Nonclassical Photon-Bundle Correlations in Quantum Rabi Models

Abstract

We investigate nonclassical photon-bundle correlations in the quantum Rabi model and its extended cases, using the quantum dressed master equation. By tuning the light--matter coupling strength at finite temperature, the quantum Rabi model exhibits controllable nonclassical transitions between two-photon bundle bunching and antibunching, allowing for the two-photon bundle emission and statistics. We further introduce anisotropic coupling and nonlinear Stark interactions, which enrich the photon statistical behaviors and provide additional tunability of photon-bundle correlations. Extreme correlation behaviors are found to be closely linked to excited-state quantum phase transitions, suggesting a potential pathway for predicting and exploiting excited-state phenomena. These effects can be controlled solely by tuning intrinsic system parameters, without the need for an external modulating field. The quantum Rabi model family thus provides a flexible and experimentally feasible platform for high-purity photon bundle generation and controllable multi-photon sources.

Figures (6)

• Figure 1: Photon correlation properties in the QRM. (a) Logarithm of the zero-delay two-photon bundles correlation $G_2^{(2)}(0)$ versus temperature $T$ and coupling strength $g$. (b) Logarithm of the zero-delay $m$-photon bundles correlation $G_m^{(2)}(0)$ at $T=0.07$ as a function of $g$. Parameters: $\Delta=1$, $\omega_0=1$, $r=1$, $U=0$, $\alpha_{\mathrm{c}}=\alpha_{\mathrm{q}}=10^{-3}$, $\omega_{\mathrm{c}}=10\omega_0$.
• Figure 2: The time-delayed $m$-photon bundles correlation $G_m^{(2)}(\tau)$ versus renormalized time $\alpha\tau$ with $\alpha=\alpha_c$ for the QRM. (a) $g=0.1$; (b) $g=0.25$; (c) $g=0.5$; (d) $g=0.7$. Other parameters are set as Fig. \ref{['Fig1']}(b).
• Figure 3: Photon correlation properties in the AQRM. (a) Logarithm of the zero-delay two-photon bundles correlation $G_2^{(2)}(0)$ versus anisotropic parameter $r$ and coupling strength $g$. (b) Logarithm of the zero-delay $m$-photon bundles correlation $G_m^{(2)}(0)$ at $r=0.7$ as a function of $g$. Other parameters are set as Fig. \ref{['Fig1']}(b).
• Figure 4: Photon correlation properties in the QRSM. (a) Logarithm of the zero-delay two-photon bundles correlation $G_2^{(2)}(0)$ versus Stark parameter $U$ and coupling strength $g$. Logarithm of the zero-delay $m$-photon bundles correlation $G_m^{(2)}(0)$ as a function of $g$ at (b) $U=0.3$ and (c) $U=-0.4$. Other parameters are set as Fig. \ref{['Fig1']}(b).
• Figure 5: Logarithm of the zero-delay $m$-photon bundle correlation function $G_m^{(2)}$ as a function of the coupling strength $g$ for the AQRSM. (a) $U=0$ and $r=0.9$; (b) $U=-0.4$ and $r=0.9$. Other parameters are set as in Fig. \ref{['Fig1']}(b).