Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field

For a system of charged Fermions interacting with an electromagnetic field, we derive a non-Markovian master equation in the second-order approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the well-known Markovian term of Lindblad’s form, that describes the decay of the system by correlated transitions of the system and environment particles, this equation includes new Markovian and non-Markovian terms proceeding from the fluctuations of the self-consistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the self-consistent field of the environment, and the influence of the time-evolution of the environment on the system dynamics. We derive a complementary master equation describing the environment dynamics correlated with the dynamics of the system. As an application, we obtain non-Markovian Maxwell-Bloch equations and calculate the absorption spectrum of a field propagation mode transversing an array of two-level quantum dots.     

Single atom entropy squeezing for two two-level atoms interacting with a binomial field

In this paper we consider a system of two two-level atoms interacting with a binomial field in an ideal cavity. We investigate the time evolution of the single atom entropy squeezing, atomic inversion and the linear entropy for the present system. Furthermore, the relationship between the entropy squeezing and the entanglement is investigated. It is shown that the amounts of the nonclassical effects exhibited in the entropy squeezing are dependent on the different initial conditions. The entropy squeezing can give information on the corresponding linear entropy.     

Driving light pulses with light in two-level media

A two-level medium, described by the Maxwell-Bloch system, is engraved by establishing a standing cavity wave with a linearly polarized electromagnetic field that drives the medium on both ends. A light pulse, polarized along the other direction, then scatters the medium and couples to the cavity standing wave by means of the population inversion density variations. We demonstrate that control of the applied amplitudes of the grating field allows one to stop the light pulse and to make it move backward (eventually to drive it freely). A simplified limit model of the Maxwell-Bloch system with variable boundary driving is obtained as a discrete nonlinear Schr?dinger equation with tunable external potential. It reproduces qualitatively the dynamics of the driven light pulse.     

Decoherence in the solvable dynamics of <Emphasis Type="Italic">N</Emphasis> strongly driven atoms coupled to a cavity mode

We present the exact solution of the dynamics of N two-level atoms strongly driven by an external coherent field and equally coupled on resonance to a cavity mode, in the presence of both cavity dissipation and atomic decay. Analytical results are presented for system and subsystem dynamics, showing how environment-induced decoherence leads the system from pure to mixed states. In the limit of negligible atomic decay, where the system is known to exhibit decoherence-free subspaces, we present a detailed discussion of the decoherence function that can be monitored by atomic population measurements.     

腔内混合态原子系统中辐射场的压缩效应

本文应用熵最大原理，假定腔内二能级原子起初就没有关于系统所处态的任何信息，研究了腔内原子与腔场相互作用的压缩行为，得出了原子初始处于任意统计混合态下，当初始激发足够强时，辐射场将产生极其接近于纯态情况在相同激发时的强压缩现象的重要结果，同时还讨论了产生压缩的混态范围。     

Single-atom entropy squeezing for two two-level atoms interacting with a single-mode radiation field

In this paper we consider a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via l-photon-transition mechanism. The field and the atoms are initially prepared in the coherent state and the excited atomic states, respectively. For this system we investigate the entropy squeezing, the atomic variances, the von Neumann entropy and the atomic inversions for the single-atom case. Also we comment on the relationship between spin squeezing and linear entropy. We show that the amounts of the nonclassical effects exhibited in the entropy squeezing for the present system are less than those produced by the standard Jaynes-Cummings model. The entropy squeezing can give information on the corresponding von Neumann entropy. Also the nonclassical effects obtained from the asymmetric atoms are greater than those obtained from the symmetric ones. Finally, the entropy squeezing gives better information than the atomic variances only for the asymmetric atoms.     

三纠缠原子与双模腔场相互作用系统的纠缠演化特性

研究了初始处于GHZ态的三个两能级原子与双模腔场相互作用系统的纠缠动力学特性,得到了并发度和线性熵的解析表达式.讨论了腔场初始纠缠度对腔内两原子之间纠缠的影响,对其余子系统求迹后结果表明腔内两原子之间的纠缠出现突然产生现象,腔内两原子之间产生纠缠的阈值时间和最大值依赖于双模腔场初始纠缠度;并且发现腔内两原子子系统和腔外原子与场子系统之间在整个的时间演化过程中一直保持着纠缠状态.     

Axisymmetric particle-in-cell simulations of diamagnetic-cavityformulation in vacuum

Axisymmetric simulations of the expansion of a hot plasma suddenly introduced into a vacuum containing a weak magnetic field were performed using an electromagnetic particle-in-cell code. Both uniform and gradient fields have been used, with the simulation axis along the principal field direction. The formation of a diamagnetic cavity requires an initial plasma β>1; as the expansion proceeds, β diminishes, and the field eventually recovers. The maximum spatial extent of the cavity and its duration can be obtained from simple dynamical considerations. Field-aligned ion acceleration behind the electron front is observed in all field geometries and strengths. In the case of expansion into a divergent field, the plasma is found to move down the field gradient by ambipolar diffusion. These simulations are relevant to active release experiments in the Earth's magnetosphere, to pellet ablation experiments, and to the naturally occurring diamagnetic bubbles observed at the Earth's foreshock     

The Dynamics of a Field in a Cavity with a Slowly Oscillating Metal Mirror

We have examined analytically the behavior of an electromagnetic field in a cavity of one of two metal mirrors that is stationary, while the other mirror oscillates in the vicinity of its equilibrium position. The case in which the period of the mirror oscillations substantially exceeds the characteristic roundtrip time of the electromagnetic radiation in the cavity has been considered. To solve the problem, we have applied the method of two time scales. The method makes it possible to solve the problem by using the expansion with respect to a small parameter, for which the ratio of the cavity roundtrip time to the mirror-oscillation period is used. The solution to the problem in the zeroth-order approximation with respect to the small parameter has been obtained and examined. This solution has been shown to be correct up to the mirror-oscillation amplitude being on the order of the average cavity length. We have showed that this scheme can be used to gain and generate electromagnetic radiation. We have compared our results obtained for the oscillating mirror with the results of an exact solution of the problem when the mirror moves uniformly and rectilinearly. We have showed that, in these two cases, a change in the total field energy in the cavity is inversely proportional to the current value of the cavity length.     

