Dye laser model with pump and quantum fluctuations; colored noise

A single mode dye laser model with two stochastically fluctuating forces representing pump and quantum fluctuations is discussed. In extension to a previous paper we investigate the different influences ofcolored pump noise andwhite quantum fluctuations on the laser light statistics. The corresponding two-variable Fokker-Planck equation is solved by means ofmatrix continued fractions. A comparison to the model with two white noise forces is also included. We focus especially on the intensity correlation time enhancement observed for low noise strengths which seems to be the result of a competition between (multiplicative) pump noise and (additive) quantum noise. An increase in correlation time of the colored pump noise causes the intensity correlation time enhancement to disappear.     

染料激光瞬态过程中的噪声

本文用首次通过时间的方法来分析染料激光瞬态的统计性质.提出了单模染料激光的理论模型,用白噪声简化泵浦涨落,通过福克-曾朗克方程求出首次通过时间分布的平均值、方差和偏斜度的解析解.与实验数据和用蒙特卡罗模拟获得的曲线相比较,解析解的结果与实验测量和数值计算符合得很好.     

Statistical fluctuations in a saturation laser model with correlated noises

We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker--Planck equation and analytic expressions of the steady-state probability distribution function (SPD) of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that (i) the correlation strength \lambda of correlated noises always enhances the fluctuation of laser intensity; (ii) the correlation time \tau of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but \tau weakens it for the above-threshold case.     

偏置信号调制下色关联噪声驱动的单模激光的光强相对涨落

采用线性化近似，计算了由具有色关联的受偏置信号调制的色泵噪声和色量子噪声驱动 的单模激光增益模型的光强相对涨落，发现相对涨落随噪声强度的变化曲线中存在极小值，分析了偏置信号的强度、周期信号频率、噪声间的互关联强度和互关联时间对曲线的影响； 对单模激光增益模型在偏置信号调制和直接信号调制两种方式下的输出光强相对涨落进行了比较，发现光强涨落与偏置信号的强度密切相关. 关键词： 偏置信号调制 光强相对涨落 线性化近似     

The Time-Dependent Moments and Correlation Functions of the Intensity of a Single-Mode Dye Lase

By combining linear approximation with Novikov theorem we derive first the time-dependen tmoments of laser intensity for colored saturation loss-noise, colored gain-noise and coloredloss-noise models of a singlemode dye laser. We analyze and compare the time-evolutioncharacter of timedependent moments of laser intensity for three models. The intensitycorrelation functions and correlation time for the colored saturation loss-noise model arederived and compared to the corresponding quantities for colored gain-noise and coloredloss-noise models. We show that, due to saturation effects in the considered laser model, theeffect of which the correlation time of the noise hides the differences between the in tensitycorrelation functions of the models is weakened. It can be seen from the evolution curves ofthe intensity correlation time versus the pump parameter that the dye laser exists criticalslowing-down.     

Nonclassical light generation in quasi-phase-matched parametric self-frequency conversion

We present a quantum theory of the parametric self-conversion of the laser radiation frequency in active nonlinear crystals with a regular domain structure. Such crystals feature simultaneous lasing and quasi-phase-matched parametric conversion of the laser radiation frequency. These processes are described using the Heisenberg-Langevin equations in two regimes of the subharmonic generation: super-and subthreshold. The spectral properties of the quadrature components of the laser frequency and its subharmonic and the photon statistics have been studied as dependent on the pump power, crystal length, and reflectance of the laser cavity output mirror. Using the obtained analytical expressions, these characteristics are calculated for a active nonlinear Nd:Mg:LiNbO₃ crystal with a regular domain structure. In the subthreshold regime, the maximum decrease in the spectral density of fluctuations in the subharmonic quadrature component relative to the standard quantum limit may reach 90%; in the above-threshold regime, these fluctuations are virtually not suppressed. A decrease in the spectral density of fluctuations of the laser frequency quadrature does not exceed 10%. In the subthreshold excitation regime, the subharmonic photons obey a super-Poisson statistics; in the above-threshold regime, the photon statistics is Poisson-like.     

