Chaotic dynamics in a nonautonomous Dicke model without the rotating-wave approximation

The properties of a system consisting of two-level atoms interacting with a mode of the electromagnetic field in a cavity are considered for the case when the cavity detuning or the coefficient of the atom-field interaction is modulated. The consideration is performed with account taken of the Hamiltonian terms that are neglected in the rotating-wave approximation. It is shown that in the semiclassical equations for such a model, the effect of extension (compared to the autonomous system) of the range of variation of the quantity characterizing the number of photons can manifest itself; in this case, the energy oscillations have a chaotic character. The dependence of this phenomenon on parameters characterizing the model is studied. It is numerically demonstrated that with account taken for the relaxation, the system studied can have attractors different from the equilibrium positions, i.e., the number of photons in the mode does not tend to a constant value. The limits of validity of the rotating-wave approximation in the parametrically perturbed Dicke model are discussed.     

Damping of a harmonic oscillator in a squeezed vacuum without rotating-wave approximation

A single harmonic oscillator interacting with a broadband squeezed reservoir is analyzed within the framework of master equation without invoking the rotating-wave approximation. The dynamical evolution and photon statistics of the system are investigated by studying mean photon number and second order intensity-intensity correlation function, respectively, under resonance condition which show transient oscillations at twice the harmonic oscillator frequency. The transient fluorescent spectrum reveals asymmetric features. Inclusion of vacuum and field-dependent frequency shifts affects the thermal equilibrium value of the average photon number of the harmonic oscillator.     

Energy spectrum of the Hamiltonian of the Jaynes-Cummings model without rotating-wave approximation

The energy spectrum of the Hamiltonian of the Jaynes-Cummings model without a rotating-wave approximation is studied. The trajectories of eigenvalues as functions of the dimensionless coupling constant are constructed. It is shown that the spectrum approaches the equidistant spectrum, i.e., the oscillator spectrum, as the coupling constant increases. As a result, each energy level becomes doubly degenerate.     

Squeezing and rabi oscillations in the Dicke model within and without rotating-wave approximation

The Dicke model is investigated within and without rotating-wave approximation in the case of a lossless resonant cavity. Numerical results for the time evolution of the atomic population inversion, dipole moment and atomic and field squeezing parameters for an initial field are presented for different numbers of atoms. The significant influence of the counter-rotating terms on the squeezing and collapse (revival) phenomena is pointed out.     

Spontaneous emission of an excited two-level atom without both rotating-wave and Markovian approximation

The spontaneous emission of an excited atom is analyzed by quantum stochastic trajectory approach without both rotating-wave approximation and Markovian approximation. The atom finite size effect is also taken into account. We show by an example that the correction due to the counter-rotating wave term is rather small, even for the largest atomic number of real nuclei. Received 10 July 2002 / Received in final form 12 November 2002 Published online 4 February 2003     

非旋波近似下频率变化的场与原子的相互作用

研究了非旋波近似下频率随时间变化的相干态光场与二能级原子的相互作用，主要讨论了光场频率随时间作正弦和方波变化两种典型情况下，原子布居数反转随时间的演化特性. 当光场频率随时间作正弦变化时，原子布居数反转的崩塌-回复过程和由虚光子过程引起的快速振荡均会受到影响. 当光场频率随时间以方波形式变化时，脉冲调制不仅在原子布居数反转随时间演化过程中诱导出新的崩塌-回复过程，而且可以引起虚光子快速振荡的突变. 关键词： Jaynes-Cummings模型 非旋波近似 原子布居数反转     

Dipole squeezing in the multi-photon Jaynes-Cummings model with and without the rotating-wave approximation

By virtue of the numerical method of Graham and Höhnerbach [12], we have investigated the quantum fluctuations of the atomic dipole variables in the multiphoton Jaynes-Cummings model with and without the rotating wave approximation (RWA) when it is restricted to the following initial condition: the atom in its superposition state and the field in the vacuum state. We found that even under the conditions in which the RWA is considered to be valid there are significant effects of virtual-photon field on dipole squeezing predicted in the RWA, and dipole squeezing turns to disappear for sufficiently strong coupling.     

Dipole squeezing in the multi-photon Jaynes-Cummings model with and without the rotating-wave approximation

By virtue of the numerical method of Graham and Höhnerbach [12], we have investigated the quantum fluctuations of the atomic dipole variables in the multiphoton Jaynes-Cummings model with and without the rotating wave approximation (RWA) when it is restricted to the following initial condition: the atom in its superposition state and the field in the vacuum state. We found that even under the conditions in which the RWA is considered to be valid there are significant effects of virtual-photon field on dipole squeezing predicted in the RWA, and dipole squeezing turns to disappear for sufficiently strong coupling.     

