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.     

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.     

Vacuum Rabi Oscillation of an Atom without Rotating-Wave Approximation

We have investigated vacuum Rabi oscillation of an atom coupled with single-mode cavity field exactly, and compared the results with that of the Jaynes-Cummings （J-C） model. The results show that for resonant ease, there is no Rabi oscillation for an atom. For small detuning and weak coupling case, the probability for the atom in excited state oscillates against time with different frequencies and amplitudes from that of the J-C model. It exhibits that the counter-rotating wave interaction could significantly effect the dynamic behaviour of the atom, even under the condition in which the RWA is considered to be justified.     

A Radio Frequency Field Guide Using Field Induced Adiabatic Potential

We study the behaviour of atoms in a field with both static magnetic field and radio frequency （rf） magnetic field. We calculate the adiabatic potential of atoms numerically beyond the usually rotating wave approximation, and it is pointed that there is a great difference between using these two methods. We find the preconditions when RWA is valid. In the extreme of static field almost parallel to rf field, we reach an analytic formula. Finally, we apply this method to 87 Rb and propose a guide based on an rf field on atom chip.     

Entangled Radiation through an Atomic Reservoir Controlled by Coherent Population Trapping

We show that it is possible to generate Einstein-Podolsky-Rosen （EPR） entangled radiation using an atomic reservoir controlled by coherent population trapping. A beam of three-level atoms is initially prepared in nearcoherent population trapping （CPT） state and acts as a long-lived coherence-controlled reservoir. Four-wave mixing leads to amplification of cavity modes resonant with RabJ sidebands of the atomic dipole transitions. The cavity modes evolve Jnto an EPR state, whose degree of entanglement is controlled by the intensities and the frequencies of the driving fields. This scheme uses the long-lived CPT coherence and is robust against spontaneous emission of the atomic beam. At the same time, this scheme is implemented in a one-step procedure, not in a two-step procedure as was required in Phys. Rev. Lett. 98 （2007） 240401.     

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.     

Radiative Energy Shifts of an Atom Coupled to the Derivative of a Scalar Field near a Reflecting Boundary

We study the radiative energy level shifts of a two-level atom in dipole coupling to the derivative of a massless scalar quantum field in a spacetime with a perfectly reflecting boundary, and calculate the contributions of vacuum fluctuations and radiation reaction to the level shift. It is found that the energy level shift of the excited state is an oscillating function of the atom＇s distance from the boundary and it can either be positive or negative, while that of the ground state is always positive. The most remarkable feature is that the energy level shift of the ground state behaves like 1/z^4 when the atom＇s distance from the boundary, z, is very large as compared to the transition wavelength of the atom, while it behaves like 1/z^3 when z is very small     

Quantum interferences in coherent population trapping of a cold double Λ-type atom

We investigate quantum interferences in coherent population trapping of a cold double Λ-type four-level atomic system driven by two counterpropagating laser fields. We study both decoherence and enhanced-coherence actions resulting from the multi-transition pathways in building up the trapping state, and analyze the system operating with and without external coherences in various configurations of the atomic dipole moments.     

Three-Photon Resonant Nondegenerate Six-Wave Mixing in a Dressed Atomic System

We report a three-photon resonant nondegenerate six-wave mixing （NSWM） in a dressed cascade five-level system. It has advantages that phase match condition is not stringent and NSWM signal is enhanced tremendously due to the multiple resonance with the atomic transition frequencies. In the presence of a strong coupling field, the threephoton resonant NSWM spectrum exhibits＂ Autler-Townes splitting. This technique provides a spectroscopic tool for measuring not only the resonant frequency and dephasing rate but also the transition dipole moment between two highly excited atomic states.     

Quantum NOT operation and integrability in two-level systems

We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the rotating wave approximation (RWA), on the other hand to two different “average” systems, according to whether a certain parameter is small or large. Of particular independent interest is the fact that both the RWA and the averaging theorem are seen to hold well beyond their expected region of validity. Finally, we determine conditions for the realization of the quantum NOT operation by means of classical stroboscopic maps.     

Anomalous Effects of Driving Field Linewidth on a One-Atom Dressed-State Laser

We examine the effects of driving field linewidth on a one-atom dressed state laser. Unexpectedly, the linewidth leads to anomalous effects on the cavity field. The mean photon number of the cavity field is raised or the normalized variance is reduced to a certain degree as the linewidth increases for an appropriate range of parameters. The responsible mechanism is attributed to the fluctuation-induced modification of the electromagnetic reservoir where the atom stays.     

Efficient atomic quantum memory for photonic qubits in cavity QED

We investigate a scheme of atomic quantum memory to store photonic qubits of polarization in cavity QED. It is observed that the quantum state swapping between a single-photon pulse and a Λ-type atom can be made via scattering in an optical cavity [T. W. Chen, C. K. Law, P. T. Leung, Phys. Rev. A 69 (2004) 063810]. This swapping operates limitedly in the strong coupling regime for Λ-type atoms with equal dipole couplings. We extend this scheme in cavity QED to present a more feasible and efficient method for quantum memory combined with projective measurement. This method works without requiring such a condition on the dipole couplings. The fidelity is significantly higher than that of the swapping, and even in the moderate coupling regime it reaches almost unity by narrowing sufficiently the photon-pulse spectrum. This high performance is rather unaffected by the atomic loss, cavity leakage or detunings, while a trade-off is paid in the success probability for projective measurement.     

