Chaotic dynamics of coupled two-level atoms in the optical cavity

Spin systems are one of the most promising candidates for quantum computation. At the same time, control of a system's quantum state during time evolution is one of the main problems. It is usually considered that in magnetic resonance the so-called resonance condition is sufficient to control the spin system. However, because of the nonlinearity of the system, obstructions to the control of the system's quantum state may emerge. In particular, the quantum dynamics of coupled two-level atoms in the optical cavity are studied in this work. The problem under consideration is a generalization of the paradigmatic model for Cavity Quantum Electrodynamics of the Jaynes-Cummings model in the case of interacting spins. In this work, it is shown that the dynamics are chaotic when taking into account the center-of-mass motion of the system and the recoil effect. Furthermore, even in the case of zero detuning, chaotic dynamics emerge in the system. It is also shown in this work that, because of the chaotic dynamics the system executes an irreversible transition from a pure quantum-mechanical state to a mixed one. Irreversibility, in turn, is an obstacle for controlling the state of the quantum-mechanical system.     

Quantum model of the Thomson helium atom

A quantum model of the Thomson helium atom is considered within the framework of stationary perturbation theory. It is shown that from a formal point of view this problem is similar to that of two-electron states in a parabolic quantum dot. The ground state energy of the quantum Thomson helium atom is estimated on the basis of Heisenberg’s uncertainty principle. The ground state energies obtained in the first order of perturbation theory and qualitative estimate provide, respectively, upper and lower estimates of eigenvalues derived by numerically solving the problem for a quantum model. The conditions under which the Kohn theorem holds in this system, when the values of resonance absorption frequencies are independent of the Coulomb interaction between electrons, are discussed.     

Generation of Entangled Coherent States in Circuit-QED

We study theoretically the generation of entangled states of microwaves in a circuit quantum electrodynamics (QED) system. Our system includes a transmission-line resonator and a Cooper-pair box which acts as an artificial atom. It is shown that in the dispersive regime of the circuit-QED system, a cross-Kerr interaction can be obtained by properly preparing the initial state of the qubit. Based on this cross-Kerr interaction, we show that the coherent coupling of the two lowest-lying cavity modes through the qubit can generate a macroscopic entangled state.     

压缩真空中的三能级原子的自发辐射强场高次谐波时间特性的理论分析

对压缩真空与V型三能级原子的相互作用作了理论分析, 探讨了量子干涉效应对压缩真空中原子自发辐射的影响。当原子的上能级简并时强的量子干涉效应影响原子的定态和定态出射光谱, 使它们对原子的初态敏感。这种情况下, 压缩使谱线趋于关于压缩真空中心频率对称, 量子干涉使谱线趋于不对称。通过用单电子近似求解含时薛定谔方程, 用加窗傅里叶分析的方法, 分析了单原子产生的高次谐波的时间特性。理论分析表明, 基态粒子数消耗对不同级次谐波辐射的影响程度不一样; 谐波辐射随着入射激光场强度的增加会出现饱和; 随着谐波级次的增加, 谐波辐射越来越趋向于集中在更短的时间间隔内, 相应的线宽也随着谐波级次的增加而增加。     

Electrodynamics and thermodynamics of a paramagnetic system in a metallic resonator

The well-known problem of the phase transition in a two-level system coupled with the radiation field of a resonator is considered subject to the conduction electrons of the resonator walls. It is shown that the conduction electrons are important for consideration of the high-frequency properties of the system to cut off the frequency spectrum of the radiation field at the plasma frequency. In the vicinity of the phase transition the conduction electrons lead to the damping of the soft mode.     

Correlation or decoherence? Quantum beats of atomic inversion in a resonant coherent field

It is shown that the standard reduction procedure (i.e., the calculation of the density matrix of the observable subsystem from the density matrix of a closed quantum system) bringing about decoherence corresponds to the limiting approximation, where the unobservable subsystem is assumed to be in the stationary state with minimum information (infinite temperature). An approximate set of interrelation (correlation) equations for the density matrices of the subsystems is derived. It is shown that the correlation of atom and field can be manifested as the inversion beats of a two-level atom in the known experimental scheme of resonator QED. Experimental observation of such beats would indicate that the observable subsystem (atom) generally conserves information about quantum coherence of the unobservable subsystem (field).     

