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arXiv:2603.27160 · Optics Express

Nonclassical Photon-Bundle Correlations in Quantum Rabi Models

Yong-Xin Zhang, Chen Wang, Qing-Hu Chen

quant-phSubmitted Mar 28, 2026• Announced Mar 31, 2026• 0 citations
arXivHTMLPDF

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.

Journal reference
Opt. Express 34, 21141-21160 (2026)
DOI
10.1364/OE.596808

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We investigate photon correlations in the open anisotropic quantum Rabi model via quantum dressed master equation. Multiple antibunching-to-bunching transitions are generally exhibited at deep-strong qubit-photon coupling, which becomes vanishing in the standard open quantum Rabi model. The observed two-photon statistics can be well described analytically within a few lowest eigenstates at low temperatures. It is revealed that the additional photon antibunching effect mainly originates from the selection rule of the correlation-measurement-induced eigenstate transitions. Furthermore, we also unravel the phenomena that higher-order correlation function lifts up dramatically once passing the crossing point of excited states, which is attributed to the on-off switch of dominant cooperative transition with level crossing. We hope these results may fertilize the analysis of the nonclassical photon statistics in anisotropic coupled qubit-photon systems.
ABSTRACT This study investigates nonclassical effects of photons in the anisotropic quantum Rabi‐Stark model by using a quantum dressed master equation. We analyze second‐ and higher‐order correlation functions, and demonstrate that the nonlinear Stark coupling significantly modulates photon statistics, inducing distinct and tunable photon antibunching and bunching effects. Successive transition signatures of correlation functions provide a potential experimental probe for predicting quantum phase transitions. We further reveal that Stark coupling provides direct control over photon squeezing, achieving significant enhancement and suppression. These findings not only uncover rich nonclassical phenomena in the anisotropic quantum Rabi‐Stark model, but also establish the nonlinear Stark coupling as a crucial new dimension for quantum detection. It may open a new avenue for precise manipulation of strongly coupled light‐matter systems, with potential applications in quantum information processing and quantum‐enhanced technologies.
Quantum correlations and nonclassical states are at the heart of emerging quantum technologies. Efforts to produce long-lived states of such quantum resources are a subject of tireless pursuit. Among several platforms useful for quantum technology, the mature quantum system of light-matter interactions offers unprecedented advantages due to current on-chip nanofabrication, efficient quantum control of its constituents, and its wide range of operational regimes. Recently, a continuous transition between the Jaynes-Cummings model and the Rabi model has been proposed by exploiting anisotropies in their light-matter interactions, known as the anisotropic quantum Rabi model. In this work, we study the long-lived quantum correlations and nonclassical states generated in the anisotropic Rabi model and how these indeed persist even at thermal equilibrium. To achieve this, we thoroughly analyze several quantumness quantifiers, where the long-lived quantum state is obtained from a dressed master equation that is valid for all coupling regimes and with the steady state ensured to be the canonical Gibbs state. Furthermore, we demonstrate a stark distinction between virtual excitations produced beyond the strong coupling regime and the quantumness quantifiers once the light-matter interaction has been switched off. This raises the key question about the nature of the equilibrium quantum features generated in the anisotropic quantum Rabi model and paves the way for future experimental investigations, without the need for challenging ground-state cooling.
Abstract Nonclassical two-photon statistics and photon squeezing are considered as representative features of the nonclassicality of light. In this work we investigate two-photon correlation function and quadrature photon squeezing in the dissipative mixed quantum Rabi model (QRM), which includes both the one-photon and two-photon qubit–resonator interactions. The quantum dressed master equation combined with squeezed-coherent states is applied to obtain the steady state. Based on the zero-time delay two-photon correlation function, it is found that with the increase of the two-photon qubit–resonator interaction strength the photon antibunching behavior is monotonically suppressed, whereas the photon bunching signature persists. One additional giant photon bunching feature is unraveled at deep-strong two-photon coupling, which mainly stems from efficient successive transition trajectories. The finite-time delay two-photon correlation function asymptotically approaches the unit by raising the delayed time. Moreover, the steady-state quadrature photon squeezing becomes significant at strong two-photon coupling, which may become perfect in the zero temperature limit.
Abstract The generation of nonclassical photons via quantum light–matter interactions is of fundamental importance in quantum optics. Here we investigate steady-state two-photon correlation function and photon squeezing in an open anisotropic Rabi lattice by applying quantum dressed master equation embedded with the mean-field approximation. The expanded antibunching effect of photons due to anisotropic qubit–photon interaction, is strongly suppressed by including inter-site photon tunneling, whereas the giant photon bunching keeps robust with weak inter-site photon tunneling strength. The microscopic processes for photon antibunching and bunching effects are presented based on incoherent transitions between eigenstates. The photon squeezing is also analyzed under the influences of qubit–photon coupling and anisotropic factor. The quadrature squeezing shows persistency by tuning on the inter-site photon tunneling, and becomes dramatically pronounced at the small anisotropic factor. Moreover, the increasing number of qubits significantly enhances quadrature squeezing with strong qubit–photon interaction. We hope such results may provide physical insights into efficient generation and manipulation of nonclassical features of photons in quantum light–matter interacting lattice systems.
Quantum correlations and nonclassical states are at the heart of emerging quantum technologies. Efforts to produce long-lived states of such quantum resources are a subject of tireless pursuit. Among several platforms useful for quantum technology, the mature quantum system of light-matter interactions offers unprecedented advantages due to current on-chip nanofabrication, efficient quantum control of its constituents, and its wide range of operational regimes. Recently, a continuous transition between the Jaynes-Cummings model and the Rabi model has been proposed by exploiting anisotropies in their light-matter interactions, known as the anisotropic quantum Rabi model. In this paper, we study the long-lived quantum correlations and nonclassical states generated in the anisotropic Rabi model and how these indeed persist even at thermal equilibrium. To achieve this, we thoroughly analyze several quantumness quantifiers, where the long-lived quantum state is obtained from a dressed master equation that is valid for all coupling regimes and with the steady state ensured to be the canonical Gibbs state. Furthermore, we demonstrate a stark distinction between virtual excitations produced beyond the strong coupling regime and the quantumness quantifiers once the light-matter interaction has been switched off. This raises the key question about the nature of the equilibrium quantum features generated in the anisotropic quantum Rabi model and paves the way for future experimental investigations, without the need for challenging ground-state cooling. Published by the American Physical Society 2024