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.     

Virtual photon effects on classical chaos in a periodically kicked Rydberg atom system

We study classical chaos in the system of a two-level Rydberg atom interacting with a pulsed standing microwave. This model approaches the form of an atom optics realization of a usual delta-kicked rotor under the rotating-wave approximation (RWA). We find that the non-energy-conserving processes or virtual photon processes neglected in the RWA have a strong effect on the classical chaos, which can enhance, reduce and even completely suppress the chaos under certain kicked conditions. The system displays non-KAM dynamical behavior for rational and irrational kicks.     

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.     

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.     

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.     

Star products and geometric algebra

The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the deformation to the bosonic coefficients of superanalysis one obtains quantum mechanics for systems with spin. This approach clarifies on the one hand the relation between Grassmann and Clifford structures in geometric algebra and on the other hand the relation between classical mechanics and quantum mechanics. Moreover it gives a formalism that allows to handle classical and quantum mechanics in a consistent manner.     

Absence of vacuum induced Berry phases without the rotating wave approximation in cavity QED

We revisit earlier studies on Berry phases suggested to appear in certain cavity QED settings. It has been especially argued that a nontrivial geometric phase is achievable even in the situation of no cavity photons. We, however, show that such results hinge on imposing the rotating wave approximation (RWA), while without the RWA no Berry phases occur in these schemes. A geometrical interpretation of our results is obtained by introducing semiclassical energy surfaces which in a simple way brings out the phase-space dynamics. With the RWA, a conical intersection between the surfaces emerges and encircling it gives rise to the Berry phase. Without the RWA, the conical intersection is absent and therefore the Berry phase vanishes. It is believed that this is a first example showing how the application of the RWA in the Jaynes-Cummings model may lead to false conclusions, regardless of the mutual strengths between the system parameters.     

Exact eigenstates of the two-photon Jaynes-Cummings model with the counter-rotating term

We have investigated the eigenenergy spectrum of the two-photon Jaynes-Cummings (JC) model with and without the rotating-wave approximation (RWA). Our analysis has indicated that the counter-rotating term dramatically changes the nature of the RWA energy spectrum and that the non-RWA spectrum can be approximated by the RWA spectrum only in the range of a sufficiently small coupling constant. Furthermore, unlike the one-photon counterpart, the two-photon JC model without the RWA is well defined only if the coupling parameter is below a certain critical value. As a result, the dynamics of the two-photon JC model without the RWA is significantly different from its RWA counterpart. For instance, the counter-rotating term can dramatically enhance the field squeezing effect. Besides, we would expect that the quantum dynamics of the two-photon JC model without the RWA is qualitatively different from that of the usual one-photon case.     

On the Transition Probability for the Near or Exact Resonance with the RWA

Rotating wave approximation (RWA) has been used to evaluate the transition probability and solve the Schrödinger equation approximately in quantum optics. Examples include the invalidity of the traditional adiabatic condition for the adiabaticity invoking a two-level coupled system near resonance. Here, using a two-state system driven by an oscillatory force, we derive the exact transition probability by solving the Schrödinger equation analytically for a general wave function. Our results reveal that the application of the RWA may lead to false conclusions on the transition probability for the near resonance with weak coupling, especially when the coupling strength is about a half of the transition frequency. We also investigate conditions for which RWA may work or fail.     

Series solution to the laser-ion interaction in a Raman-type configuration

The Raman interaction of a ultracold ion trapped with two travelling wave lasers is studied analytically with series solutions, in the absence of the rotating wave approximation (RWA) and without restrictions of both the Lamb-Dicke limit and the weak excitation regime. The comparison is made between our solutions and those obtained under the RWA in order to demonstrate the validity region of the RWA. As a practical example, the preparation of Schr?dinger-cat states is proposed beyond the weak excitation regime, using our calculations. Received 12 March 2001 and Received in final form 16 October 2001     

Rotating electrons in quantum dots: Classical limit

We solve the problem of a few electrons in a two-dimensional harmonic confinement using a quantum mechanical exact diagonalization technique, on the one hand, and classical mechanics, on the other. The quantitative agreement between the results of these two calculations suggests that, at low filling factors, all the low energy excitations of a quantum Hall liquid are classical vibrations of localized electrons. The Coriolis force plays a dominant role in determining the classical vibration frequencies.     

The reduced width amplitude in the reaction theory for composite particles

The derivation of the reduced width amplitude (RWA) in the reaction theory for composite particles is investigated. This is done in theα-decay theory without loss of generality for the basic expressions. We find that in a consistent theory we have to not only take into account the antisymmetrization—as it is usually done — but also to introduce a renormalization of our basis states due to the antisymmetrization. This cannot be done by a normalization constant, but by a well-defined normalization operator. As a result of this investigation we give a redefinition of the RWA. A rough estimate of the effect of this renormalization is presented. In a simplified oscillator model numerical values are given for the change in the RWA.     

Fisher Information of Wavefunctions： Classical and Quantum

A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first, defined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second, defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions. It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.     

