Nonclassical microwave radiation from the parametric dynamical Casimir effect in the reversed-dissipation regime of circuit optomechanics

TL;DR

This work addresses generating nonclassical microwave photons via the parametric dynamical Casimir effect in a circuit optomechanical system operated in the reversed-dissipation regime. By adiabatically eliminating the mechanically damped mode, the authors derive an effective Kerr-nonlinear cavity Hamiltonian and show that time-modulating the driving laser frequency induces a parametric DCE, with the Kerr term saturating photon growth and producing oscillatory dynamics. They obtain both numerical results (master-equation simulations) and analytical insights (Wei-Norman solution in the weak-coupling, dissipationless limit), demonstrating simultaneous sub-Poissonian statistics and Wigner-function negativity, as well as controllable quadrature squeezing. The proposal leverages experimentally accessible circuit-QED–OMS parameters and outlines practical routes to reach the strong-coupling regime, positioning the scheme as a versatile source for quantum information processing and microwave sensing. The work highlights a unique regime where optomechanical Kerr nonlinearity enables nonclassical DCE features not present in standard DCE implementations, with tunable dynamics via modulation depth and temperature.

Abstract

We propose an experimentally feasible optomechanical system (OMS) that is dispersively driven and operates in the reversed dissipation regime (RDR), where the mechanical damping rate far exceeds the cavity decay rate. We demonstrate that coherent, fast-time modulation of the driving laser frequency on time scales longer than the mechanical decoherence time allows for adiabatic elimination of the mechanical mode, resulting in strong parametric amplification of quantum vacuum fluctuations of the intracavity field. This mechanism, known as the parametric dynamical Casimir effect (parametric-DCE), leads to the generation of Casimir photons. In the dispersive RDR, we find that the total system Hamiltonian-including the DCE term-is intrinsically modified by a generalized optomechanical Kerr-type nonlinearity. This nonlinearity not only saturates the mean number of radiated Casimir photons on short time scales, even without dissipation, but also induces oscillatory behavior in their dynamics and quantum characteristics. Remarkably, the presence of the Kerr nonlinearity causes the generated DCE photons to exhibit nonclassical features, including simultaneous sub-Poissonian statistics and negative Wigner function, as well as quadrature squeezing, which can be controlled by adjusting the system parameters. Surprisingly, the controllable simultaneous nonclassical dynamics in the same physical parameter regime, which is induced by the optomechanical Kerr nonlinearity to the parametric DCE cannot occur in the standard DCE or Kerr-type systems. The proposed nonclassical microwave radiation source possesses the potential to be applied in quantum information processing, quantum computing as well as microwave quantum sensing.

Figures (9)

• Figure 1: (Color online) (a) Schematic diagram of the considered microwave optomechanical circuit Toth2017 composed of two inductively coupled microwave LC resonators which are inductively coupled to a microwave feedline as a common bath. The two hybridized dark and bright modes of the circuit that are, respectively, used as the primary $\hat{a}$ and auxiliary $\hat{a}_{\rm aux}$ interact with the vibration of the suspended top electrode of a shared capacitor, acting as a MO with resonance frequency $\omega_m$. The auxiliary (primary) mode is driven by a classical laser field of frequency $\omega_L^{\rm aux}(\omega_L)$ and amplitude $E_L^{\rm aux}(E_L)$. (b) To prepare a cold, dissipative mechanical reservoir for microwave photons the dissipation rate $\gamma_m$ of the MO should be increased to match the much larger dissipation rate $\kappa$ of the primary mode having resonance frequency $\omega_c$. For this purpose, the auxiliary mode with resonance frequency $\omega_{\rm aux}$ and dissipation rate $\kappa_{\rm aux}$ is used to damp out the MO via optomechanical sideband cooling and, hence, prepare it as a strongly dissipative, cold reservoir for the primary mode. (c) A schematic overview of the process to derive Hamiltonian \ref{['H_DCE2']}.
• Figure 2: Time evolution of the mean number of generated Casimir photons $n_{\rm Casimir} =\bra{0}\hat{n}(t)\ket{0}$ based on the exact numerical solution of the master equation \ref{['master-equation']} with Hamiltonian $\hat{H}_{\rm DCE}$ in Eq. \ref{['H_DCE2']} for different values of the scaled Kerr nonlinearity parameter $C_K$. The other system parameters are set as $\omega_m/2\pi=5.33 \text{MHz}$, $\bar{\Delta}_c=\omega_m$, $\widetilde{C}_\epsilon=10^{-1}$, $C_E=10^{-2}$, $\kappa/2\pi=118 \text{kHz}$.
• Figure 3: Time evolution of the mean number of generated Casimir photons $n_{\rm Casimir}(t) = \langle 0 | \hat{n}(t) | 0 \rangle$ in the WCR, obtained from both the analytical expression in Eq. \ref{['n_Casimir']} and numerical simulations based on Hamiltonian \ref{['H_WR']}. The orange dashed line shows the evolution in the absence of dissipation. The system parameters are set as $\omega_m/2\pi = 5.33~\text{MHz}$, $\bar{\Delta}_c = \omega_m$, $C_E = 10^{-2}$, and $\kappa/2\pi = 118~\text{kHz}$. Here, the Kerr nonlinearity strength is fixed to $C_K=10^{-3}$ while $\widetilde{C}_\epsilon$ is varied to explore its influence on photon generation.
• Figure 4: Time evolution of the Mandel parameter obtain by the exact numerical solution of master equation \ref{['master-equation']} with the Hamiltonian $\hat{H}_{\rm DCE}$ in Eq. \ref{['H_DCE2']} for different values of the scaled Kerr nonlinearity parameter. The other system parameters are the same as in Fig. \ref{['fig2']}.
• Figure 5: Time evolution of the Mandel parameter in the WCR, obtained from both the analytical expression in Eq. \ref{['Mandel-analytical']} and numerical simulations based on Hamiltonian \ref{['H_WR']}. The orange dashed line shows the evolution in the absence of dissipation. The system parameters are set as $\omega_m/2\pi = 5.33~\text{MHz}$, $\bar{\Delta}_c = \omega_m$, $C_E = 10^{-2}$, and $\kappa/2\pi = 118~\text{kHz}$, while $\widetilde{C}_\epsilon$ is varied to explore its influence on photon counting statistics.