Chaos Generation in Opto-Mechanical Coupling System Assisted by Two-Level Atoms

Chaos is important in nonlinear science and promotes the development of fundamental studies, such as neural networks, extreme event statistics, and electron transport. In this paper, a theoretical scheme for generating dynamical chaos in a Fabry–Perot cavity with two-level atoms is investigated. Through the injection of atoms, controllable chaos of the cavity and mechanical oscillator is achieved simultaneously by the external laser field. The trajectory and the maximal Lyapunov exponent that characterize the properties of the chaos could be optimized by adjusting the coupling constant, driving field, injection of atoms, the frequency of the cavity, and the frequency of the mechanical oscillator. This study provides a new idea to manipulate the cavity and mechanical chaos assisted by two level atoms. It is hoped that the results presented can benefit controllable chaos generation and its applications.     

Coupled-channel cavity QED model and Semi-classical solution

A semi-classical scheme is presented to solve the coupled-channel cavity QED (CQED) model. Such model exhibits remarkable characteristics as shown by numerical calculations. A relation between the swing or angular velocity of the detuning and the motion of the atoms is discussed. With the augmentation of the optical field intensity or frequency, the atoms are trapped firstly and then they move stochastically and finally chaos sets in.     

Dynamical complexity in a quantum-optical model with a simple lie-algebraic structure

The evolution of a quantum-optical system, possessing the SU(2) dynamical symmetry and consisting of an ensemble of two-level atoms that move through a single-mode high-quality cavity, is investigated. Even in the rotating-wave approximation, the system can demonstrate very complicated semiclassical dynamics that is shown to be chaotic in the sense of extreme sensitivity to initial conditions. It is shown that the respective equations of motion can be transformed to a parametrically perturbed complex Duffing equation. The homoclinic structure is found for an integrable version of the system with atoms at rest. Numerical simulation confirms that perturbations, produced by a modulation of the coupling between moving atoms and a cavity mode, provide a mechanism responsible for chaos.     

Intermittency and dynamical chaos in reversible spontaneous emission

It is shown that a type of reversible spontaneous emission, the chaotic vacuum Rabi oscillations, may occur in the interaction of two-level atoms strongly coupled with a single cavity mode under a modulation of the atom-field coupling. Such a modulation arises naturally if the atoms move through a cavity in maserlike experiments. The existence of homoclinic chaos in reversible spontaneous emission is proven analytically. Evidence of intermittency associated with the spatial modulation of the vacuum Rabi frequency is shown numerically for the values of parameters that are achievable in present-day experiments with Rydberg atoms moving through a high-Q microwave cavity in the strong-coupling regime.     

Chaos in an electromagnetically induced transparent medium inside an optical cavity

We theoretically predict and experimentally demonstrate chaotic behaviors in a system comprising of three-level atoms inside an optical ring cavity. This electromagnetically induced transparency (EIT) system is driven to chaos through period-doubling route by reducing the frequency detuning of the coupling laser beam. The chaos occurs in a different parametric regime as previously predicted and is believed to be caused by the enhanced dispersion and nonlinearity due to induced atomic coherence in such EIT system.     

包含三能级原子环形腔的动态非稳与混沌过渡

在包含三能级原子的环形腔的输出光场中，观察到了由电磁感应透明（EIT）效应导致的动态非稳及混沌．该动态非稳及向混沌的过渡可以通过耦合光场而加以很好地控制．同时，由三能级EIT导致的原子相干改变了系统的吸收、色散及非线性效应，从而极大地增强了系统的动态非稳和混沌过渡特性．建立了一个理论模型来定量地解释观察到的现象．     

A mechanism of emergence of Hamiltonian chaos in a basic quantum-optical model

A mechanism of emergence of Hamiltonian chaos is considered for the model describing the interaction between two-level atoms and their own radiation field in an ideal single-mode cavity. The analysis of the semiclassical Maxwell-Bloch equations shows that the Hamiltonian terms that are neglected in the rotating-wave approximation (RWA) give rise to the formation of a stochastic layer near the RWA-system separatrix. The Mel’nikov method is used to prove that the splitting of the separatrix takes place for arbitrarily small vacuum Rabi frequencies Ω_N. The computation of Poincare sections shows that the stochastic layer, which is exponentially narrow for small Ω _N, expands with increasing Ω_N, and at Ω_N ? 1, the system exhibits global chaos that manifests itself in irregular oscillation of the atomic population inversion and the broadening of the power spectrum. Promising candidates for observing manifestations of dynamic chaos in this basic quantum-optical system are Rydberg atoms placed in a high-Q superconducting microwave cavity.     

