Strongly driven cavity quantum electrodynamical-optomechanical hybrid system

TL;DR

This work tackles the challenge of generating and transferring non-Gaussian states from a cavity QED system to a mechanical oscillator by exploiting a strongly driven hybrid cavity QED-optomechanical setup. The authors propose a two-stage protocol: first synthesize a non-Gaussian cavity state in the dispersive regime, then coherently drive the cavity to the bare regime to enhance optomechanical coupling and transfer the state to the mechanical mode, supported by an efficient adaptive displaced-frame simulation framework. They identify and quantify the dominant cavity-state deformations (phase shifts and squeezing) and show these can be suppressed by strong driving, enabling high-fidelity transfer (F_m > 0.9) to the mechanical oscillator, with potential applications in non-Gaussian quantum memories and sensors. The approach is argued to be feasible with current circuit-QED technologies and robust to counter-rotating terms and multi-level qubits, offering a practical pathway toward hybrid quantum devices that exploit non-Gaussian resources.

Abstract

Hybrid quantum systems harness the distinct advantages of different physical platforms, yet their integration is not always trivial due to potential incompatibilities in operational principles. Here, we theoretically propose and demonstrate a scheme for generating non-Gaussian mechanical states using a strongly driven hybrid system that combines cavity quantum electrodynamics (QED) and cavity optomechanics. Our protocol prepares a non-Gaussian cavity state in the dispersive regime of cavity QED and subsequently transfers it to a mechanical oscillator using the optomechanical interaction enhanced by a coherent cavity drive. While non-Gaussian cavity state control in cavity QED is well established in the dispersive regime, its behavior under strong cavity drive, essential for cavity optomechanics, remains largely unexplored. To bridge this gap, we develop an efficient simulation framework to model cavity QED dynamics in the high-photon-number regime. We show that a strong cavity drive can coherently displace the cavity state with minimal perturbations, effectively decoupling it from the qubit. The resulting large coherent cavity field enhances the optomechanical coupling strength, enabling high-fidelity transfer of non-Gaussian cavity states to the mechanical mode. These results reveal new dynamical features of driven cavity QED and open a pathway toward realizing non-Gaussian mechanical quantum memories and sensors.

Figures (12)

• Figure 1: (a) Schematic of the cavity QED-optomechanical hybrid system. The qubit (green) is coupled to a cavity field (blue) to construct a cavity QED system. One mirror of the cavity is vibrating, acting as a mechanical oscillator (red) that is coupled to the cavity field to construct a cavity optomechanical system. The cavity and the qubit can be individually controlled through the cavity drive and the qubit drive, respectively. (b) Frequency landscape of the cavity QED-optomechanical hybrid system. The non-Gaussian cavity state is generated in the dressed regime and successively transferred to the bare cavity regime by a strong cavity drive. (c) Drive scheme of our protocol. During the preparation step, a sequence of pulses are applied to both the qubit and the cavity to generate an arbitrary non-Gaussian cavity state. To transfer the state to the mechanical oscillator, the cavity is first driven to a sufficiently high photon number, thereby enhancing the optomechanical coupling rate. In the transfer step, the cavity coherent field is in a forced oscillation at the red-detuned cavity frequency, which triggers the stationary optomechanical interaction and transfers the cavity state to the mechanical oscillator. (d) Simulation method. The system is simulated in the time-dependent displaced frame for each bosonic mode, which are adaptively updated to minimize the required Hilbert space, as indicated by the blue circles with dashed outline.
• Figure 2: (a) Cavity-state dynamics under a displaced JC Hamiltonian and illustration of the leading effects of cavity-state deformations: phase shift and squeezing. (b) Wigner distribution of the displaced cavity states after $t = 3~\mu\text{s}$ of evolution, shown for different initial coherent cavity photon numbers. (c,d) Photon number change $\Delta n$ for $\ket{P} = \ket{0}$ and $\ket{P} = \ket{1}$ as functions of time and the initial coherent photon number, respectively. (e) Squeezing ratio $\Delta \hat{x}^2_{\text{a.sq}} / \Delta \hat{x}^2_{\text{sq}}$, averaged for $\ket{P} \in \{\ket{0}, \ket{1}\}$. (f) Phase shift $\Delta\varphi$, averaged over $\ket{P} \in \{\ket{\pm}, \ket{\pm i}\}$. (g) Fidelity of the cavity state to the initial state, averaged over $\ket{P} \in \mathcal{S}_6$. The red dashed line indicates the boundary $n_{\mathrm{cav}} / n_{\text{crit}} = 1$. In the simulations, the cavity and the qubit are considered lossless, i.e., $\kappa/2\pi = \gamma/2\pi = 0$.
• Figure 3: (a, b) Effective frequency shift and squeezing rate as a function of the initial coherent cavity photon number in the displaced JC model. Both quantities are normalized by their analytical maximum values: $\chi_0 = g^2/\Delta$ and $J_0 = \chi_0/6\sqrt{3}$. The blue dots are the numerically simulated results, while the black solid lines correspond to the theoretical predictions. In the simulations, $\kappa/2\pi = \gamma/2\pi = 0$ are used.
• Figure 4: (a) Cavity-state dynamics under the driven JC Hamiltonian and illustration of the leading effects of cavity-state deformations: phase shift and squeezing. (b) Wigner distribution of the cavity states centered around the coherent amplitudes after $t = 3~\mu\text{s}$ of evolution, shown for different cavity drive amplitudes. (c,d) Photon number change $\Delta n$ for $\ket{P} = \ket{0}$ and $\ket{P} = \ket{1}$ as functions of time and cavity drive amplitude, respectively. (e) Squeezing ratio $\Delta \hat{x}^2_{\text{a.sq}} / \Delta \hat{x}^2_{\text{sq}}$, averaged over $\ket{P} \in \{\ket{0}, \ket{1}\}$. (f) Phase shift $\Delta\varphi$, averaged for $\ket{P} \in \{\ket{\pm}, \ket{\pm i}\}$. (g) Fidelity of the cavity state to the initial state, averaged over $\ket{P} \in \mathcal{S}_6$. The contour lines indicate the ratio of the coherent cavity photon number to the critical photon number. In the simulation, the cavity and the qubit are considered lossless, i.e., $\kappa/2\pi = \gamma/2\pi = 0$.
• Figure 5: Cumulative squeezing ratio in resonantly driven JC model. The dots correspond to the numerically simulated results and the solid lines correspond to the analytical predictions, as given by Eq. \ref{['eq:CSA_ana']}.