The effect of a permanent dipole moment on the polar molecule cavity quantum electrodynamics

A dressed-state perturbation theory beyond the rotating wave approximation(RWA) is presented to investigate the interaction between a two-level electronic transition of polar molecules and a quantized cavity field. Analytical expressions can be explicitly derived for both the ground- and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments(PDM) and the counter-rotating wave term(CRT) can be shown separately.The validity of these explicit results is discussed by comparison with the direct numerical simulation. Compared to the CRT coupling, PDM results in the coupling of more dressed states and the energy shift is proportional to the square of the normalized permanent dipole difference, and a greater Bloch–Siegert shift can be produced in the giant dipole molecule cavity QED. In addition, our method can also be extended to the solution of the two-level atom Rabi model Hamiltonian beyond the RWA.     

Radiative Energy Shifts of an Accelerated Multilevel Atom Coupled to the Derivative of a Scalar Field

We study the energy level shifts of an accelerated multilevel atom in dipole coupling to the derivative of a quantum massless scalar field and separately calculate the contributions of vacuum fluctuations and radiation reaction to the shifts. It is found that, in contrast to the case of a monopole-like interaction, both the vacuum fluctuations and radiation reaction contributions are changed by acceleration, and they all contain non-thermal correction terms. Our results suggest that the effect of acceleration on the energy shifts is dependent on the type of the interaction between the atom and the quantum field.     

Analytical analysis of the “collapse-revival” effect in the Jaynes-Cummings model

The evolution of the atomic state population in a two-level system coupled to a single-mode quantum field is calculated in the analytical form. Essential characteristics of the “collapse-revival” effect are expressed in terms of the physical parameters of the system by means of simple formulas in both the resonant and the non-resonant cases. The obtained results are of great importance for the qualitative analysis of the phenomenon.     

Variance squeezing and information entropy squeezing via Bloch coherent states in two-level nonlinear spin models

The nonclassical squeezing effect emerging from a nonlinear coupling model (generalized Jaynes–Cummings model) of a two-level atom interacting resonantly with a bimodal cavity field via two-photon transitions is investigated in the rotating wave approximation. Various Bloch coherent initial states (rotated states) for the atomic system are assumed, i.e., (i) ground state, (ii) excited state, and (iii) linear superposition of both states. Initially, the atomic system and the field are in a disentangled state, where the field modes are in Glauber coherent states via Poisson distribution. The model is numerically tested against simulations of time evolution of the based Heisenberg uncertainty relation variance and Shannon information entropy squeezing factors. The quantum state purity is computed for the three possible initial states and used as a criterion to get information about the entanglement of the components of the system. Analytical expression of the total density operator matrix elements at t > 0 shows, in fact, the present nonlinear model to be strongly entangled, where each of the definite initial Bloch coherent states is reduced to statistical mixtures. Thus, the present model does not preserve the modulus of the Bloch vector.     

Atomic transition transfer, field statistics and squeezing of the off-resonant cascade three-level Jaynes-Cummings model with a Kerr medium

Atomic population dynamics and the non-classical properties of the field in the system consisting of a cascade three-level atom interacting non-resonantly with a single-mode field are investigated in the presence of a Kerr medium. The atom and the field are assumed to be in the upper state and the coherent state initially, respectively. It is found that an atomic transition transfer may occur by varying the initial field intensity under the condition of a reasonably large one-photon detuning. Varying the initial field intensity can also control the field statistics. Quasiprobability distribution Q-function of the field state is also calculate to reveal its relation to the field statistics and normal squeezing effect.     

Spectral line suppression and sideband narrowing via quantum interference

We reveal that for a realistic system, interference effects are obtained such as the suppression of central line and inner sidebands and the narrowing of the outer fluorescence sidebands. For this purpose, we consider a spontaneous decay from an excited state to a metastable state when the excited and metastable states are resonantly coupled to an auxiliary metastable state by a laser field and a microwave field, respectively. The fluorescence spectrum evolves from a five-peaked structure into a doublet of ultrasharp lines as the ratio of the laser field Rabi frequency to the microwave Rabi frequency is decreased. The physical origin is presented in terms of dressed states.     

薛定谔猫态光场与二能级原子相互作用系统的量子特性

在非旋波近似下,通过采用相干态正交化展开的方法,研究了薛定谔猫态光场与二能级原子相互作用系统中,原子的布局数和光场的反聚束效应,并与旋波近似下的结果进行了对比.在旋波近似与非旋波近似下,讨论了初始光场强度、相干态间的相位角以及失谐量对原子布局数和光场反聚束效应的影响;在非旋波近似下,讨论了强弱耦合情况下光场的反聚束效应.研究结果表明:旋波近似与非旋波近似下,原子的布局数随着初始光场强度的不同,表现出不同的特性;当初始光场强度较小时,旋波近似与非旋波近似下,原子的布局数表现出相同的特性;随着初始光场强度的增大,旋波近似下,原子的布局数将表现出坍塌现象.耦合强度较大时,光场的聚束与反聚束效应在非旋波近似与旋波近似下有较大的区别;非旋波近似下,随着初始光场强度的增大,光场一直处于聚束效应状态;而旋波近似下,光场的聚束效应与反聚束效应交替出现.     

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.