Quantum fluctuations of superfluorescence delay observed with ultrashort optical excitations

We present an observation of fluctuations in delay times of the yoked-superfluorescence pulses generated in atomic rubidium. The yoked-superfluorescence was induced through two-photon excitation of cascade transitions by ultrashort (∼100 fs) laser pulses. A statistical distribution and fluctuations of delay times were studied as the pump pulse energy varied, effectively changing the number of participating atoms. The standard deviation in the delay-time statistics decreases when the pump power increases. The experimental data support the theoretical model of the quantum fluctuations of superfluorescence.     

实虚部关联的量子噪声和泵噪声对单模激光动力学性质的影响

采用具有实虚部关联的量子噪声和泵噪声驱动的单模激光损失模型，用线性化近似方法研究了反映激光动力学性质的光强关联函数，讨论了光强关联函数随时间的演化；并对线性化近似方法的适用范围进行了详细分析，分别讨论了量子噪声强度、泵噪声强度、量子噪声实虚部关联系数对光强相对涨落的影响，得出在小噪声、远离阈值时，线性化近似方法适用范围扩大；小噪声、远离阈值且当量子噪声实虚部无关联时，线性化近似方法适用范围最大的结论. 关键词： 单模激光 光强关联函数 光强相对涨落     

Asymmetric Evolution of Two Two-Level Atoms Induced by Position-Dependent Excitation Phase

We report a phenomenon of asymmetric evolution of two two-level atoms which results from pump laser phase based on the model of[Phys.Rev.Lett.101(2008) 153601].Other than investigating the dynamical behavior of whole system,in this paper we investigate the effects of the pump laser phase on dynamic behavior of each atom.We find that two atoms show asymmetry both in time evolution of(population) excitation probability and quantum correlation with environment due to the quantum interference induced by pump laser phase as well as the dipole-dipole interaction.These phenomena are deeply related to the dynamical behavior of the whole system,therefore we can understand the dynamical behavior of whole system caused by pump laser phase from this point of view.     

Microscopic Features of Bosonic Quantum Transport and Entropy Production

The microscopic features of bosonic quantum transport in a nonequilibrium steady state, which breaks time reversal invariance spontaneously, are investigated. The analysis is based on the probability distributions, generated by the correlation functions of the particle current and the entropy production operator. The general approach is applied to an exactly solvable model with a point‐like interaction driving the system away from equilibrium. The quantum fluctuations of the particle current and the entropy production are explicitly evaluated in the zero frequency limit. It is shown that all moments of the entropy production distribution are non‐negative, which provides a microscopic version of the second law of thermodynamics. On this basis a concept of efficiency, taking into account all quantum fluctuations, is proposed and analyzed. The role of the quantum statistics in this context is also discussed.     

Influence of fluctuations of a laser pump on the intensity correlation of resonance fluorescence radiation

The influence of fluctuations of a relatively weak laser pump on the intensity correlation of resonance fluorescence radiation is studied for a laser acting both below and above the threshold. Below the threshold the radiation of the laser is characterized by Gaussian properties causing non-factorization of the intensity correlation function. Above the threshold the laser shows non-linear filter properties and, therefore, the deviation of the exact intensity correlation function from its factorized value is small.     

Stability of Semiclassical Gravity Solutions with Respect to Quantum Metric Fluctuations

We discuss the stability of semiclassical gravity solutions with respect to small quantum corrections by considering the quantum fluctuations of the metric perturbations around the semiclassical solution. We call the attention to the role played by the symmetrized 2-point quantum correlation function for the metric perturbations, which can be naturally decomposed into two separate contributions: intrinsic and induced fluctuations. We show that traditional criteria on the stability of semiclassical gravity are incomplete because these criteria based on the linearized semiclassical Einstein equation can only provide information on the expectation value and the intrinsic fluctuations of the metric perturbations. By contrast, the framework of stochastic semiclassical gravity provides a more complete and accurate criterion because it contains information on the induced fluctuations as well. The Einstein–Langevin equation therein contains a stochastic source characterized by the noise kernel (the symmetrized 2-point quantum correlation function of the stress tensor operator) and yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. These points are illustrated with the example of Minkowski space-time as a solution to the semiclassical Einstein equation, which is found to be stable under both intrinsic and induced fluctuations.     

Multimode description of stimulated parametric down-conversion

We derive multimode generating functions, photon-number distributions, integrated-intensity distributions, moments and quadrature fluctuations for stimulated parametric down-conversion in relation to experiments measuring joint distributions. The border between classical and quantum behaviour is given.     

