Entanglement in the interaction between two quantum oscillator systems

The fundamental quantum dynamics of two interacting oscillator systems are studied in two different scenarios. In one case, both oscillators are assumed to be linear, whereas in the second case, one oscillator is linear and the other is a non-linear, angular-momentum oscillator; the second case is, of course, more complex in terms of energy transfer and dynamics. These two scenarios have been the subject of much interest over the years, especially in developing an understanding of modern concepts in quantum optics and quantum electronics. In this work, however, these two scenarios are utilized to consider and discuss the salient features of quantum behaviors resulting from the interactive nature of the two oscillators, i.e., coherence, entanglement, spontaneous emission, etc., and to apply a measure of entanglement in analyzing the nature of the interacting systems. ... For the coupled linear and angular-momentum oscillator system in the fully quantum-mechanical description, we consider special examples of two, three, four-level angular momentum systems, demonstrating the explicit appearances of entanglement. We also show that this entanglement persists even as the coupled angular momentum oscillator is taken to the limit of a large number of levels, a limit which would go over to the classical picture for an uncoupled angular momentum oscillator

Thermal Properties of an Inflationary Universe

An energetic justification of a thermal component during inflation is given. The thermal component can act as a heat reservoir which induces thermal fluctuations on the inflaton field system. We showed previously that such thermal fluctuations could dominate quantum fluctuations in producing the initial seeds of density perturbations. A Langevin-like rate equation is derived from quantum field theory which describes the production of fluctuations in the inflaton field when acted upon by a simple modeled heat reservoir. In a certain limit this equation is shown to reduce to the standard Langevin equation, which we used to construct "Warm Inflation" scenarios in previous work. A particle physics interpretation of our system-reservoir model is offered.Comment: 28 pages, 0 figures, In Press Physical Review D 199

Thermalized Displaced and Squeezed Number States in Coordinate Representation

Within the framework of thermofield dynamics, the wavefunctions of the thermalized displaced number and squeezed number states are given in the coordinate representation. Furthermore, the time evolution of these wavefunctions is considered by introducing a thermal coordinate representation, and we also calculate the corresponding probability densities, average values and variances of position coordinate, which are consistent with results in the literature.Comment: 12 pages, no figures, Revtex. v3: substantially revise

Radiative energy shifts of accelerated atoms

We consider the influence of acceleration on the radiative energy shifts of atoms in Minkowski space. We study a two-level atom coupled to a scalar quantum field. Using a Heisenberg picture approach, we are able to separate the contributions of vacuum fluctuations and radiation reaction to the Lamb shift of the two-level atom. The resulting energy shifts for the special case of a uniformly accelerated atom are then compared with those of an atom at rest.Comment: 12 pages, Latex, 1 figure as uuencoded eps file, shorter version will appear in Phys. Rev.

Path Integrals and Their Application to Dissipative Quantum Systems

Introduction Path Integrals - Introduction - Propagator - Free Particle - Path Integral Representation of Quantum Mechanics - Particle on a Ring - Particle in a Box - Driven Harmonic Oscillator - Semiclassical Approximation - Imaginary Time Path Integral Dissipative Systems - Introduction - Environment as Collection of Harmonic Oscillators - Effective Action Damped Harmonic Oscillator - Partition Function - Ground State Energy and Density of States - Position Autocorrelation FunctionComment: 55 pages, 13 figures. To be published in "Coherent Evolution in Noisy Environments", Lecture Notes in Physics (http://link.springer.de/series/lnpp/) (Springer Verlag, Berlin-Heidelberg-New York

Perspectives for a mixed two-qubit system with binomial quantum states

The problem of the relationship between entanglement and two-qubit systems in which it is embedded is central to the quantum information theory. This paper suggests that the concurrence hierarchy as an entanglement measure provides an alternative view of how to think about this problem. We consider mixed states of two qubits and obtain an exact solution of the time-dependent master equation that describes the evolution of two two-level qubits (or atoms) within a perfect cavity for the case of multiphoton transition. We consider the situation for which the field may start from a binomial state. Employing this solution, the significant features of the entanglement when a second qubit is weakly coupled to the field and becomes entangled with the first qubit, is investigated. We also describe the response of the atomic system as it varies between the Rabi oscillations and the collapse-revival mode and investigate the atomic inversion and the Q-function. We identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. Most interestingly, it is shown that features of the entanglement is influenced significantly when the multi-photon process is involved. Finally, we obtain illustrative examples of some novel aspects of this system and show how the off-resonant case can sensitize entanglement to the role of initial state setting.Comment: 18 pages, 9 figure

