Deconstructing Decoherence

The study of environmentally induced superselection and of the process of decoherence was originally motivated by the search for the emergence of classical behavior out of the quantum substrate, in the macroscopic limit. This limit, and other simplifying assumptions, have allowed the derivation of several simple results characterizing the onset of environmentally induced superselection; but these results are increasingly often regarded as a complete phenomenological characterization of decoherence in any regime. This is not necessarily the case: The examples presented in this paper counteract this impression by violating several of the simple ``rules of thumb''. This is relevant because decoherence is now beginning to be tested experimentally, and one may anticipate that, in at least some of the proposed applications (e.g., quantum computers), only the basic principle of ``monitoring by the environment'' will survive. The phenomenology of decoherence may turn out to be significantly different.Comment: 13 two-column pages, 3 embedded figure

Stochastic Theory of Accelerated Detectors in a Quantum Field

We analyze the statistical mechanical properties of n-detectors in arbitrary states of motion interacting with each other via a quantum field. We use the open system concept and the influence functional method to calculate the influence of quantum fields on detectors in motion, and the mutual influence of detectors via fields. We discuss the difference between self and mutual impedance and advanced and retarded noise. The mutual effects of detectors on each other can be studied from the Langevin equations derived from the influence functional, as it contains the backreaction of the field on the system self-consistently. We show the existence of general fluctuation- dissipation relations, and for trajectories without event horizons, correlation-propagation relations, which succinctly encapsulate these quantum statistical phenomena. These findings serve to clarify some existing confusions in the accelerated detector problem. The general methodology presented here could also serve as a platform to explore the quantum statistical properties of particles and fields, with practical applications in atomic and optical physics problems.Comment: 32 pages, Late

Hydrodynamic modes of a 1D trapped Bose gas

We consider two regimes where a trapped Bose gas behaves as a one-dimensional system. In the first one the Bose gas is microscopically described by 3D mean field theory, but the trap is so elongated that it behaves as a 1D gas with respect to low frequency collective modes. In the second regime we assume that the 1D gas is truly 1D and that it is properly described by the Lieb-Liniger model. In both regimes we find the frequency of the lowest compressional mode by solving the hydrodynamic equations. This is done by making use of a method which allows to find analytical or quasi-analytical solutions of these equations for a large class of models approaching very closely the actual equation of state of the Bose gas. We find an excellent agreement with the recent results of Menotti and Stringari obtained from a sum rule approach.Comment: 15 pages, revtex, 1 figure

Bragg spectroscopy with an accelerating Bose-Einstein condensate

We present the results of Bragg spectroscopy performed on an accelerating Bose-Einstein condensate. The Bose condensate undergoes circular micro-motion in a magnetic TOP trap and the effect of this motion on the Bragg spectrum is analyzed. A simple frequency modulation model is used to interpret the observed complex structure, and broadening effects are considered using numerical solutions to the Gross-Pitaevskii equation.Comment: 5 pages, 3 figures, to appear in PRA. Minor changes to text and fig

Quantum Computing with Atomic Josephson Junction Arrays

We present a quantum computing scheme with atomic Josephson junction arrays. The system consists of a small number of atoms with three internal states and trapped in a far-off resonant optical lattice. Raman lasers provide the "Josephson" tunneling, and the collision interaction between atoms represent the "capacitive" couplings between the modes. The qubit states are collective states of the atoms with opposite persistent currents. This system is closely analogous to the superconducting flux qubit. Single qubit quantum logic gates are performed by modulating the Raman couplings, while two-qubit gates result from a tunnel coupling between neighboring wells. Readout is achieved by tuning the Raman coupling adiabatically between the Josephson regime to the Rabi regime, followed by a detection of atoms in internal electronic states. Decoherence mechanisms are studied in detail promising a high ratio between the decoherence time and the gate operation time.Comment: 7 figure

