Micromaser operation in correlated atoms

Stimulated emission of two-level atoms in a high-Q cavity is considered under conditions when pumping produces correlated many-atomic states. Based on the many-body problem, a kinetic equation is obtained for the Glauber–Sudarshan probability, which describes the field in the Fokker–Planck approximation. The statistics of light in this approximation are determined by the atomic correlation functions of the order of no higher than the second. The noise of light is found in the regime of micromaser operation for two types of pumping producing the initial separable states with a classical correlation and entangled states. It is shown that the presence of the initial diatomic correlation enhances the intensity noise. The entangled state of atoms is found from which nonclassical light is generated with a steady-state phase and noise, which can be almost completely suppressed in the low-frequency spectral region.     

Covariant formulation of non-equilibrium statistical thermodynamics

The Fokker Planck equation is considered as the master equation of macroscopic fluctuation theories. The transformation properties of this equation and quantities related to it under general coordinate transformations in phase space are studied. It is argued that all relations expressing physical properties should be manifestly covariant, i.e. independent of the special system of coordinates used. The covariance of the Langevin-equations and the Fokker Planck equation is demonstrated. The diffusion matrix of the Fokker Planck equation is used as a contravariant metric tensor in phase space. Covariant drift vectors associated to the Langevin- and the Fokker Planck equation are found. It is shown that special coordinates exist in which the covariant drift vector of the Fokker Planck equation and the usual non-covariant drift vector are equal.The physical property of detailed balance and the equivalent potential conditions are given in covariant form. Finally, the covariant formulation is used to study how macroscopic forces couple to a system in a non-equilibrium steady state. A general fluctuation-dissipation theorem for the linear response to such forces is obtained.     

Mollow triplet under incoherent pumping

A counterpart of the Mollow triplet (luminescence line shape of a two-level system under coherent excitation) is obtained for the case of incoherent excitation in a cavity. The system acquires coherence through the strong-coupling between the cavity and the emitter. Analytical expressions, in excellent agreement with numerical results, pinpoint analogies and differences between the conventional resonance fluorescence spectrum and its cavity QED analogue under incoherent excitation. Most notably, the satellites broaden and split sublinearly with increasing incoherent pumping.     

Similarity solutions of the Fokker–Planck equation with time-dependent coefficients

In this work, we consider the solvability of the Fokker–Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker–Planck equation is reduced to an ordinary differential equation. Adopting the natural requirement that the probability current density vanishes at the boundary, the resulting ordinary differential equation turns out to be integrable, and the probability density function can be given in closed form. New examples of exactly solvable Fokker–Planck equations are presented, and their properties analyzed.     

Short-time correlations of many-body systems described by nonlinear Fokker–Planck equations and Vlasov–Fokker–Planck equations

Analytical expressions for short-time correlation functions, diffusion coefficients, mean square displacement, and second order statistics of many-body systems are derived using a mean field approach in terms of nonlinear Fokker–Planck equations and Vlasov–Fokker–Planck equations. The results are illustrated for the Desai–Zwanzig model, the nonlinear diffusion equation related to the Tsallis statistics, and a Vlasov–Fokker–Planck equation describing bunch particles in particle accelerator storage rings.     

A generalized Lenard—Balescu equation including longitudinal and transverse interaction

A generalized Lenard—Balescu equation, which includes longitudinal and transverse interaction in a plasma, is derived from a Green function approach. The collision integral is rewritten in a Fokker—Planck representation, it corresponds to the result of Klimontovich. The classical limit is discussed.     

A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence

ABSTRACT

We develop a theory for the cascade mixing terms in a moment closure approach to binary active scalar mixing in variable-density turbulence. To address the variable-density complications we apply, as a principle and constraint, the conservation of the probability density function (PDF) through a Fokker–Planck equation with bounded sample space whose attractor is the beta PDF with skewness. Mixing is related to a single-point PDF as a realisability principle to provide mathematically rigorous expressions for the small scale statistics in terms of largescale moments. The problem of the unknown small-scale mixing is replaced with the determination of the drift and diffusion terms of a Fokker–Planck equation in a beta-PDF-convergent stochastic process. We find that realisability of a beta-convergent process requires the mixing time-scale ratio, taken as a constant in passive scalar mixing, to be a function of the mean mass fraction, mean fluid density, the Atwood number, the density-volume correlation and moments of the density field. We develop and compare the new model with direct numerical simulations data of non-stationary homogeneous variable-density turbulence.     

