Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1203.2410

Jaynes-Cummings model: What emerges first beyond the rotating-wave approximation?

S. M. He, Qing‐Hu Chen, Xuezao Ren, Tao Liu, Kelin Wang

Published Mar 12, 2012• 0 citations
arXivHTMLPDF

Abstract

The Jaynes-Cummings model without the rotating-wave approximation can be solved exactly by extended Swain's ansatz with the conserved parity. The analytical approximations are then performed at different levels. The well-known rotating-wave approximation is naturally covered in the present zero and first approximations. The effect of the counter rotating-wave term emerges clearly in the second order approximation. The concise analytical expressions are given explicitly and can be applicable up to the ultra-strong coupling regime. The preliminary application to the vacuum Rabi splitting is shown to be very successful.

DOI
10.48550/arxiv.1203.2410

Related papers

First-order corrections to the rotating-wave approximation in the Jaynes-Cummings model

Shu He, Chen Wang, Qing‐Hu Chen +3 more

The Jaynes-Cummings model without the rotating-wave approximation can be solved exactly by an extended Swain ansatz with conserved parity. Analytical approximations are then performed at different levels. The well-known rotating-wave approximation (RWA) is naturally covered in the present zeroth- and first-order approximations. A first-order correction to the RWA can be obtained in a second-order approximation, by which the effect of the counter-rotating-wave term emerges clearly. Concise analytical expressions are given explicitly and can be applicable up to the ultrastrong-coupling regime. A preliminary application to vacuum Rabi splitting is shown to be very successful.

Physical Review A•Sep 25, 2012•40 citations

Jaynes-Cummings model:Counter rotating effect on the vacuum Rabi splitting and atom-cavity dynamics

Yuyu Zhang, Qing‐Hu Chen, Shi-Yao Zhu

he effect of the counter-rotating terms in the Jaynes-Cummings model is investigated with an extended coherent-state approach. The counter-rotating terms greatly modify the vacuum Rabi splitting. Two peaks with different heights in the weak coupling regime and more than two peaks in the intermediate coupling regime are predicted. The collapses and revivals in the evolution of the atomic population inversion disappear in the intermediate coupling regime, but reappear in the strong coupling regime. This reappearance is similar to that under the rotating-wave approximation, attributed to the summation of periodic cosine functions of the evolution.

arXiv:1106.2191•Jun 11, 2011•0 citations

Vacuum Rabi Splitting and Dynamics of the Jaynes—Cummings Model for Arbitrary Coupling

Yuyu Zhang, Qing‐Hu Chen, Shi-Yao Zhu

The effects of counter-rotating terms (CRTs) on Rabi splitting and the dynamic evolution of atomic population in the Jaynes—Cummings model are studied with a coherent-state approach. When the coupling strength increases, the Rabi splitting becomes of multi-Rabi frequencies for the initial state of an excited atom in a vacuum field, and the collapses and revivals gradually disappear, and then reappear with quite good periodicity. Without the rotating-wave approximation (RWA), the initial excited state contains many eigenstates rather than two eigenstates under the RWA, which results in the multi-peak emission spectrum. An analytical approximate solution for the strong coupling regime is obtained, which gives a new oscillation frequency and explains the recovery of collapses and revivals due to the equal energy spacing.

Chinese Physics Letters•Nov 1, 2013•15 citations

Analytical Solution for the Anisotropic Rabi Model: Effects of Counter-Rotating Terms

Guofeng Zhang, Han‐Jie Zhu

The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.

arXiv:1503.06538•Scientific Reports•Mar 4, 2015•22 citations

Effective Hamiltonian of the Jaynes–Cummings model beyond rotating-wave approximation*

Yifan Wang, Hong-Hao Yin, Ming-Yue Yang +2 more

The Jaynes–Cummings model with or without rotating-wave approximation plays a major role to study the interaction between atom and light. We investigate the Jaynes–Cummings model beyond the rotating-wave approximation. Treating the counter-rotating terms as periodic drivings, we solve the model in the extended Floquet space. It is found that the full energy spectrum folded in the quasi-energy bands can be described by an effective Hamiltonian derived in the high-frequency regime. In contrast to the Z 2 symmetry of the original model, the effective Hamiltonian bears an enlarged U(1) symmetry with a unique photon-dependent atom-light detuning and coupling strength. We further analyze the energy spectrum, eigenstate fidelity and mean photon number of the resultant polaritons, which are shown to be in accordance with the numerical simulations in the extended Floquet space up to an ultra-strong coupling regime and are not altered significantly for a finite atom-light detuning. Our results suggest that the effective model provides a good starting point to investigate the rich physics brought by counter-rotating terms in the frame of Floquet theory.