Spontaneous excitation of an accelerated atom: The contributions of vacuum fluctuations and radiation reaction

We consider an atom in interaction with a massless scalar quantum field. We discuss the structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom through the quantum vacuum. Our main intention is to identify and to analyze quantitatively the distinct contributions of vacuum fluctuations and radiation reaction to the spontaneous excitation of a uniformly accelerated atom in its ground state. This gives an understanding of the role of the different physical processes underlying the Unruh effect. The atom's evolution into equilibrium and the Einstein coefficients for spontaneous excitation and spontaneous emission are calculated.Comment: 13 pages, KONS-RGKU-94-09, to appear in Phys. Rev.

Coupling Classical and Quantum Variables using Continuous Quantum Measurement Theory

We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously and imprecisely measured by the classical system. The effective equations of motion for the classical system therefore consist of treating the quantum variable $x$ as a stochastic c-number \x (t) the probability distibution for which is given by the theory of continuous quantum measurements. The resulting theory is similar to the usual mean field equations (in which $x$ is replaced by its quantum expectation value) but with two differences: a noise term, and more importantly, the state of the quantum subsystem evolves according to the stochastic non-linear Schrodinger equation of a continuously measured system. In the case in which the quantum system starts out in a superposition of well-separated localized states, the classical system goes into a statistical mixture of trajectories, one trajectory for each individual localized state.Comment: 11 pages, plain Tex (with revised settings for \vsize and \voffset to accommodate US paper sizes

Quantum System under Periodic Perturbation: Effect of Environment

In many physical situations the behavior of a quantum system is affected by interaction with a larger environment. We develop, using the method of influence functional, how to deduce the density matrix of the quantum system incorporating the effect of environment. After introducing characterization of the environment by spectral weight, we first devise schemes to approximate the spectral weight, and then a perturbation method in field theory models, in order to approximately describe the environment. All of these approximate models may be classified as extended Ohmic models of dissipation whose differences are in the high frequency part. The quantum system we deal with in the present work is a general class of harmonic oscillators with arbitrary time dependent frequency. The late time behavior of the system is well described by an approximation that employs a localized friction in the dissipative part of the correlation function appearing in the influence functional. The density matrix of the quantum system is then determined in terms of a single classical solution obtained with the time dependent frequency. With this one can compute the entropy, the energy distribution function, and other physical quantities of the system in a closed form. Specific application is made to the case of periodically varying frequency. This dynamical system has a remarkable property when the environmental interaction is switched off: Effect of the parametric resonance gives rise to an exponential growth of the populated number in higher excitation levels, or particle production in field theory models. The effect of the environment is investigated for this dynamical system and it is demonstrated that there existsComment: 55 pages, LATEX file plus 13 PS figures. A few calculational mistatkes and corresponding figure 1 in field theory model corrected and some changes made for publication in Phys. Rev.D (in press

Effective Theories of Coupled Classical and Quantum Variables

We address the issue of coupling variables which are essentially classical to variables that are quantum. Two approaches are discussed. In the first (based on collaborative work with L.Di\'osi), continuous quantum measurement theory is used to construct a phenomenological description of the interaction of a quasiclassical variable $X$ with a quantum variable $x$, where the quasiclassical nature of $X$ is assumed to have come about as a result of decoherence. The state of the quantum subsystem evolves according to the stochastic non-linear Schr\"odinger equation of a continuously measured system, and the classical system couples to a stochastic c-number \x (t) representing the imprecisely measured value of $x$. The theory gives intuitively sensible results even when the quantum system starts out in a superposition of well-separated localized states. The second approach involves a derivation of an effective theory from the underlying quantum theory of the combined quasiclassical--quantum system, and uses the decoherent histories approach to quantum theory.Comment: 25 pages, plain Tex. To appear in proceedings of the conference Open Systems and Measurement in Relativistic Quantum Theory, Naples, April 3-4, 1998, edited by H.P.Breuer and F.Petruccion