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.     

Concurrence evolution of two qubits coupled with one-mode cavity separately

The concurrence evolution of two qubits coupled with one-mode cavity separately is investigated exactly without adopting the rotating-wave approximation. The results show that for the resonant case, the concurrence evolution behaviour of the system is similar to that of the Markovian case when the coupling strength is weak, while the concurrence vanishes in a finite time and might revive fractional initial entanglement before it permanently vanishes when the coupling strength is strong. And for the detuning case, the entanglement could periodically recover after complete disentanglement. These results are quite different from those of system subjected to Jaynes--Cummings model.     

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.     

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.     

Non-chaotic behavior in the semiclassical Jaynes-Cummings model

The semiclassical model, describing interaction of a collection of two-level atoms with a single-mode electric field, known as the Jaynes-Cummings model, without the assumption of the rotating-wave approximation, is considered. A solution, based on an asymptotic expansion, describing small oscillations is presented. This solution also yields a relation between the coupling and detuning parameters, which is the condition for the existence of regular and chaotic behaviour. We confirmed numerically, by calculation of the Lyapunov exponent and the Fourier spectrum, that the condition is valid for both weak and strong coupling.     

Exact periodic solutions and chaos in the semiclassical Jaynes-Cummings model

Exact periodic solutions for the semiclassical Jaynes-Cummings model without the assumption of the rotating-wave approximation are studied. They are valid for some specific values of the coupling constant, detuning parameter and the energy of the system. The behaviour of the system in the vicinity of this special solution is studied numerically. By computation of the Fourier spectrum, it is shown that the behaviour of the system changes from a non-chaotic to a chaotic one when the energy of the system increases.     

Ground State of Jaynes-Cummings Model: Comparison of Solutions with and without the Rotating-Wave Approximation

The eigenenergy spectrum of the Jaynes-Cummings （JC） model with and without the rotating-wave approx- imation （RWA） is investigated. The numerical analysis indicates that the non-RWA spectrum can only be approximated by the RWA in the range of sufficiently small coupling constant and detuning. In other region, the counter-rotating terms remarkably change the nature of the RWA energy spectrum. A simple expression with high accuracy for ground eigenenergy and eigenvector non-RWA shows that the ground state is not a dark state state. for non-RWA is available. The ground eigenvector for and very different from that of RWA which is a dark state.     

掺杂稀土离子晶体中的电磁感应光透明现象

对在掺杂稀土离子晶体中实现电磁感应光透明进行了实验研究。首先,以Er3＋∶YAG晶体为样品,用旋转波近似下的密度矩阵方程理论计算了探测场的吸收特性随Er3＋离子浓度的变化规律,结果表明：在探测场失谐Δp=0时,形成了一个对于探测光透明的窗口,从而在理论上论证了在掺杂稀土离子晶体中实现电磁感应光透明效应的可行性。设计了一个以Pr3＋∶Y2SiO5晶体为样品的实验激发方案,吸收光谱显示,当温度为6 K时其在共振吸收峰处可形成一个完全透明的窗口,实现了在掺杂离子晶体中的电磁感应光透明。实验还分析了工作温度、耦合场失谐对探测光透过率的影响,结果显示：当样品温度上升到15 K时,透明窗口消失;耦合场的失谐量越大,透射率越小。     

Ultrafast coherent population transfer driven by two few-cycle laser pulses

We investigate ultrafast coherent population transfer driven by few-cycle pump and Stokes laser pulses in the Λ-type three-level system with the stimulated Raman adiabatic passage technique beyond the rotating-wave approximation. In contrast to the case with the rotating wave approximation, the most efficient population transfer may be realized without the satisfaction of the one-photon resonances or two-photon resonance and the transfer efficiency depends critically on the Rabi frequencies and initial optical phases of the two laser fields when the peak Rabi frequencies are much larger than the respective transition frequencies. Moreover, complete and robust population transfer can still be obtained with the variations of the Rabi frequencies, pulse durations, and one-photon or two-photon detuning in a moderate range, though a considerable transient population may reside in the excited state. These abnormal behaviors result from the counterrotating terms, which are not taken into account in the traditional rotating wave approximation.     