Normal mode splitting in hybrid BEC-optomechanical system

We consider an opto-mechanical cavity system consisting of Bose-Einstein condensate (BEC), trapped inside the optical cavity and driven by single mode laser field. The intracavity field acts as nonlinear spring which couples the condensate mode with moving end mirror of the cavity. We study the occurrence of normal mode splitting in the position spectra of the mechanical oscillator and condensate mode as a consequence of hybridization of the fluctuations of intracavity field, mechanical mode and condensate mode. We also discuss the modification in the dynamics of the mechanical oscillator due to frequency of the collective oscillations of cold atoms and the back action of the atoms on the mechanical mirror. Moreover, we investigate the normal mode splitting in the transmission spectrum of cavity field.     

Parametric instability and Hamiltonian chaos in cavity semiclassical electrodynamics

We study the nonlinear dynamics of the interaction of two-level atoms and a selected mode of a high-Q cavity with frequency modulation analytically and numerically. In the absence of modulation, the corresponding semiclassical Heisenberg equations for the expectation values of the collective atomic observables and the field-mode amplitudes allow, in the rotating wave approximation and in the strong-coupling limit, an exact solution with arbitrary detuning. Using this solution, we detect the coherent effect of trapping of the population of atomic levels and of trapping of the number of photons in the cavity. The explanation for this effect lies in the destructive interference of the atomic dipoles and the field mode. The integrable version of the system of equations exhibits a separatrix near which a stochastic layer is formed when modulation is introduced. The width of the layer is found to gradually increase with degree of modulation, and finally it fills the entire energy-permissible volume of the phase space. We show that the rotating wave approximation does not hinder the formation of Hamiltonian chaos in cavity semiclassical electrodynamics. The calculation of the maximum Lyapunov indices of nonlinear (in this approximation) equations of motion as functions of the modulation frequency δ and the frequency of natural Rabi oscillations of the atom-field system, Ω, suggests that Hamiltonian chaos appears first in the area of the fundamental parametric resonance, δ/2Ω≃1. Parametric instability increases with increasing modulation and decreasing detuning from the atom-field resonance, generating at exact resonance new areas of chaos corresponding to multiple parametric resonances. The results of numerical experiments and estimates of the characteristic parameters show that Rydberg atoms placed in a high-Q microwave cavity are possible objects for observing parametric instability and dynamical chaos. Zh. éksp. Teor. Fiz. 115, 740–753 (February 1999)     

Quantum chaos of atoms in a resonant cavity

A system of atoms interacting with a radiation field in a resonant cavity is studied under conditions when the dynamics in the classical limit is stochastic. This situation is called quantum chaos. Equations of motion are obtained for the quantum-mechanical expectation values which take into account the quantum correlation functions. It is shown that in a situation corresponding to quantum chaos, the quantum corrections grow exponentially, making the evolution of the system essentially quantal after a certain time tau( variant Planck's over 2pi ) has elapsed. Analytical and numerical analysis show that in this regime the time tau( variant Planck's over 2pi ) obeys the logarithmic law tau( variant Planck's over 2pi ) approximately ln N (N is the number of atoms), and not the law tau( variant Planck's over 2pi ) approximately N(alpha) (alpha is a certain constant of order unity), as would be the case in the absence of chaos.     

Chaos, fractals, and atomic flights in cavities

A semiclassical study is carried out of the nonlinear interaction dynamics between two-level atoms and a standing-wave field in a high-finesse cavity. As a result of atomic movement or wave amplitude modulation, a dynamic local instability occurs in a strongly coupled atom-field system. The appearance of dynamical Hamiltonian chaos, fractals, and Lévy flights is demonstrated for the models of two experimental devices: a (micro)maser with thermal Rydberg atoms and a microlaser with cold atoms. Numerical simulation showed that the manifestations of classical chaos, atomic fractals, and flights can be observed in the appropriate real experiments. Attention is drawn to the prospects provided by work on the atom-field systems in the coupling-modulated high-finesse cavities for further investigation of the quantum-classical correspondence, quantum chaos, and decoherence.     

Tunable second-order sideband effects in hybrid optomechanical cavity assisted with a Bose—Einstein condensate

We theoretically investigated a second-order optomechanical-induced transparency (OMIT) process of a hybrid optomechanical system (COMS), which a Bose—Einstein condensate (BEC) in the presence of atom—atom interaction trapped inside a cavity with a moving end mirror. The advantage of this hybrid COMS over a bare COMS is that the frequency of the second mode is controlled by the s-wave scattering interaction. Based on the traditional linearization approximation, we derive analytical solutions for the output transmission intensity of the probe field and the dimensionless amplitude of the second-order sideband (SS). The numerical results show that the transmission intensity of the probe field and the dimensionless amplitude of the SS can be controlled by the s-wave scattering frequency. Furthermore, the control field intensities, the effective detuning, the effective coupling strength of the cavity field with the Bogoliubov mode are used to control the transmission intensity of the probe field and the dimensionless amplitude of the SS.     

