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Programmable spectral symmetries in an anisotropic quantum Rabi simulator

Yu Liu, Jia-Cheng Song, M Wang, Ke-Xiong Yan, H N Yang, Yun‐Hao Shi, Wei-Ping Yuan, Cheng-Lin Deng, Li Li, Zhen-Ting Bao, Yuehua Chen, Xu-Yang Gu, Tian-Ming Li, Gui-Han Liang, Zheng-He Liu, Wei-Guo Ma, Zhenyu Peng, Shuai-Li 帅立 Wang 王, Yong-Xi Xiao, Yi-Han Yu, Jia-Chi Zhang, Kui Zhao, Zhou Min-xuan, Kaixuan Huang, Yu-Ran Zhang, Yu-Xiang Zhang, Zhongcheng Xiang, Dongning Zheng, Ye‐Hong Chen, Kai Xu, Heng Fan

Published Jun 30, 2026• 0 citations
Publisher

Abstract

Abstract The quantum Rabi model captures fundamental aspects of light--matter interaction, where symmetry dictates both spectra and dynamics. Over the past years, experiments have explored many of its nonperturbative properties, but have mostly focused on the isotropic limit, where rotating and counterrotating processes are locked together, leaving the broader symmetry landscape largely unexplored. Here we realize a programmable anisotropic quantum Rabi model in a superconducting processor, with independent control of the rotating and counterrotating couplings $(g_1,g_2)$ and of a transverse bias $\varepsilon$. Continuous anisotropy tuning, combined with a duality mapping, gives access to the full parameter space from the Jaynes-Cummings to the anti-Jaynes-Cummings limits. In the deep-strong-coupling regime, we show that anisotropy reconstructs the spectrum and turns complete collapse-revival dynamics into incomplete revivals even near degeneracy. With adiabatic state preparation and joint tomography, we resolve an anisotropy-induced ground-state parity switch, a crossing that has no analogue in the isotropic model. We further observe selective tunnelling associated with hidden symmetry in biased Rabi models and track its anisotropic displacement within the same device. These results establish a controllable route to engineering nonperturbative light--matter Hamiltonians, where symmetry, spectrum, and dynamics can be programmed independently.

