对称双势阱玻色-爱因斯坦凝聚系统在周期驱动下的动力学相变及其量子纠缠熵表示

研究了在对称双势阱玻色-爱因斯坦凝聚体系粒子间相互作用项上外加周期调制而引起的系统动力学相变,特别地研究了该系统通向混沌的相变过程.发现在一定驱动参数下,当外加调制频率与系统固有频率达到共振时,相平面会出现不稳定性现象,即混沌.在混沌区域,粒子在各量子态随机分布,平均布居数差在零附近波动.特别地,研究表明,混沌现象的出现可以用量子纠缠熵来表征,混沌现象出现时,两种平均纠缠熵都趋于它们的最大值. 关键词： 玻色-爱因斯坦凝聚 双势阱 混沌 纠缠熵     

对称双势阱玻色-爱因斯坦凝聚系统在周期驱动下的动力学相变及其量子纠缠熵表示

研究了在对称双势阱玻色-爱因斯坦凝聚体系粒子间相互作用项上外加周期调制而引起的系统动力学相变，特别地研究了该系统通向混沌的相变过程.发现在一定驱动参数下，当外加调制频率与系统固有频率达到共振时，相平面会出现不稳定性现象，即混沌.在混沌区域，粒子在各量子态随机分布，平均布居数差在零附近波动.特别地，研究表明，混沌现象的出现可以用量子纠缠熵来表征，混沌现象出现时，两种平均纠缠熵都趋于它们的最大值.     

Two unstable oscillations in the multimode laser with modulated inversion

We present comprehensive results of numerical studies on the dynamical properties of a multimode ring laser under modulation of the population inversion in the bad-cavity condition. Incoherent properties of unstable oscillations in this system are investigated in detail as a function of two control parameters: the dc component of the population inversion and the modulation amplitude. Two kinds of optical chaos in two limiting regions reported in a previous paper are extensively studied to clarify their different characteristics from deterministic and stochastic points of view. The competition between their different origins is revealed. Statistical properties of their stochasticity are investigated to clarify their non-Gaussian natures. Comparison with analytical results for a single-mode laser with fluctuations is also made.     

激光回馈引起的微片Nd:YAG激光器频差调制

微片激光器由于自身的内应力会输出频率分裂的正交偏振的两个模式.研究了回馈对微片激光器频差的影响.研究发现:在回馈的作用下微片激光器的频差大小呈现出以初始频差为中心的类正弦的频差调制,周期为λ/2;频差调制曲线的幅度与回馈水平成正比,但是当回馈水平过强时会出现偏振态跳变,从而使频差消失;在一定的回馈外腔范围内,频差调制曲线的幅度与初始频差亦成正比.并利用复合腔模型和激光器的自洽理论进行了理论分析和模拟,所得结果与实验结果相符.此调制现象在精密测量领域有潜在应用.     

Effect of Phase Shifted Frequency Modulation on Two Level Atom-Field Interaction

We have studied the effect of phase shifted frequency modulation on two level atom with field interaction using Jaynes-Cummings model.Here the frequency of the interacting field is sinusoidally varying with time with a constant phase.Due to the presence of phase in the frequency modulation,the variation of population inversion with time is different from the standard case.There are no exact collapses and revivals in the variation of population inversion but it oscillates sinusoidally with time.In coherent field atom interaction the population inversion behaves as in the case of Fock state atom interaction,when frequency modulation with a non zero phase is applied.The study done with squeezed field has shown the same behavior of the population inversion.     

Dynamic theory of an optical transistor

The amplification of a modulation by an optical transistor is shown to depend on the modulation frequency. At high frequency there is no amplification whereas at low frequency the expected amplification occurs. The critical frequency which separates these two domains depends on the modulation amplitude. These results are derived analytically for purely dispersive optical bistability in the bad cavity case. The modulation can be applied to the holding beam, to the refraction index or to the detuning with similar results for the output field intensity.     

Dynamical Casimir effect in superradiant light scattering by Bose–Einstein condensate in an optomechanical cavity

We investigate the effects of dynamical Casimir effect in superradiant light scattering by Bose-Einstein condensate in an optomechanical cavity. The system is studied using both classical and quantized mirror motions. The cavity frequency is harmonically modulated in time for both the cases. The main quantity of interest is the number of intracavity scattered photons. The system has been investigated under the weak and strong modulations. It has been observed that the amplitude of the scattered photons is more for the classical mirror motion than the quantized mirror motion. Also, initially, the amplitude of scattered photons is high for lower modulation amplitude than higher modulation amplitude. We also found that the behavior of the plots are similar under strong and weak modulations for the quantized mirror motion.     