Mass exchange and angular distribution in a dynamical treatment of heavy ion collisions

We present a first numerical computation of the absolute value of the double differential cross section as a function of mass asymmetry and detection angle including a dynamical coupling between relative motion and mass asymmetry. We apply it to the⁶³Cu+¹⁹⁷Au experiment at two different energies. The equation of motion used is a Fokker Planck equation for the distribution function in classical phase space. The coefficients needed are those known from classical model calculations, besides a friction coefficient introduced for the mass asymmetry degree. We find encouraging agreement between the calculated and experimental curves.     

Stochastic Resonance in Finely Dispersed Magnetics: a Comparison of Discrete and Continuous Models

The phenomenon of a stochastic resonance in a system of single-domain particles with easy-axis magnetic anisotropy is treated theoretically for the thermally activated system. The results of calculations for the discrete model based on the control equation for the Kramers transition rates of the magnetic moment vector and for the continuous model based on numerical solution of the Fokker–Planck equation with a periodic drift term are analyzed. The phase shifts between input and output signals and the values of the signal-to-noise ratio calculated for iron superparamagnetic particles in the context of these two models are compared.     

Temporal Diffusion: From Microscopic Dynamics to Generalised Fokker–Planck and Fractional Equations

The temporal Fokker–Planck equation (Boon et al. in J Stat Phys 3/4: 527, 2003) or propagation–dispersion equation was derived to describe diffusive processes with temporal dispersion rather than spatial dispersion as in classical diffusion. We present two generalizations of the temporal Fokker–Planck equation for the first passage distribution function \(f_j(r,t)\) of a particle moving on a substrate with time delays \(\tau _j\). Both generalizations follow from the first visit recurrence relation. In the first case, the time delays depend on the local concentration, that is the time delay probability \(P_j\) is a functional of the particle distribution function and we show that when the functional dependence is of the power law type, \(P_j \propto f_j^{\nu - 1}\), the generalized Fokker–Planck equation exhibits a structure similar to that of the nonlinear spatial diffusion equation where the roles of space and time are reversed. In the second case, we consider the situation where the time delays are distributed according to a power law, \(P_j \propto \tau _j^{-1-\alpha }\) (with \(0< \alpha < 2\)), in which case we obtain a fractional propagation-dispersion equation which is the temporal analog of the fractional spatial diffusion equation (with space and time interchanged). The analysis shows how certain microscopic mechanisms can lead to non-Gaussian distributions and non-classical scaling exponents.     

Markovian master equation for a two-level atom in a strong field and/or a tailored reservoir

The master equation for a two-level atom driven by a strong classical field and damped into a tailored reservoir with nonflat density of modes is derived under the Born-Markov approximation. To derive the master equation, the dressing transformation on the atomic operators is performed first, and, next, the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The effects of a strong field and/or structured reservoir are seen as nonstandard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The master equation leads to the generalized optical Bloch equations that can easily be solved for the steady state and, together with the quantum regression theorem, allow for analytical expressions for the fluorescence, as well as absorption spectra.     

Generalization of the Bennett equilibrium condition for a relativistic electron beam propagating in the Ohmic plasma channel and ion focusing regime along an external magnetic field

The problem of formulating the generalization of the Bennett equilibrium condition is considered for a relativistic electron beam propagating in the Ohmic plasma channel, as well as in the ion focusing regime in the presence of an external longitudinal uniform magnetic field. We assume that the electron component of the background plasma is not completely removed from the region occupied by the beam. This equilibrium condition is derived using the mass and momentum transport equations obtained for a paraxial monoenergetic beam from the Fokker–Planck kinetic equation.     