Generalized rotating-wave approximation for arbitrarily large coupling

A generalized version of the rotating-wave approximation for the single-mode spin-boson Hamiltonian is presented. It is shown that performing a simple change of basis prior to eliminating the off-resonant terms results in a significantly more accurate expression for the energy levels of the system. The generalized approximation works for all values of the coupling strength and for a wide range of detuning values, and may find applications in solid-state experiments.     

Interactions of a two-level atom and a field with a time-varying frequency without rotating-wave approximation

The interactions between a two-level atom and a field with a time-varying frequency without rotating-wave approximation have been investigated. The frequency of the field varies in the form of rectangle. The dynamic behaviors of the atomic population inversion, photon anti-bunching and atomic dipole squeezing are investigated numerically as function of time. A number of novel phenomena are discovered and discussed.     

Dynamics of two-level systems beyond the rotating-wave approximation

We study the dynamics of quantum discord and entanglement in a two-qubit system coupled to the same quantized field without rotating-wave approximation. In the absence of initial correlations, we show that maximal quantum discord (entanglement) can be obtained in the strong coupling regime. Analytical result corresponding to an effective Hamiltonian is given. In a deep strong coupling regime, sudden death and sudden birth of entanglement are observed, while the peak value of quantum discord is reached periodically. The results of our investigation also suggest that some special quantum state with non-zero quantum discord may be created.     

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

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 highfrequency 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.     

Analytical approach to dynamics of transformed rotating-wave approximation with dephasing

We study the dynamics of the Jaynes-Cummings model within transformed rotating-wave approximation （TRWA）. We analyze this model coupled to a dephasing reservoir, through the Lindblad formalism in the master equation. Then, we examine the expectation value of the number operator. Finally, we investigate the validity of this model under dephasing using the Mandel parameter and the total number of quanta.     

Geometric phases in qubit-oscillator system beyond conventional rotating-wave approximation

In this work we investigated the geometric phases of a qubit-oscillator system beyond the conventional rotating- wave approximation. We find that in the limiting of weak coupling the results coincide with that obtained under rotating-wave approximation while there exists an increasing difference with the increase of coupling constant. It was shown that the geometric phase is symmetric with respect to the sign of the detuning of the quantized field from the one-photon resonance under the conventional rotating-wave approximation while a red-blue detuning asymmetry occurs beyond the conventional rotating-wave approximation.     

Entanglement evolution of a two-qubit system with decay beyond the rotating-wave approximation

The entanglement property of two identical atoms, initially entangled in Bell states, coupled to a single-mode cavity is considered. Based on the reduced non-perturbative quantum master equation method, the entanglement evolution of the two atoms with decay is investigated beyond the conventional rotating-wave approximation. We show that the counter-rotating wave terms, usually neglected, have a great influence on the disentanglement behaviour of the system. The phenomena of entanglement sudden death and entanglement sudden birth will occur. In addition, we show that the entanglement can be strengthened by introducing the dipole--dipole interaction of the two atoms.     

The effect of the cavity damping on the squeezing in the Jaynes-Cummings model within and without rotating-wave approximation for a squeezed field

Summary The squeezing is investigated in the Jaynes-Cummings model within and without rotating-wave approximation in the case of a damped cavity. The time behaviour of the atomic and field squeezing parameters for initially squeezed and coherent fields is calculated numerically.     

Dynamics of a two-level system coupled to a quantum oscillator: transformed rotating-wave approximation

For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but still keeps the simple mathematical structure of the ordinary rotating-wave approximation. We have calculated the energy levels of ground and lower-lying excited states, as well as the time-dependent quantum dynamics. It is obvious that the approach is quite simple and can be easily extended to more complicated situation. Besides, the results are compared with the numerically exact ones to show that for weak to intermediate coupling and moderate detuning our analytic calculations are quantitatively in good agreement with the exact ones.     

The influence of the cavity damping on the Rabi oscillations in the few-atom Jaynes-Cummings model within and without rotating-wave approximation for initial coherent field

Summary The influence of the cavity damping and the counter-rotating terms on the Rabi oscillations in the few-atom Jaynes-Cummings model is investigated for an initial coherent field. The time behaviour of the atomic population inversion and dipole moment is calculated numerically.