Entanglement Evolution of a Two-Qubit System beyond Rotating-Wave Approximation

Two noninteracting qubits, initially entangled in Bell states, are coupled to a one-mode cavity and evolve under its influence. The entanglement evolution of the two qubits is investigated beyond the rotating-wave approximation. It is shown that the counter-rotating wave terms have a great influence on the disentanglement behavior.     

附加Kerr介质Λ型三能级原子与非关联双模相干态光场的压缩特性

采用旋波近似分析了附加克尔介质非关联双模相干态场与A型三能级原子相互作用系统的态矢量演化过程,叙述了两种光场压缩效应及应用,给出了光子数压缩和正交相位压缩计算公式,通过数值计算,绘出压缩光场随时间的演化过程并讨论了克尔介质对光场压缩特性的影响,结果表明强的克尔效应可以使光场的压缩随时间演化呈周期性变化,失谐较大时,光子数压缩品质差.     

飞秒激光场中原子所受光学偶极力研究

通过求解全波矢布洛赫方程研究了两能级原子与飞秒超快激光脉冲的相互作用过程,计算了不同拉比频率取值下原子所受光学偶极力和粒子数布居随时间的演化情况,分析了光场失谐量对光学势分布情况的影响.研究发现:由飞秒激光场产生的横向光力的时间平均值并不等于零,而是随着拉比频率的增加呈现振荡的增大趋势;纵向光力的时间平均作用也并非是拉比频率的单调函数,而是随着拉比频率的增加呈现周期性的振荡分布特性;光学势的分布对光场的失谐量具有明显的依赖性,随着失谐量的变化,光学势的性质也随之发生了改变.     

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.     

Electromagnetically induced left handedness in a V-type four-level atomic system

A closed four-level system in atomic vapor is proposed, which is made to possess left handedness by means of the technique of quantum coherence. The method of density matrix is utilized in view of the rotating-wave approximation and the effect of local-field in dense gas. The result of the numerical simulation shows that the negative permittivity and negative permeability of the medium can be achieved simultaneously （i.e., the left handedness） in a wider frequency band under appropriate parameter conditions. Furthermore, when analyzing the dispersion property of the left-handed material, we find that the probe beam can be controlled to change from superluminal to subluminal or vice versa via changing the detuning of the probe field.     

Geometric curvature and phase of the Rabi model

We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to measure in the qubit–cavity system. We also calculate the geometric phase beyond the RWA and find an anomalous sudden change, which implies the breakdown of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution are ill-defined near the anti-crossing point in the spectrum.     

Negative refractive index in a four-level atomic system

A closed four-level system in atomic vapour is proposed, which is made to possess left handedness by using the technique of quantum coherence. The density matrix method is utilized in view of the rotating-wave approximation and the effect of a local field in dense gas. The numerical simulation result shows that the negative permittivity and the negative permeability of the medium can be achieved simultaneously (i.e. the left handedness) in a wider frequency band under appropriate parameter conditions. Furthermore, when analysing the dispersion property of the left-handed material, we can find that the probe beam propagation can be controlled from superluminal to subluminal, or vice versa via changing the detuning of the probe field.     

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.     

Nonlocality and the Rotating Wave Approximation

The effect of the rotating-wave approximation (RWA) on the coupling between an atom and the electromagnetic field is studied in the dipole approximation. It is demonstrated that use of the RWA results in an explicitly nonlocal interaction.     

一维Klein-Gordon双原子链中的能隙呼吸子

采用旋转波近似，讨论一维Klein-Gordon双原子链中的能隙呼吸子. 在驻波边界条件下数值求解一维Klein-Gordon双原子链晶格振动的运动方程组，得到不同耦合系数、不同非线性系数以及不同原子质量比情况下的以重原子为中心的对称模能隙呼吸子. 随着耦合系数的增大，原子之间的耦合作用增强，呼吸子的空间扩展范围增大；非线性作用越大，能隙呼吸子局域化越强；随着原子质量差的增大，呼吸子在空间越来越局域. 关键词： 能隙呼吸子 一维Klein-Gordon双原子链 耦合系数 非线性