Markovian and non-markovian behavior in two-level atom fluorescence

We extend the quantum source field method to demonstrate the non-Markovian character of the quantum electrodynamic Bloch equations. Explicit solutions are obtained, via a natural perturbation technique, for the vacuum expectation value of the two-level atomic inversion operator. The most obvious evidence for the non-Markovian character of the Bloch equations is the nonexponential nature of the fluorescence decay law. We demonstrate our perturbation technique further by applying it to the two-level strong-field resonance fluorescence problem, obtaining the results of Torrey, of Mollow, and of Heitler, in the appropriate limits. The entire analysis is carried out in the Heisenberg picture, allowing us to deal directly at every state with the relevant dynamical variable of interest.     

腔场耦合的二能级原子荧光谱

过光与物质相互作用的主方程计算了强场激励的二能级原子与单模腔耦合的稳态荧光谱。在腔场的强耦合作用下,三峰Mollow谱的每个成分都分裂为多重的,这种现象由腔场使原子修饰态能级漂移而导致的,荧光谱的具体结构则依赖于驱动场的拉比频率和原子-腔的耦合系数。     

A review of Vlasov–Fokker–Planck numerical modeling of inertial confinement fusion plasma

The interaction of intense lasers with solid matter generates a hot plasma state that is well described by the Vlasov–Fokker–Planck equation. Accurate and efficient modeling of the physics in these scenarios is highly pertinent, because it relates to experimental campaigns to produce energy by inertial confinement fusion on facilities such as the National Ignition Facility. Calculations involving the Vlasov–Fokker–Planck equation are computationally intensive, but are crucial to proper understanding of a wide variety of physical effects and instabilities in inertial fusion plasmas. In this topical review, we will introduce the background physics related to Vlasov–Fokker–Planck simulation, and then proceed to describe results from numerical simulation of inertial fusion plasma in a pedagogical manner by discussing some key numerical algorithm developments that enabled the research to take place. A qualitative comparison of the techniques is also given.     

Resonance fluorescence statistics of a two-level atom in feedback loop

Statistics of photoemission events into the components of a triplet of resonance fluorescence of a two-level atom in a classical optical field, the phase of which changes by π upon the detection of spontaneous photon, is compared with the case when the feedback is absent. In contrast to the known problem on the statistics of resonance fluorescence of a two-level atom, a grouping of photocounts should be observed in each separate side component of the triplet. Anticorrelation of photoemission into side components is also predicted, and the type of correlations between the emission into the central component of the triplet and into any of the side ones can be controlled by varying the detuning of the radiation frequency from the resonant value.     

Variability and Self-Organization in Nanosystems

In supersaturated media nanoparticles grow with fluctuating rate. On a surface of growing nanoparticles a mechanism of synchronization of molecular fluctuations operates increasing their scale up to macroscopic one. Thereof the kinetic equation for states distribution function of nanoparticles approaches the Fokker–Planck equation that is experimentally established on an example of nanoparticles of different nature. In a series of suspensions and aerosols, where the ordered aggregates of nanoparticles are formed, aggregation is multistage process, and at each stage the change of a size distribution function of aggregates is also described by the Fokker–Planck equation. Multistage aggregation is completed by appearance of the particles in system with multilevel hierarchical texture having tendency to accept polyhedral shape. Aforementioned features of nanosystems can be treated as development of variability and ability of systems to self-organization.     

飞秒激光场中原子所受光学偶极力研究

通过求解全波矢布洛赫方程研究了两能级原子与飞秒超快激光脉冲的相互作用过程,计算了不同拉比频率取值下原子所受光学偶极力和粒子数布居随时间的演化情况,分析了光场失谐量对光学势分布情况的影响.研究发现:由飞秒激光场产生的横向光力的时间平均值并不等于零,而是随着拉比频率的增加呈现振荡的增大趋势;纵向光力的时间平均作用也并非是拉比频率的单调函数,而是随着拉比频率的增加呈现周期性的振荡分布特性;光学势的分布对光场的失谐量具有明显的依赖性,随着失谐量的变化,光学势的性质也随之发生了改变.     

Solution of Fokker Planck equations with and without manifest detailed balance

Previous work on Fokker Planck equations with manifest detailed balance is generalized to include also the case without manifest detailed balance. The two cases are unified by exhibiting a general time reversal transformation with respect to which any Fokker Planck equation satisfies detailed balance, provided its steady state distribution exists. We also introduce a new method for solving some Fokker Planck equations with nonvanishing steady state drift by analytic continuation of the solution of a hermitian eigenvalue problem.