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arXiv:2603.09114 · New Journal of Physics

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

Yan-Song Hu, Yuan Qiu, Ye-Hong Chen, XinYu Zhao, Yan Xia

quant-phSubmitted Mar 10, 2026• Announced Mar 11, 2026• 0 citations
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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.

Comments
10 pages, 8 figures

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•Oct 28, 2019•3 citations
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.
The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.An analog quantum simulation scheme has been explored with a quantum hardware based on a superconducting circuit. Here the authors investigate the time evolution of the quantum Rabi model at ultra-strong coupling conditions, which is synthesized by slowing down the system dynamics in an effective frame.
The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.
The interaction of a two-level system (TLS) with a single bosonic mode (BM) is one of the most fundamental processes in quantum optics. Microscopically, it is described by the quantum Rabi model (QRM). Here we propose a versatile implementation of this model based on single trapped cold atoms. Assuming realistic experimental conditions, we show that our approach is not restricted to the Jaynes-Cummings regime but also allows exploring the regimes of ultrastrong coupling, deep strong coupling, and dispersive deep strong coupling. In contrast to most other QRM platforms, all important system parameters, i.e., the emitter-field detuning and the coupling strength of the emitter to the mode, can be dynamically tuned over a wide range. The quantum state of the BM and the TLS can be prepared and read-out using standard cold-atom techniques, enabling the study of the QRM and its dynamics with unprecedented control. Our scheme implements the TLS using atomic Zeeman states, while the atom's vibrational states in the trap represent the BM. The coupling is mediated by a suitable fictitious magnetic field pattern. Finally, we show that our scheme also enables the implementation of important generalizations, namely, the driven QRM, the QRM with quadratic coupling, or the Dicke model.
We present a non-perturbative Hamiltonian mapping method for quantum systems strongly coupled to a quantized field mode (cavity), yielding compact closed-form representations of hybrid light-matter systems. The mapping method builds on an entangling transformation of photonic and atomic degrees of freedom. By truncating the resulting cavity-dressed Hamiltonian (CDH) to successively larger excitation sectors, we construct a series of compact models that converge to the exact limit, outpacing conventional approaches even in the challenging resonant and ultrastrong light-matter regime. The mapping principle also applies to multimode cavities coupled to matter through noncommuting operators and to leaky cavities. We benchmark the CDH framework on the quantum Rabi model, demonstrating accurate spectral predictions in both weak and strong coupling regimes, together with converging ground-state and thermal observables. We study the Dicke-Heisenberg lattice model and determine its phase diagram under resonant and strong light-matter coupling, achieving significant computational savings over brute-force simulations and identifying cavity-mediated spin correlations both analytically and numerically. The closed-form and compactness of the CDH provide both physical insight and enhanced computational efficiency, facilitating studies of strongly coupled hybrid light-matter systems.
The quantum Rabi model describing the fundamental interaction between light and matter is a cornerstone of quantum physics. It predicts exotic phenomena like quantum phase transitions and ground-state entanglement in ultrastrong and deep-strong coupling regimes, where coupling strengths are comparable to or larger than subsystem energies. Demonstrating dynamics remains an outstanding challenge, the few experiments reaching these regimes being limited to spectroscopy. Here, we employ a circuit quantum electrodynamics chip with moderate coupling between a resonator and transmon qubit to realise accurate digital quantum simulation of deep-strong coupling dynamics. We advance the state of the art in solid-state digital quantum simulation by using up to 90 second-order Trotter steps and probing both subsystems in a combined Hilbert space dimension of ∼80, demonstrating characteristic Schrödinger-cat-like entanglement and large photon build-up. Our approach will enable exploration of extreme coupling regimes and quantum phase transitions, and demonstrates a clear first step towards larger complexities such as in the Dicke model.
We propose the effective simulation of light-matter ultrastrong-coupling phenomena with strong-coupling systems. Recent theory and experiments have shown that the single-atom quantum Rabi model can be simulated by the Jaynes-Cummings model with two additional classical drives. Here, we show that quantum nonlinear optical phenomena, relying on the counter-rotating terms of the Rabi model, can be implemented by the Jaynes-Cummings and Tavis-Cummings models with only a single classical drive. We analyze three examples: a single atom exciting two photons, frequency conversion, and a single photon exciting two atoms.