Quantum-classical correspondence in resonant and nonresonant Rabi-Stark model

Testing the correspondence principle in nonlinear quantum systems is a fundamental pursuit in quantum physics. In this paper, we employed mean field approximation theory to study the semiclassical dynamics in the Rabi-Stark model (RSM) and showed that the nonlinear Stark coupling significantly modulates the semiclassical phase space structure. By analyzing the linear entanglement entropy of coherent states prepared in the classical chaotic and regular regions of the semiclassical phase space, we demonstrate that quantum-classical correspondence can be achieved in the RSM with large atom-light frequency ratios. While this correspondence fails in the resonant Rabi model because its truncated photon number is insufficient to approach the large quantum number limit, we discovered that in the resonant RSM when the nonlinear Stark coupling $U \to \pm 1$ , the time-averaged linear entanglement entropy correlates strongly with the semiclassical phase space. In particular, when $U \to -1$ , the truncated photon number in the resonant RSM is very close to that in the resonant Rabi model, but the time-averaged linear entanglement entropy still corresponds well with the semiclassical phase space. This result demonstrates that quantum-classical correspondence can be realized in the few-body resonant RSM.Testing the correspondence principle in nonlinear quantum systems is a fundamental pursuit in quantum physics. In this paper, we employed mean field approximation theory to study the semiclassical dynamics in the Rabi-Stark model (RSM) and showed that the nonlinear Stark coupling significantly modulates the semiclassical phase space structure. By analyzing the linear entanglement entropy of coherent states prepared in the classical chaotic and regular regions of the semiclassical phase space, we demonstrate that quantum-classical correspondence can be achieved in the RSM with large atom-light frequency ratios. While this correspondence fails in the resonant Rabi model because its truncated photon number is insufficient to approach the large quantum number limit, we discovered that in the resonant RSM when the nonlinear Stark coupling $U \to \pm 1$, the time-averaged linear entanglement entropy correlates strongly with the semiclassical phase space. In particular, when $U \to -1$, the truncated photon number in the resonant RSM is very close to that in the resonant Rabi model, but the time-averaged linear entanglement entropy still corresponds well with the semiclassical phase space. This result demonstrates that quantum-classical correspondence can be realized in the few-body resonant RSM.

quant-pharXiv:2512.08303Dec 10, 20250 citations

Quantum and Classical Resonances

F. J. Arranz, R. M. Benito, F. Borondo

AIP conference proceedingsJan 1, 20070 citations

Effect of nonresonant states in near-resonant two-photon ionization of hydrogen

Xu Zhang, Yueming Zhou, Yijie Liao +6 more

By numerically solving the three-dimensional time-dependent Schr\"odinger equation, two-photon ionization of hydrogen is investigated at the near-resonant frequencies of the $1s\text{\ensuremath{-}}2p$ transition. Due to the Rabi oscillations between the $1s$ and $2p$ states, the photoelectron energy spectra exhibit the Autler-Townes (AT) doublets and we focus on the energy spacing and the asymmetry of the doublets. Our results show that the laser frequency for the minimum energy spacing of AT doublets locates at the resonant frequency of the ac-stark-shifted states, while the symmetry of the AT doublets is affected both by the ac-stark shift and the nonresonant ionization pathway. Developing the minimal three-state model including all of the nonresonant (nonessential) states, the effects of the ac-stark shift and the nonresonant ionization pathway on the AT doublets due to the nonresonant states are identified. Furthermore, due to the nonresonant ionization pathway, the photoelectron angular distributions are distinctly different for the lower- and higher-energy peaks in the AT doublets and these angular distributions sensitively depend on the laser intensity and pulse duration. These results are well reproduced by our minimal three-state model.By numerically solving the three-dimensional time-dependent Schr\"odinger equation, two-photon ionization of hydrogen is investigated at the near-resonant frequencies of the $1s\text{\ensuremath{-}}2p$ transition. Due to the Rabi oscillations between the $1s$ and $2p$ states, the photoelectron energy spectra exhibit the Autler-Townes (AT) doublets and we focus on the energy spacing and the asymmetry of the doublets. Our results show that the laser frequency for the minimum energy spacing of AT doublets locates at the resonant frequency of the ac-stark-shifted states, while the symmetry of the AT doublets is affected both by the ac-stark shift and the nonresonant ionization pathway. Developing the minimal three-state model including all of the nonresonant (nonessential) states, the effects of the ac-stark shift and the nonresonant ionization pathway on the AT doublets due to the nonresonant states are identified. Furthermore, due to the nonresonant ionization pathway, the photoelectron angular distributions are distinctly different for the lower- and higher-energy peaks in the AT doublets and these angular distributions sensitively depend on the laser intensity and pulse duration. These results are well reproduced by our minimal three-state model.