LC-DLA: A fair congestion-aware Distributed Lightpath Allocation mechanism

One of the main challenges in all-optical WDM networks is the problem of Routing and Wavelength Assignment (RWA). In large-scale networks with heavy traffic load, distributed RWA is more suitable than centralized RWA. One of the distributed algorithms proposed recently is Distributed Lightpath Allocation (DLA) [1]. We use the DLA as our basic algorithm to design a new congestion-aware RWA algorithm, called Least-Congested Distributed Lightpath Allocation (LC-DLA). We consider congestion in the network as a decision point for solving RWA. Selection of the least congested path among available paths from source to destination can improve the blocking probability of the network. Fairness is one of the crucial metrics that network designers should consider. We define a new concept for fairness in RWA. Our performance evaluations show that LC-DLA can provide good blocking and fairness performances in WDM networks.     

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.     

Micro-vibration model and parameter estimation method of a reaction wheel assembly

Reaction wheel assemblies (RWAs) are a source of disturbance in satellites, and they are regarded as the largest jitter contributor in optical payloads. In order to ensure a stringent jitter requirement, the wheel disturbance effects on spacecraft should be predicted precisely prior to launch through analytical or experimental approaches. For this purpose, the wheel disturbance should be identified and modeled accurately. In the present study, a micro-vibration model of the RWA is introduced through coupling an analytical wheel model and an empirical disturbance model; furthermore, a parameter estimation process of the coupled model from the micro-vibration disturbance data is proposed. In order to verify the modeling and estimation techniques, a micro-vibration model of a numerical RWA is established and its estimation error is validated. Then, the micro-vibration model is extended to consider an axial disturbance and a measurement offset effect. Finally, the micro-vibration model is applied to a commercial RWA and the model parameters are extracted from the disturbance test data of the RWA using the parameter estimation process. The analytical and experimental results demonstrate that the proposed micro-vibration model and parameter estimation process are effective in the dynamic disturbance modeling of RWAs.     

Effect of dissipation and reservoir temperature on squeezing exchange and emergence of entanglement between two coupled bosonic modes

We study the effect of a thermal reservoir on the squeezing transfer and entanglement between two identical harmonic oscillators, caused by a bilinear coupling of the RWA type. We analyze the evolution of the invariant squeezing coefficients of each mode for arbitrary initially factorized mixed states, as well as the separability coefficient based on Simon's criterion for Gaussian states. We show the importance of initial squeezing for the emergence of entanglement and the existence of critical temperatures above which no squeezing transfer or entanglement are possible.     

Chaotic behavior in quantum optics and the failure of the Rotating-Wave Approximation at high intensities

We consider the semiclassical theory of a collection of two level atoms interacting with a single mode electric field. In this model the in quantum optics usually applied RWA fails at high field intensities. It is shown that the theory without applying the RWA can lead to a chaotic behavior, which can be described by a parametrically forced pendulum equation. The dynamics become more and more complicated if the electric field is increased. For extremely high intensities we obtain again a regular behavior described by a pendulum equation with a modified potential. In this case the dynamics is greatly different from the results obtained within RWA.     

DEVELOPMENT AND VALIDATION OF REACTION WHEEL DISTURBANCE MODELS: EMPIRICAL MODEL

Accurate disturbance models are necessary to predict the effects of vibrations on the performance of precision space-based telescopes, such as the Space Interferometry Mission (SIM). There are many possible disturbance sources on such spacecraft, but mechanical jitter from the reaction wheel assembly (RWA) is anticipated to be the largest. A method has been developed and implemented in the form of a MATLAB toolbox to extract parameters for an empirical disturbance model from RWA micro-vibration data. The disturbance model is based on one that was used to predict the vibration behaviour of the Hubble Space Telescope (HST) wheels and assumes that RWA disturbances consist of discrete harmonics of the wheel speed with amplitudes proportional to the wheel speed squared. The MATLAB toolbox allows the extension of this empirical disturbance model for application to any reaction wheel given steady state vibration data. The toolbox functions are useful for analyzing RWA vibration data, and the model provides a good estimate of the disturbances over most wheel speeds. However, it is shown that the disturbances are under-predicted by a model of this form over some wheel speed ranges. The poor correlation is due to the fact that the empirical model does not account for disturbance amplifications caused by interactions between the harmonics and the structural modes of the wheel. Experimental data from an ITHACO Space Systems E-type reaction wheel are used to illustrate the model development and validation process.     

RWA方法对WDM网络P圈优化性能的影响

研究不同的路由和波长分配（RWA）方法对无波长变换WDM网络P圈优化性能的影响.提出了用负载均衡的方法对各波长层的工作容量进行均衡,以降低网络总容量.分别研究了动态分层通用RWA（DL-GRWA）、最短路径RWA（SP-RWA）、动态分层负载均衡（DL-LB）、最短路径负载均衡（SP-LB）、固定波长负载均衡（FW-LB）5种方法对网络总容量的影响.仿真发现,无论何种RWA方法,随着圈最大跳数限制的变大,网络总容量都逐渐降低,其中SP-LB方法所需要的网络总容量最小.