Chinese Physics B•Jan 8, 2021•5 citations

The Jaynes–Cummings model beyond the rotating-wave approximation as an intensity-dependent model: quantum statistical and phase properties

M. H. Naderi

In this paper, we investigate various dynamical properties of the Jaynes–Cummings (JC) model beyond the rotating wave approximation (RWA). We first show that in the absence of the RWA, the JC Hamiltonian can be transformed into an intensity-dependent Hamiltonian. Corrections produced by the counter-rotating terms (CRTs) appear in the first order as the intensity-dependent detuning, i.e. the dynamical Stark shift and in the second order as the intensity-dependent atom–field coupling. Then, by determining the atom–field wavefunction evolution, we study the effects of CRTs on various dynamical properties of the JC model, including the atomic population inversion, atomic dipole squeezing, atomic entropy squeezing, photon counting statistics, quadrature field squeezing, field entropy squeezing and quantum phase properties of the cavity field.

Journal of Physics A Mathematical and Theoretical•Jan 4, 2011•30 citations
The Jaynes-Cummings model without the rotating-wave approximation can be solved exactly by extended Swain's ansatz with the conserved parity. The analytical approximations are then performed at different levels. The well-known rotating-wave approximation is naturally covered in the present zero and first approximations. The effect of the counter rotating-wave term emerges clearly in the second order approximation. The concise analytical expressions are given explicitly and can be applicable up to the ultra-strong coupling regime. The preliminary application to the vacuum Rabi splitting is shown to be very successful.
The Jaynes-Cummings model without the rotating-wave approximation can be solved exactly by an extended Swain ansatz with conserved parity. Analytical approximations are then performed at different levels. The well-known rotating-wave approximation (RWA) is naturally covered in the present zeroth- and first-order approximations. A first-order correction to the RWA can be obtained in a second-order approximation, by which the effect of the counter-rotating-wave term emerges clearly. Concise analytical expressions are given explicitly and can be applicable up to the ultrastrong-coupling regime. A preliminary application to vacuum Rabi splitting is shown to be very successful.
he effect of the counter-rotating terms in the Jaynes-Cummings model is investigated with an extended coherent-state approach. The counter-rotating terms greatly modify the vacuum Rabi splitting. Two peaks with different heights in the weak coupling regime and more than two peaks in the intermediate coupling regime are predicted. The collapses and revivals in the evolution of the atomic population inversion disappear in the intermediate coupling regime, but reappear in the strong coupling regime. This reappearance is similar to that under the rotating-wave approximation, attributed to the summation of periodic cosine functions of the evolution.
The effects of counter-rotating terms (CRTs) on Rabi splitting and the dynamic evolution of atomic population in the Jaynes—Cummings model are studied with a coherent-state approach. When the coupling strength increases, the Rabi splitting becomes of multi-Rabi frequencies for the initial state of an excited atom in a vacuum field, and the collapses and revivals gradually disappear, and then reappear with quite good periodicity. Without the rotating-wave approximation (RWA), the initial excited state contains many eigenstates rather than two eigenstates under the RWA, which results in the multi-peak emission spectrum. An analytical approximate solution for the strong coupling regime is obtained, which gives a new oscillation frequency and explains the recovery of collapses and revivals due to the equal energy spacing.
The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.
The Jaynes–Cummings model with or without rotating-wave approximation plays a major role to study the interaction between atom and light. We investigate the Jaynes–Cummings model beyond the rotating-wave approximation. Treating the counter-rotating terms as periodic drivings, we solve the model in the extended Floquet space. It is found that the full energy spectrum folded in the quasi-energy bands can be described by an effective Hamiltonian derived in the high-frequency regime. In contrast to the Z 2 symmetry of the original model, the effective Hamiltonian bears an enlarged U(1) symmetry with a unique photon-dependent atom-light detuning and coupling strength. We further analyze the energy spectrum, eigenstate fidelity and mean photon number of the resultant polaritons, which are shown to be in accordance with the numerical simulations in the extended Floquet space up to an ultra-strong coupling regime and are not altered significantly for a finite atom-light detuning. Our results suggest that the effective model provides a good starting point to investigate the rich physics brought by counter-rotating terms in the frame of Floquet theory.
In this paper, we investigate various dynamical properties of the Jaynes–Cummings (JC) model beyond the rotating wave approximation (RWA). We first show that in the absence of the RWA, the JC Hamiltonian can be transformed into an intensity-dependent Hamiltonian. Corrections produced by the counter-rotating terms (CRTs) appear in the first order as the intensity-dependent detuning, i.e. the dynamical Stark shift and in the second order as the intensity-dependent atom–field coupling. Then, by determining the atom–field wavefunction evolution, we study the effects of CRTs on various dynamical properties of the JC model, including the atomic population inversion, atomic dipole squeezing, atomic entropy squeezing, photon counting statistics, quadrature field squeezing, field entropy squeezing and quantum phase properties of the cavity field.