Exact solution of the Hu-Paz-Zhang master equation

The Hu-Paz-Zhang equation is a master equation for an oscillator coupled to a linear passive bath. It is exact within the assumption that the oscillator and bath are initially uncoupled . Here an exact general solution is obtained in the form of an expression for the Wigner function at time t in terms of the initial Wigner function. The result is applied to the motion of a Gaussian wave packet and to that of a pair of such wave packets. A serious divergence arising from the assumption of an initially uncoupled state is found to be due to the zero-point oscillations of the bath and not removed in a cutoff model. As a consequence, worthwhile results for the equation can only be obtained in the high temperature limit, where zero-point oscillations are neglected. In that limit closed form expressions for wave packet spreading and attenuation of coherence are obtained. These results agree within a numerical factor with those appearing in the literature, which apply for the case of a particle at zero temperature that is suddenly coupled to a bath at high temperature. On the other hand very different results are obtained for the physically consistent case in which the initial particle temperature is arranged to coincide with that of the bath

Persistent currents in a circular array of Bose-Einstein condensates

A ring-shaped array of Bose-Einstein condensed atomic gases can display circular currents if the relative phase of neighboring condensates becomes locked to certain values. It is shown that, irrespective of the mechanism responsible for generating these states, only a restricted set of currents are stable, depending on the number of condensates, on the interaction and tunneling energies, and on the total number of particles. Different instabilities due to quasiparticle excitations are characterized and possible experimental setups for testing the stability prediction are also discussed.Comment: 7 pages, REVTex

Exact Diagonalization of Two Quantum Models for the Damped Harmonic Oscillator

The damped harmonic oscillator is a workhorse for the study of dissipation in quantum mechanics. However, despite its simplicity, this system has given rise to some approximations whose validity and relation to more refined descriptions deserve a thorough investigation. In this work, we apply a method that allows us to diagonalize exactly the dissipative Hamiltonians that are frequently adopted in the literature. Using this method we derive the conditions of validity of the rotating-wave approximation (RWA) and show how this approximate description relates to more general ones. We also show that the existence of dissipative coherent states is intimately related to the RWA. Finally, through the evaluation of the dynamics of the damped oscillator, we notice an important property of the dissipative model that has not been properly accounted for in previous works; namely, the necessity of new constraints to the application of the factorizable initial conditions.Comment: 19 pages, 2 figures, ReVTe

Decoherence from a Chaotic Environment: An Upside Down "Oscillator" as a Model

Chaotic evolutions exhibit exponential sensitivity to initial conditions. This suggests that even very small perturbations resulting from weak coupling of a quantum chaotic environment to the position of a system whose state is a non-local superposition will lead to rapid decoherence. However, it is also known that quantum counterparts of classically chaotic systems lose exponential sensitivity to initial conditions, so this expectation of enhanced decoherence is by no means obvious. We analyze decoherence due to a "toy" quantum environment that is analytically solvable, yet displays the crucial phenomenon of exponential sensitivity to perturbations. We show that such an environment, with a single degree of freedom, can be far more effective at destroying quantum coherence than a heat bath with infinitely many degrees of freedom. This also means that the standard "quantum Brownian motion" model for a decohering environment may not be as universally applicable as it once was conjectured to be.Comment: RevTeX, 29 pages, 5 EPS figures. Substantially rewritten analysis, improved figures, additional references, and errors fixed. Final version (to appear in PRA

Scattering of light and atoms in a Fermi-Dirac gas with BCS pairing

We theoretically study the optical properties of a Fermi-Dirac gas in the presence of a superfluid state. We calculate the leading quantum-statistical corrections to the standard column density result of the electric susceptibility. We also consider the Bragg diffraction of atoms by means of light-stimulated transitions of photons between two intersecting laser beams. Bardeen-Cooper-Schrieffer pairing between atoms in different internal levels magnifies incoherent scattering processes. The absorption linewidth of a Fermi-Dirac gas is broadened and shifted. Bardeen-Cooper-Schrieffer pairing introduces a collisional local-field shift that may dramatically dominate the Lorentz-Lorenz shift. For the case of the Bragg spectroscopy the static structure function may be significantly increased due to superfluidity in the nearforward scattering.Comment: 13 pages, 6 figures; to appear in PR