Numerical simulation of gas bubble motion in a flow-through resonator

The problem of gas bubble motion in an acoustic resonator with a fluid flow is solved using numerical methods. It is shown that the distribution of the bubble concentration, which is nonuniform over the resonator length, is formed upon homogeneous introduction of bubbles. The problem on the bubble concentration distribution the along the resonator axis (with fluctuations of the bubble introduction period taken into account) is considered, and the fluctuation parameters are determined at which the periodic structure of the concentration distribution is preserved. The distribution of bubbles with different sizes over the resonator length is determined. It is shown that a resonator with a fluid flow accomplishes bubble selection by size (the average bubble concentration in the resonator increases with an increase in bubble size). The field in the resonator was calculated taking into account the effect of bubbles on sound velocity and damping.     

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.     

二能级原子体系的二项式态

本文引进二能级原子体系能够的产生二项式分布的二项式态,讨论了它的产生及其压缩、反聚束和亚泊松统计特性,在一定的极限下,二项式态趋于Glauber相干态,此时二项式分布也趋于泊松分布。这一极限使体系的一切非经典效应消失。同时采用Bloch矢量模型讨论了单原子一般二项式态的量子特性。最后把原子体系的二项式态与玻色子体系的二项式态作了比较,并指出二能级原子体系中并不能产生玻色子二项式态。 关键词：     

Dynamics of Entropy and Nonclassicality Features of the Interaction between a ◊-type Four-Level Atom and a Single-Mode Field in the Presence of Intensity-Dependent Coupling and Kerr Nonlinearity

The interaction between a ◊-type four-level atom and a single-mode field in the presence of Kerr medium with intensity-dependent coupling involving multi-photon processes has been studied. Using the generalized (nonlinear) Jaynes-Cummings model, the exact analytical solution of the wave function for the considered system under particular condition, has been obtained when the atom is initially excited to the topmost level and the field is in a coherent state. Some physical properties of the atom-field entangled state such as linear entropy showing the entanglement degree, Mandel parameter, mean photon number and normal squeezing of the resultant state have been calculated. The effects of Kerr medium, detuning and the intensity-dependent coupling on the temporal behavior of the latter mentioned nonclassical properties have been investigated. It is shown that by appropriately choosing the evolved parameters in the interaction process, each of the above nonclassicality features, which are of special interest in quantum optics as well as quantum information processing, can be revealed.     

Quantum theory of a dissipative oscillator

The nonlinear equation of dissipative quantum mechanics is considered in the relaxation-time approximation. It is shown that the steady current-free state does not change when dissipation is taken into account; in particular, there is no ground-state damping, and the zero energy is conserved. A solution is obtained to the problem of the excitation of a harmonic oscillator, serving as a model of single-mode radiation in an open resonator; the solution obtained describes the evolution of the oscillator from an arbitrary steady state under the action of a constraining force. Transition probabilities between the oscillator steady states are calculated. The results are found to be in agreement with the classical theory of damping oscillations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 99–105, September, 1978.     

Electromagnetically induced transparency and light slowdown for Λ-like systems with a structured continuum

Electric susceptibility of a laser-dressed atomic medium is calculated for a model Λ-like system including two lower states and a continuum structured by a presence of an autoionizing state or a continuum with a laser-induced structure. Depending on the strength of a control field, it is possible to obtain a significant reduction of the light velocity in a narrow frequency window in the conditions of a small absorption. It is shown that increasing the values of the asymmetry parameters leads to an increase of the values of both real and imaginary parts of the medium susceptibility and to an increase of the width of the transparency window, compared with the case of a flat continuum. A smooth transition is shown between the case of a flat continuum and that of a discrete state serving as the upper state of a Λ system.     

Fractal walk and walk on fractals

The one-dimensional walk of a particle executing instantaneous jumps between the randomly distributed “atoms” at which it resides for a random time is considered. The random distances between the neighboring atoms and the time intervals between jumps are mutually independent. The asymptotic (t → ∞) behavior of this process is studied in connection with the problem of interpretation of the generalized fractional diffusion equation (FDE). It is shown that the interpretation of the FDE as the equation describing the walk (diffusion) in a fractal medium is incorrect in the model problem considered. The reason is that the FDE implies that the consecutive jumps (fractal walk) are independent, whereas they are correlated in the case under consideration: a particle leaving an atom in the direction opposite to the preceding direction traverses the same path until arriving at the atom.     