DOI
10.21203/rs.3.rs-9871970/v1

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Abstract The quantum Rabi model captures fundamental aspects of light--matter interaction, where symmetry dictates both spectra and dynamics. Over the past years, experiments have explored many of its nonperturbative properties, but have mostly focused on the isotropic limit, where rotating and counterrotating processes are locked together, leaving the broader symmetry landscape largely unexplored. Here we realize a programmable anisotropic quantum Rabi model in a superconducting processor, with independent control of the rotating and counterrotating couplings (g1,g2)(g_1,g_2)(g1​,g2​) and of a transverse bias ε\varepsilonε. Continuous anisotropy tuning, combined with a duality mapping, gives access to the full parameter space from the Jaynes-Cummings to the anti-Jaynes-Cummings limits. In the deep-strong-coupling regime, we show that anisotropy reconstructs the spectrum and turns complete collapse-revival dynamics into incomplete revivals even near degeneracy. With adiabatic state preparation and joint tomography, we resolve an anisotropy-induced ground-state parity switch, a crossing that has no analogue in the isotropic model. We further observe selective tunnelling associated with hidden symmetry in biased Rabi models and track its anisotropic displacement within the same device. These results establish a controllable route to engineering nonperturbative light--matter Hamiltonians, where symmetry, spectrum, and dynamics can be programmed independently.
The quantum Rabi model captures fundamental aspects of light--matter interaction, where symmetry dictates both spectra and dynamics. Over the past years, experiments have explored many of its nonperturbative properties, but have mostly focused on the isotropic limit, where rotating and counterrotating processes are locked together, leaving the broader symmetry landscape largely unexplored. Here we realize a programmable anisotropic quantum Rabi model in a superconducting processor, with independent control of the rotating and counterrotating couplings (g1,g2)(g_1,g_2)(g1​,g2​) and of a transverse bias ε\varepsilonε. Continuous anisotropy tuning, combined with a duality mapping, gives access to the full parameter space from the Jaynes-Cummings to the anti-Jaynes-Cummings limits. In the deep-strong-coupling regime, we show that anisotropy reconstructs the spectrum and turns complete collapse-revival dynamics into incomplete revivals even near degeneracy. With adiabatic state preparation and joint tomography, we resolve an anisotropy-induced ground-state parity switch, a crossing that has no analogue in the isotropic model. We further observe selective tunnelling associated with hidden symmetry in biased Rabi models and track its anisotropic displacement within the same device. These results establish a controllable route to engineering nonperturbative light--matter Hamiltonians, where symmetry, spectrum, and dynamics can be programmed independently.
We propose a circuit QED architecture that realizes the full anisotropic Rabi model (ARM) with in-situ tunability of its interaction symmetry. The circuit comprises a superconducting qubit coupled to a resonator through two simultaneous channels: a direct inductive path and a flux-tunable capacitive path mediated by a transmon coupler. By controlling the external magnetic flux, the destructive and constructive interferences between these paths continuously tune the ratio of the Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) couplings, sweeping the system across the entire ARM parameter space---from pure JC, through the standard Rabi regime, to pure AJC---without requiring rotating-wave approximations or external parametric drives. Furthermore, we identify a coherence sweet spot where the dispersive shift and photon shot-noise dephasing are suppressed. In the pure AJC regime, we demonstrate that the vacuum Rabi splitting vanishes and the Purcell decay rate is strongly mitigated while preserving high qubit readout contrast.
We present the quantum anisotropic Rabi model as a potential resource for a noise biased qubit. The system-environment coupling can be biased by tuning the relative strengths of the rotating-wave and counter-rotating-wave interactions, characterized by the anisotropy parameter ηηη. This anisotropy selectively suppresses dominant decoherence pathways, thereby enabling the construction of a protected logical qubit in the ultrastrong and deep-strong coupling regimes. The logical states (formed by the ground and first excited states of the anisotropic Rabi model) possess coherence times that are enhanced compared to the isotropic case. Moreover, we construct a set of universal gate operations within the logical-state subspace and demonstrate that the gate operations associated with different values of ηηη exhibit robustness against external noise. These findings are expected to inspire applications and research directions for the anisotropic Rabi model with promising potential impacts.
The quantum Rabi model is a standard effective Hamiltonian in studies of light-matter interaction, capturing the simplest nontrivial setting in which a qubit couples to a single harmonic oscillator. Within the broader Rabi family, we focus on two special cases: the Jaynes-Cummings (JC) model, which carries an explicit U(1)U(1)U(1) symmetry, and the asymmetric quantum Rabi model (AQRM), which possesses a parameter-dependent "hidden'' symmetry that appears only at integer bias, ε/ω∈Z\varepsilon/ω\in\mathbb{Z}ε/ω∈Z, and is not manifest in the Hamiltonian. We use the time-averaged entangling power as an operator-level diagnostic of these symmetry structures. Since the oscillator Hilbert space is infinite-dimensional, we compare two finite input ensembles: a Haar average after Fock-space truncation and a coherent-state average at fixed mean occupation nˉ\bar{n}nˉ. Both diagnostics show peaks at the integer-bias points of the AQRM, where the hidden symmetry resides. In contrast, the manifest U(1)U(1)U(1) symmetry at the JC point instead gives a weak dip. Thus, the time-averaged entangling power responds to both the hidden symmetry and the U(1)U(1)U(1) symmetry in the Rabi family, with the sign of the response indicating how the symmetry reorganizes the spectral expansion. These results demonstrate that the entangling power can serve as an operator diagnostic to reveal the presence and properties of hidden and manifest symmetries in light-matter systems.
The anisotropic quantum Rabi model provides a continuous interpolation between the quantum Rabi model and the Jaynes-Cummings model. In this paper, we study the norm-resolvent limit of the anisotropic quantum Rabi model as the coupling strength tends to infinity. After subtracting an explicit quadratic renormalization term, we identify the limiting Hamiltonian, which determines the asymptotic spectral structure of the model. Our result provides a unified description connecting the Jaynes-Cummings model and the full quantum Rabi model in the strong-coupling limit, thereby revealing the dominant role of the counter-rotating interaction.
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.