Enhancing light-matter coupling for exploring chaos in the quantum Rabi model

Abstract

Accessing chaos in the quantum Rabi model (QRM) usually requires operating far from resonance, combined with ultra- or deep-strong light-matter coupling. This makes direct experiments challenging. In this manuscript, we propose a solution to this challenge by employing an anti-squeezing transformation to the bosonic field. Specifically, we demonstrate that this transformation maps a weakly coupled, two-photon driven Jaynes-Cummings model (JCM) to an effective deep-strong-coupling QRM in the squeezed-light frame. Using out-of-time-order correlator, Husimi distribution, and linear entanglement entropy, we numerically probe chaos in this coupling-enhanced platform and observe the similar chaotic phenomena as in the ideal QRM. We also find the coupling-enhanced model can drive the system deeper into the chaotic regime. This establishes coupling-enhanced method as a practical approach to study QRM chaos without requiring intrinsic ultra-strong coupling.

Figures (8)

• Figure 1: Poincaré section $(q_{2}=0, p_{2}>0)$ of semiclassical effective Hamiltonian. (a) System parameters are set to $\delta_{a}=0.02\delta_{c}$, $g=2\times10^{-4}\delta_{c}$, $r=4$, with energy $E=0.018\delta_{c}$. Points $C_{1}(\tau=0.825,\beta=5.4461i)$ and $R_{1}(\tau=7,\beta=3.5384i)$ represent the chaotic and regular trajectories, respectively. (b) System parameters are $\delta_{a}=0.75\delta_{c}$, $g=0.0375\delta_{c}$, $r=2$, and energy $E=0.75\delta_{c}$. Points $C_{2}(\tau=0.0999+0.4081i,\beta=5.3065i)$ and $R_{1}(\tau=-0.9419+1.4653i,\beta=3.9644i)$ represent the chaotic and regular trajectories, respectively.
• Figure 2: Time evolution of the Loschmidt echo and fidelity versus $r$. (a), (c) Time evolution of the Loschmidt echo for two different parameter sets. The system parameters and initial states are the same as in Figs. \ref{['fig1']}(a) and Figs. \ref{['fig1']}(b), respectively. (b), (d) Fidelity as a function of the squeezing parameter $r$ at a fixed time, with all other parameters and the initial states identical to those in (a) and (c), respectively.
• Figure 3: Time evolution of the fidelity for several representative squeezing parameters $r$. The system parameters and initial state are the same as in Fig. \ref{['fig2']}(b).
• Figure 4: Time evolution of $\text{var}[\hat{G}(t)]$ under different system parameters, with the initial state prepared as $\ket{\phi}=\ket{+}\otimes\ket{0}$. (a) Dependence on the squeezing parameter $r$, while all other parameters are identical to those in Fig. \ref{['fig1']}(a). (b) System parameters are the same as in Fig. \ref{['fig1']}(b).
• Figure 5: Time evolution of the linear entanglement entropy. (a), (b) System parameters and initial states are identical to those in Fig. \ref{['fig1']}(b), with evolution driven by the effective Hamiltonian $\hat{H}_{\text{eff}}$ and the ideal Rabi Hamiltonian $\hat{H}_{\text{Rabi}}$, respectively. (c) System parameters and initial states are the same as in Fig. \ref{['fig1']}(a), under evolution driven by the effective Hamiltonian $\hat{H}_{\text{eff}}$. (d) Squeezing parameter $r=1.2$; all other parameters match those in panel (c). Evolutions for points $C_{1}^{'}$ and $R_{1}^{'}$ are driven by the ideal Rabi Hamiltonian $\hat{H}_{\text{Rabi}}$. The inset shows an enlarged view of the entropy oscillations over a selected time interval.