Acoustic coupling between the loudspeaker and the resonator in a standing-wave thermoacoustic device

Thermoacoustic refrigerators work with high amplitude sound waves, which are often created using an acoustic source coupled to a resonator. This coupling can be calculated analytically using linear acoustic equations and a linear model of the loudspeaker. This paper makes a comparison between such a coupling and measurements obtained in a large-scale thermoacoustic resonator constructed at the University of Manchester. The resonator was driven from low to large pressure amplitudes, with drive ratios up to 10%. It is shown that a good agreement is obtained for small amplitudes and this progressively worsens as the amplitude is increased. In the absence of wave harmonics and loudspeaker nonlinearities, the increasing discrepancy is attributed to the presence of minor losses.     

The roles of vibronic coupling and the Duschinsky effect in resonance Raman scattering

In most vibronic treatments of resonance Raman scattering it is assumed that the normal coordinates of electronically excited states are not rotated relative to those of the ground state, i.e., the Duschinsky effect is neglected. In the present paper this assumption is critically examined for the case of resonance Raman scattering by a non-totally symmetric vibrational mode. For consistency also the second-order Herzberg-Teller coupling is considered. It is shown that these second-order couplings introduce asymmetry in the excitation profile of appearance similar to that due to nonadiabatic coupling. Also it is shown that even small rotations give rise to noticeable effects in the polarization dispersion curve. Analytical formulas for the Franck-Condon factors and for the Raman tensor (valid for an arbitrary number of normal modes) for the case of small rotations are given, and illustrative calculations of excitation and polarization dispersion curves for a two mode system are presented and discussed.     

Study of Nonclassical Features and Quantum Dynamics in the Jaynes-Cummings Model

Some nonclassical features, including photon antibunching, atomic squeezing and quantum collapse-revival phenomenon, were numerically studied in thp vacuum field Jaynes-Cummings model (JCM). The influence of the initial atomic coherence on these features was discussed. It is shown that the squeezing can appear only if the atom is initiaJly prepared in the coherent state, and photon antibunching cHn occur if the atom is initially in the excited state or the coherent one. The effect of the virtual-photon field was studied in JCM without the rotating-wave approximation (ftWA). We have shown that even undh the condition in which RWA is considered to be valid, there are significant effects on the nonc1assical features due to the interference between the virtual-photon processes and the real-photon processes. Quantum dynamics of JCM without RWA was aJso studied. We showed that regular dynamical behavior is exhibited in the cases rather close to the integrable limits, and irregular dynamical behavior is presented in the cases far from the integrable limits; in addition, all the nondassical features disappear in the cases far from the integrable limits.     

A note on safety-relevant vibrations induced by brake squeal

Brake squeal is mostly considered as a comfort problem only but there are cases in which self-excited vibrations of the brake system not only cause an audible noise but also result in safety-relevant failures of the system. In particular this can occur if lightweight design rims having very low damping are used. Considering the special conditions of lightweight design rims, a minimal model for safety-relevant self-excited vibrations of brake systems is presented. It is shown that most of the knowledge emanated from investigations of the comfort problem can be used to understand and avoid safety-relevant failures of the brake system.     

Identification of quantum cross correlations between light and an atom scattered in the field of a standing wave

To identify quantum cross correlations between a two-level atom and a cavity mode, the scattering of the atom on a standing light wave has been considered. It has been shown that, under coherent scattering conditions, a strong effect distinguishing the correlated state of the system from an independent state is observed.     

The interference between a giant atom and an internal resonator

The Jaynes–Cummings model plays an important role in quantum entanglement and state measurements. Here, we discuss how to realize it in a waveguide-mediated interaction system, which comprises a giant atom and a resonator. We show the vacuum Rabi splitting and discuss how to achieve a unidirectional transport. We extend the Purcell effect in cQED to this waveguide QED system, showing how to control the giant atom decay rate. Our design can further be built experimentally and has application in quantum manipulation.