利用原子与SU(2)相干态腔场的Raman相互作用制备原子纠缠态

利用一个参量频率转换过程,在腔中制备双模SU(2)相干态,然后注入一系列全同的Λ型三能级原子,这些原子与腔场的一个模发生拉曼相互作用,通过系列原子-腔场相互作用生成腔场-原子纠缠态,通过对腔场进行选择性测量,可获得多种形式多原子纠缠态.     

Anticontrol of Quantum Chaos in Hamiltonian Systems

We present a method of realizing anticontrol chaos in a quantum confined system consisting of N two-levelatoms within a cavity, using a time-delayed optic field. The delay time plays a construction and organization role forproducing temporal chaos, while the interaction between atoms and photons creates spatial chaos. The chaos is quitesensitive to small time delayed. The spectral decomposition of the Hamiltonian obtained by using projection methodologyreveals that evolution of the left eigenvectors shows quite complicated chaotic fashions. The method we proposed maybe easily tested in experiment, and provides a general method using a sort of driving optic field to achieve anticontrol ofchaos for quantum systems.     

速度调控的双原子纠缠

当光学腔中光场处于相干态,而原子处于运动中时,双原子的纠缠演化与光学腔场模结构相关联. 假如初始时刻原子的位置固定在腔中某一位置,双原子的纠缠演化将是无序的.然而,假如一开始双原子在光学腔相干态光场中处于运动状态,则双原子的纠缠随时间的变化将变得规则有序.如此,通过适当的选择双原子的速度和初始光场,就能对双原子的周期性纠缠进行控制,让纠缠在指定时刻出现.     

Generation of Maximally Entangled States of Two Nonidentical Atoms in Cavity QED

We have discussed the system which consists of two nonidentical two-level atoms trapped simultaneously in a large-detuned single-mode cavity field in this paper. The results show that it is possible to generate maximally entangled states for two nonidentical two-level atoms only if the cavity frequency and difference of two nonidentical atoms transition frequency are selected and the cavity-atom interacation time is controlled.     

Generation of Maximally Entangled States of Two Nonidentical Atoms in Cavity QED

We have discussed the system which consists of two nonidentical two-level atoms trapped simultaneously in a large-detuned single-mode cavity field in this paper. The results show that it is possible to generate maximally entangled states for two nonidentical two-level atoms only if the cavity frequency and difference of two nonidentical atoms transition frequency are selected and the cavity-atom interacation time is controlled.     

Exact results on cavity cooling in a system of a two-level atom and a cavity field

Using the algebraic dynamical method, this paper investigates the laser cooling of a moving two-level atom coupled to a cavity field. Analytical solutions of optical forces and the cooling temperatures are obtained. Considering Rb atoms as an example, it finds that the numerical results are relevant to the recent experimental laser cooling investigations.     

Generation of higher degree chaos by controlling harmonics of the modulating signal in EDFRL

Erbium doped fiber ring lasers (EDFRL) are being used to generate optical chaos for secure communication by modulating the cavity loss/pump power or exploiting nonlinearities. The security level in chaotic communication depends on degree of chaos quantified by the Lyapunov exponent and its variability which is determined by the number of tuneable system parameters which were limited to five main parameters, i.e. modulation index, modulation frequency, pump power, cavity gain and loss. In this study we have increased the number of tuneable parameters using square, triangular and sum of harmonics waveforms. We have analysed the effect on degree of chaos of phase and duty cycle of square modulating signal with gradual addition of harmonics. For the given cavity parameters, the Lyapunov exponents can be increased by more than fifteen times using square wave modulating signal and a duty cycle of 60%. The electrical parameters identified make generation of new chaotic sequences more flexible in a field deployed EDFRL chaotic system.     

Virtual Photon Effects on Chaos in Generalized Lorenz-Haken Equation

The dynamics of an ensemble of two-level atoms injected into a single-mode cavity is studied in the exact atom-field interaction situation, in which the counter-rotating terms describing the so-called virtual photon processes neglected in the rotating-wave approximation, are considered. The cavity mode is driven by the injected classical field,and the atom is prepared in a coherent superposition of the two levels. We first derive the generalized Lorenz-Haken equation by using the technique of quantum Langevin equation, and then numerically study the dynamics of this equation.We find that the virtual photon processes have strong effects on the dynamics, which can cause the trajectory in phase space of strange attractor spiral around four focus points, and the trajectory is modulated by virtual photon processes.The chaos region in parameter space is now enlarged. It should be stressed that the strange attractor can exist in optical bistability, and whether the atomic coherences and classical field can inhibit chaos depends on the laser frequency.