initial $N_m$. Circles (numerical): FSL model. Snowflake (numerical): SSH model at which the fidelity for different initial $N_m$ in the reaches 99%. Solid line (fitting): FSL model with $gT_m=0.29N_m+13.33$. Dashed line (fitting): SSH model with $gT_m=4.87N_m^2+9.25N_m+6.54$.
• Figure 4: Scalability and robustness of the topological quantum transducers. (a) Transducer fidelity evolution when the MW mode is initially in a coherent state (top, with $\alpha=1$) and a squeezed vacuum state (bottom, with $r=0.7$ and $\theta=0$). The Wigner functions of the initial MW photon state and the final optical photon state are shown on the leftmost and rightmost sides, respectively. The fidelity is defined by ${\mathcal{F}}(t)={\rm Tr}[{\hat{\rho}}(t)|\phi_{id}\rangle \langle\phi_{id}|]$, where the ideal state is $|\phi_{id}\rangle=|0_m,G,\alpha_o(\xi_o)\rangle$ with $|\alpha_o\rangle={\rm exp} (-\frac{1}{2}|\alpha|^2)\sum_{n=0}^{\infty}(-1)^n\frac{\alpha^n}{\sqrt{n!}}|n\rangle$ and $|\xi_o\rangle={\rm exp}[\frac{1}{2}(\xi^*{\hat{a}}^2-\xi{{\hat{a}}^{\dagger^2}})]|0_o\rangle$. (b) Evolution of the winding number of the FSL with $\eta_m=\eta_o=0.1$. For different excitation numbers, the winding number changes gradually with time. (c) Robust transducer against the disorder. We show the final ${\overline N}_o$ with initial $N_m=5$ and $T=8.2~{\rm \mu s}$. $\eta_m$ ($\eta_o$) is the disorder magnitude fluctuating coupling strength between the superatom and the MW (optical) mode: $G_{m(o)}\rightarrow G_{m(o)}[1+\epsilon_{m(o)}]$ with random samples $\epsilon_{m(o)}\in[-\eta_{m(o)},\eta_{m(o)}]$. Each data point on the surface plots is obtained through an ensemble average of 1001 sampings. In all panels, experimentally feasible decay rates of the superatom, MW mode, and optical mode are considered as $\Gamma_0/2\pi=3.6$ kHz Meesala2024PRXSahu2023Science, $\kappa_m/2\pi=2$ kHz Pirkkalainen2015NC, and $\kappa_o/2\pi=3.4$ kHz Kongkhambut2022Science, respectively.