Event-by-event fluctuations and inclusive distributions

Event-by-event observables are compared with conventional inclusive measurements. We find that moments of event-by-event fluctuations are closely related to inclusive correlation functions. Implications for upcoming heavy ion experiments are discussed.     

Correlations in classical and quantum systems far from thermal equilibrium

We consider classical systems described by a Fokker-Planck equation or a generalized Fokker-Planck equation and quantum systems described by a density matrix equation or by a generalized Fokker-Planck equation using the principle of quantum classical correspondence. We split the corresponding operators of the equation of motion into a part which refers to the proper system and another one which describes the coupling of the proper system to the external world (reservoirs). We demonstrate that by use of conservation laws, referring to the proper systems, exact relations hold for certain moments, valid for all temperatures and coupling constants of the reservoirs. Using the concepts of a previous paper we describe then a perturbation theoretical approach which allows in a simple manner to determine a number of important correlation functions (moments of the total system). The time dependent case is briefly discussed. The applicability and usefulness of the present procedure is demonstrated by the example of the single-mode laser yielding e.g. expressions for the atom-field correlation.     

Non-classical effect of quantum non-demolition measurement in presence of parametric amplification

A full quantum treatment of the problem of quantum non-demolition measurements in non-linear optical media is considered. The system consists of four different coupling parameters in addition to different phase parameters. The solution of the Heisenberg equations of motion for the dynamical operators is obtained. The phenomenon of squeezing is examined for both normal and principal squeezing and it has been shown that it is more pronounced for the compound mode case. The intensity correlation function is also calculated and discussed where the observation of the antibunching can be reported. In addition to the higher-order moments we examined the quantum correlation functions, joint quasidistribution functions, as well as photon-number distribution and its factorial moments. It has shown that the non-classical properties is apparent of this system and more pronounced for the compound mode (1,3).     

Differential equations of spin dynamics and asymptotic expansion of quantum expectation values near the classical limit. II

The method developed in Part I is used to obtain asymptotic expansions of the functions that represent spin operators and of the quantum expectation values near the classical limit J→∞. We calculate with accuracy to the first quantum correction the correlation functions responsible for the statistical properties of cooperative spontaneous emission (super-radiance) of a gas of twolevel molecules. It is shown that the light emitted by a finite number of molecules does not have coherence of higher orders. The statistics of the field of quantum fluctuations is discussed.     

Nonequilibrium quantum condensation in an incoherently pumped dissipative system

We study spontaneous quantum coherence in an out of an equilibrium system, coupled to multiple baths describing pumping and decay. For a range of parameters describing coupling to, and occupation of the baths, a stable steady-state condensed solution exists. The presence of pumping and decay significantly modifies the spectra of phase fluctuations, leading to correlation functions that differ both from an isolated condensate and from a laser.     

Simultaneously suppressing frequency and intensity noise in a Nd:YAG nonplanar ring oscillator by means of the current-lock technique

We show that frequency and intensity noise in a Nd:YAG laser are correlated to a high degree and can be traced to the same underlying cause, namely, power fluctuations of the pump source. Because of this correlation, simultaneous suppression of frequency and intensity noise by 30 dB is achieved by means of a single actuator, the pump power.     

Influence of Signal and Noise on Statistical Fluctuation of Single-Mode Laser System

On the basis of calculating the steady-state mean normalized intensity fluctuation of a signal-mode laser system driven by both colored pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, we analyze the influence of modulation signal, noise, and its correlation form on the statistical fluctuation of the laser system. We have found that when the amplitude of modulation signal weakens and its frequency quickens, the statistical fluctuation will reduce rapidly. The statistical fluctuation of the laser system can be restrained by reducing the intensity of pump noise and quantum noise. Moreover, with prolonging of colored cross-correlation time, the statistical fluctuation of laser system experiences a repeated changing process, that is, from decreasing to augmenting,then to decreasing, and finally to augmenting again. With the decreasing of the value of cross-correlation coefficient, the statistical fluctuation will decrease too. When the cross-correlation form between the real part and imaginary part of quantum noise is zero correlation, the statistical fluctuation of laser system has a minimum. Compared with the influence of intensity of pump noise, the influence of intensity of quantum noise on the statistical fluctuation is smaller.