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)     

Study of Some Properties of Two-Level Atom in Quantum Optics

With the concept of negative photon and the K-photon J C model, we investigate analytically the effect of virtual photon field on the collapse revival effect of atomic inversion and squeezing of atom, we find that there is a significant effect of virtual photon field on atomic inversion and squeezing of atom; with the one-photon model as an example, we find that the squeezing of atom occurs periodically, the time and times of squeezing are only related to the resonance frequency and the amplitude of squeezing related to coupling constant of atom field, mean photon number and resonance frequency; also we show that the effect of squeezing of atom does not exist within rotating wave approximation if K≥3. Taking the approach of nearest-neighboring spectrum in the quantum chaos field, we investigate the properties of energy spectrum in one-photon JC model and show that the integrable region,non-integrable region and transition region of this system can be illustrated by a phase diagram;also we discuss the influence of interaction of atoms on spectrum and Δ₃ statistics of adjacent energy levels, we find that the influence of interaction is little obvious in strong field but takes great important role in weak field.     

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.     

Synchronization of homoclinic chaos

Homoclinic chaos is characterized by regular geometric orbits occurring at erratic times. Phase synchronization at the average repetition frequency is achieved by a tiny periodic modulation of a control parameter. An experiment has been carried on a CO(2) laser with feedback, set in a parameter range where homoclinic chaos occurs. Any offset of the modulation frequency from the average induces phase slips over long times. Perfect phase synchronization is recovered by slow changes of the modulation frequency based upon the sign and amplitude of the slip rate. Satellite synchronization regimes are also realized, with variable numbers of homoclinic spikes per period of the modulation.     

HIRFL数字化高频低电平控制系统研究

在HIRFL加速器系统中, 需要对射频加速电压的幅度和相位进行精确控制,以实现对重离子的精确俘获、 加速和引出。传统的幅度、相位稳定控制系统采用幅度和相位两个反馈闭合环路来分别稳定腔体电压的幅度和相位。 数字化高频低电平控制系统(LLRF) 基于可编程逻辑门阵列（FPGA）和数字信号处理（DSP）, 采用直接数字频率合成（DDS）与数字正交调制解调（I/Q）技术来实现对高频功率源的控制。 相位控制精度更高, 系统更加稳定。 目前控制系统在假负载上通过了长期稳定性的实验和高功率实验, 幅度偏差小于或等于±1％, 相位偏差小于或等于±0.5°。 In order to ensure that the beam quality is well enough, we need to precisely control the frequency, amplitude and phase of cavity electric field. Traditional control system consists of amplitude loop and phase loop. And these two loops control amplitude and phase stability respectively. The digital low level radio frequency (LLRF) system, which uses advanced digital control technology, needs only one feed back loop to control amplitude and phase stability. The phase control precision and stability of the system are higher than the traditional control system. The LLRF system is based on field programmable gate array (FPGA) and digital signal processing (DSP), and implemented by direct digital frequency synthesis (DDS) and digital orthogonal modulation and demodulation (I/Q) technology. The digital LLRF system has been tested in a long term stability and high power experiments. The amplitude deviation is lower than ±1%, and phase control accuracy is within ±1°.      

Modulation Frequency Characteristics of Erbium-Doped Fiber Amplifier

The modulation frequency characteristics of an erbium-doped fiber amplifier are analyzed theoretically and experimentally for various values of modulation frequency. The theoretical predictions by the approximate equations in the low and high frequency modulation and that by the Runge-Kutta method for all modulation frequencies are in good agreement with the experimental results. In the low frequency modulation, the population inversion is depleted because of the saturation effect due to the instantaneous power of the incident light, and a distorted output is obtained without phase delay. In the high frequency modulation, the linear amplification is obtained with the gain depletion determined by the time averaged power of the incident signal. In the intermediate frequency modulation, the highly distorted output is obtained with phase delay.     

Theory of an intracavity Raman laser

The quantum mechanical Langevin equations of a cavity where laser action takes place both by ordinary population inversion and stimulated Raman scattering is discussed for both single mode and multimode oscillation of the pump and Raman laser. Expressions for amplitude correlation and linewidth due to phase diffusion are obtained both for homogeneous and inhomogeneous broadening.     

Controlling nonclassical properties of the two-photon process by a time-varying field

The interactions between a two-level atom and a field via two-photon transition without rotating wave approximation have been investigated. We emphasize the dynamic behaviors of the atomic population inversion, the field squeezing, and the atomic dipole squeezing numerically when the field frequency varies with time in the forms of sine and rectangle. Some interesting phenomena are discovered and discussed. The good periodic character of the atomic population inversion in the standard two-photon Jaynes--Cummings model is weakened by the influence of the sine field frequency modulation. The rectangular field frequency modulation can change the correlation among different oscillations suddenly and induce new collapse-revival processes of the atomic population inversion. The field squeezing increases at the beginning of time, but then decreases and loses as the time increases after it reaches the maximum due to the sine modulation. The effects of the rectangular modulation on the field squeezing depend mostly on the appearance time of the modulation. The atomic dipole squeezing is weakened under the influence of the sine or rectangular modulation. Our results indicate that it is possible to perform the dynamic controlling of the system properties by changing the parameters of the system with time. This implies that one can dynamically control a quantum information process by choosing the system modulation properly.     