Time response of a coupled atoms-cavity system

We study the time response of a quantum optical system to a step excitation. The system is composed of a collection of N two-level atoms coupled to a single mode of the electromagnetic field of an optical cavity. The size of the step excitation is not limited to the low-intensity regime. Before the system reaches steady state there is an oscillatory exchange of energy between the atoms and the cavity. We compare the experimental results quantitatively with theoretical calculations and with previous transmission spectroscopy measurements.     

Effects of Purity on Dynamics of Multipartite Entanglement

We study the effects of purity on entanglement dynamics of a multipartite system in cavity QED. Three two-level atoms A, B and C are initially prepared in an entangled state and locally coupled with independent cavities a, b and c, respectively. We consider the effects of purity of atomic initial state on the entanglement evolution of both the systems of atoms and cavities. It is found that depending on the purity of atomic initial state, the entanglement of atoms （cavities） may or may not exhibit the sudden death （birth） phenomenon.     

Rotating wave approximation: systematic expansion and application to coupled spin pairs

We propose a new treatment of the dynamics of a periodically time-dependent Liouvillian by mapping it onto a time-independent problem and give a systematic expansion for its effective Liouvillian. In the case of a two-level system, the lowest order contribution is equivalent to the well-known rotating wave approximation. We extend the formalism to a pair of coupled two-level systems. For this pair, we find two Rabi frequencies and we can give parameter regimes where the leading order of the expansion is suppressed and higher orders become important. These results might help to investigate the interaction of tunneling systems in mixed crystals by providing a tool for the analysis of echo experiments. Received 2 September 1998     

Entangling two oscillating mirrors in an optomechanical system via a flying atom

We propose a novel scheme for generating the entanglement of two oscillating mirrors in an optomechanical system via a flying atom. In this scheme, a two-level atom, in an arbitrary superposition state, passes through an optomechanical system with two oscillating cavity-mirrors, and then its states are detected. In this way, we can generate the entangled states of the two oscillating mirrors. We derive the analytical expressions of the entangled states and make numerical calculations. We find that the entanglement of the two oscillating mirrors can be controlled by the initial state of the atom,the optomechanical coupling strength, and the coupling strength between the atom and the cavity field. We investigate the dynamics of the system with dissipations and discuss the experimental feasibility.     

Berry phase in a generalized nonlinear two-level system

In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom-field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.     

Berry phase in a generalized nonlinear two-level system

In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom--field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index $k$ is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom--field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.     

Pancharatnam phase for a system of a two-level atom interacting with a quantized field in a cavity

We derive an expression for the Pancharatnam phase for the entangled state of a single two-level atom interacting with a single electromagnetic field mode in an ideal cavity with the atom undergoing either a one- or a two-photon transition. It is shown that the Pancharatnam phase explicitly contains information about the statistics of the field and atomic coherence.     

Engineering transient spectrum for a two-level system interacting with two-mode intelligent states

The problem of a single two-level atom in its excited state, placed in a bimodal cavity in which an arbitrary form of the intensity-dependent atom–field coupling is present, is solved exactly. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time-dependent unitary evolution operator of the system is given, by means of which we analyze the analytic form of the fluorescence spectrum using the transitions among the dressed states of the system. The influence of parameter misfits on the quantum system is discussed. An interesting relation between the fluorescence spectrum and the dynamical evolution is found when the initial field states are prepared in properly intelligent states. By comparison with exact numerical results, we demonstrate that features of the fluorescence spectrum are influenced significantly by the different kinds of the nonlinearity of the intensity-dependent atom–field coupling. We provide numerous examples to illustrate this correspondence, and provide evidence of its usefulness. The present work considerably extends earlier results for two-level systems.     

Langevin and generalized Langevin types of spontaneous emission of quantum particles

In the effective Hamiltonian representation, we have obtained a quantum stochastic differential equation of a generalized Langevin type for the evolution operator of an atomic ensemble in a microcavity in an external broadband quantized field and in a nonresonant field of the microcavity. We show that, depending on the number of particles in the atomic ensemble, its dynamics demonstrates both the Langevin and the generalized Langevin types of the two-photon spontaneous decay. In this case, one photon is emitted into the cavity mode, whereas the other photon is emitted into the external broadband electromagnetic field. The Langevin type is determined by a considerable Stark interaction of the atomic ensemble with the broadband photon-free quantized field. We show that, here, the Stark interaction is represented by a quantized Poisson process and, depending on its magnitude (at certain numbers of atoms in the ensemble), the two-photon collective spontaneous emission of microcavity atoms can be completely suppressed. In this case, the two-photon spontaneous emission of the singly excited atomic ensemble is described by the two-level model, while the atom-photon cluster of the microcavity under the described conditions is an artificial two-level quantum particle with a strong Stark interaction.