Physical Review ADec 30, 202232 citations

Quantum criticality of the Rabi-Stark model at finite frequency ratios

Xiang-You Chen, You-Fei Xie, Qing‐Hu Chen

In this paper, we analyze the quantum criticality of the Rabi-Stark model at finite ratios of the qubit and cavity frequencies in terms of the energy gap and the order parameter, as well as the fidelity, if the Stark coupling strength is the same as the cavity frequency. The critical exponents are derived analytically. The energy gap and the length critical exponents are different from those in the quantum Rabi model and the Dicke model. A finite-size scaling analysis for the order parameter and the fidelity susceptibility is also performed. The universal scaling behaviors are demonstrated, and several finite-size exponents then can be extracted. Furthermore, universal critical behavior also can be established in terms of the bosonic Hilbert space truncation number, and the corresponding critical scaling exponents are found. Interestingly, the critical correlation length exponents in terms of the photonic truncation number as well as the equivalently effective length scales are different in the Rabi-Stark model and the quantum Rabi model, suggesting they belong to different universality classes. The second-order quantum phase transition is convincingly corroborated in the Rabi-Stark model at finite frequency ratios; by contrast, it emerges only at the infinite frequency ratio in the original quantum Rabi model without the Stark coupling.In this paper, we analyze the quantum criticality of the Rabi-Stark model at finite ratios of the qubit and cavity frequencies in terms of the energy gap and the order parameter, as well as the fidelity, if the Stark coupling strength is the same as the cavity frequency. The critical exponents are derived analytically. The energy gap and the length critical exponents are different from those in the quantum Rabi model and the Dicke model. A finite-size scaling analysis for the order parameter and the fidelity susceptibility is also performed. The universal scaling behaviors are demonstrated, and several finite-size exponents then can be extracted. Furthermore, universal critical behavior also can be established in terms of the bosonic Hilbert space truncation number, and the corresponding critical scaling exponents are found. Interestingly, the critical correlation length exponents in terms of the photonic truncation number as well as the equivalently effective length scales are different in the Rabi-Stark model and the quantum Rabi model, suggesting they belong to different universality classes. The second-order quantum phase transition is convincingly corroborated in the Rabi-Stark model at finite frequency ratios; by contrast, it emerges only at the infinite frequency ratio in the original quantum Rabi model without the Stark coupling.

arXiv:2001.04356Physical Review ADec 29, 202020 citations

U \to \pm 1

, the time-averaged linear entanglement entropy correlates strongly with the semiclassical phase space. In particular, when

U \to -1

, the truncated photon number in the resonant RSM is very close to that in the resonant Rabi model, but the time-averaged linear entanglement entropy still corresponds well with the semiclassical phase space. This result demonstrates that quantum-classical correspondence can be realized in the few-body resonant RSM.

1s

and

2p

states, the photoelectron energy spectra exhibit the Autler-Townes (AT) doublets and we focus on the energy spacing and the asymmetry of the doublets. Our results show that the laser frequency for the minimum energy spacing of AT doublets locates at the resonant frequency of the ac-stark-shifted states, while the symmetry of the AT doublets is affected both by the ac-stark shift and the nonresonant ionization pathway. Developing the minimal three-state model including all of the nonresonant (nonessential) states, the effects of the ac-stark shift and the nonresonant ionization pathway on the AT doublets due to the nonresonant states are identified. Furthermore, due to the nonresonant ionization pathway, the photoelectron angular distributions are distinctly different for the lower- and higher-energy peaks in the AT doublets and these angular distributions sensitively depend on the laser intensity and pulse duration. These results are well reproduced by our minimal three-state model.