Semiclassical interaction of moving two-level atoms with a cavity field: from integrability to Hamiltonian chaos

The dynamics of an ensemble of two-level atoms moving through a single-mode lossless cavity is investigated in the semiclassical and rotating-wave approximations. The dynamical system for the expectation values of the atomic and field observables is considered as a perturbation to one of the following integrable versions: (i) a model with atoms moving through a spatially inhomogeneous resonant field, and (ii) a model with atoms interacting with a nonresonant eigenmode which is assumed to be homogeneous on the cavity size. We find the general exact solutions for both the models and show that they contain special solutions describing a coherent effect of population and radiation trapping. Using the Melnikov method, we prove analytically transverse intersections of stable and unstable manifolds of a hyperbolic fixed point under a small modulation of the vacuum Rabi frequency. These intersections are believed to provide the Smale horseshoe mechanism of Hamiltonian chaos. The analytical results are accompanied with direct computation of topographical maps of maximal Lyapunov exponents that give a representative image of regularity and chaos in the atom-field system in different ranges of its control parameters--the frequency detuning, the number, and the velocity of atoms.     

外部扰动信号对混合光学双稳系统中混沌的调制

以液晶体作为非线性介质 ,构建了混合光学双稳模型系统。在外部正弦信号扰动下 ,利用应用功能强大的工程计算数值分析软件Matlab 5 3,数值研究了正弦调制对液晶混合光学双稳系统中混沌特性的影响。结果表明 ,在正弦信号的调制下 ,系统状态出现了周期 1、周期 2、间歇性混沌及多种演化模式 ,呈现了一系列新的动力学效应。研究发现 ,幅度调制的影响不仅比相位调制的影响要大 ,而且迅速     

相对论速调管中间腔与调制电子束间的非线性互作用

在强流相对论电子束驱动的相对论速调管放大器中, 由于强流和高场强的影响, 尤其是中间腔具有高Q值, 微波腔与电子束之间的非线性作用很明显, 严重影响器件性能. 根据麦克斯韦方程组以及电子在微波场作用下运动方程给出了中间腔的束-波互作用自洽方程. 从这些方程出发, 研究了调制深度和调制频率对间隙电压幅度和相位的影响. 对比常规速调管的等效电路模型, 自洽公式给出的间隙电压幅值同粒子模拟结果更接近, 尤其是较高调制深度的情况. 同时器件带宽随调制深度的增加而变宽, 这也同粒子模拟结果一致. 由此设计了一个S波段高增益相对论放大器, 在LTD (长脉冲螺旋线)加速器上开展了相应的实验工作, 实验上获得了1.1 GW的输出功率, 器件增益49 dB. 关键词： 相对论速调管 非线性互作用 自洽方程     

CW-pumped polarization-maintaining Brillouin fiber ring laser: II. Active mode-locking by phase modulation

Stimulated Brillouin backscattering in a cw-pumped long optical polarization-maintaining fiber ring cavity excites spontaneous stable mode-locking. But the shortest pulses allowed by the Brillouin gain bandwidth imply an active mode-locking, which we have achieved by using a phase modulator inside the ring. The experiment is carried out in the infrared at 1.319 μm, and in narrow frequency domains, close to N integer multiples of the ring FSR, we observe two type of mode-locking: either a maximum compression of the Brillouin solitons, or a stable splitting into N equally spaced pulses. Case N = 3 is more detailed. Experiment implies a slight polarization modulation by the phase modulation. Simulations carried out through the coherent three-wave model are in very good agreement for both mode-locking mechanisms. Introduction of a small amplitude modulation together with the intra-cavity phase modulation satisfactorily explains the stable splitting domain as well as the compression domain.     

四能级双V型原子系统中考虑自发辐射相干的无粒子数反转激光

提出了一个由两个弱探测场和两个强耦合场驱动的四能级双V型原子系统, 研究发现在四波混频共振条件下, 两探测场均可被放大而无须粒子数反转. 值得注意的是, 由于所选择的激发态为超精细结构的两个近能级, 这里必须考虑自发辐射相干效应的影响. 与不考虑自发辐射相干相比, 同样参数条件下探测场的增益得到大幅度提高.而且, 探测场增益对相位非常敏感, 即增益-吸收线型受相位周期性调制, 同时也受两个偶极矩之间夹角θ制约. 此外还分析了相干抽运场 (强耦合场)的失谐对增益谱线产生的影响. 关键词： 无粒子数反转激光 四波混频 自发辐射相干