65 research outputs found
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
Second-quantized Landau-Zener theory for dynamical instabilities
State engineering in nonlinear quantum dynamics sometimes may demand driving
the system through a sequence of dynamically unstable intermediate states. This
very general scenario is especially relevant to dilute Bose-Einstein
condensates, for which ambitious control schemes have been based on the
powerful Gross-Pitaevskii mean field theory. Since this theory breaks down on
logarithmically short time scales in the presence of dynamical instabilities,
an interval of instabilities introduces quantum corrections, which may possibly
derail a control scheme. To provide a widely applicable theory for such quantum
corrections, this paper solves a general problem of time-dependent quantum
mechanical dynamical instability, by modelling it as a second-quantized
analogue of a Landau-Zener avoided crossing: a `twisted crossing'.Comment: 4 pages, 3 figure
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
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
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
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
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
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
Out-of-equilibrium quantum fields with conserved charge
We study the out-of-equilibrium evolution of an O(2)-invariant scalar field
in which a conserved charge is stored. We apply a loop expansion of the
2-particle irreducible effective action to 3-loop order. Equations of motion
are derived which conserve both total charge and total energy yet allow for the
effects of scattering whereby charge and energy can transfer between modes.
Working in (1+1)-dimensions we solve the equations of motion numerically for a
system knocked out of equilibrium by a sudden temperature quench. We examine
the initial stages of the charge and energy redistribution. This provides a
basis from which we can understand the formation of Bose-Einstein condensates
from first principles.Comment: 11 pages, 5 figures, replacement with improved presentatio
Nonlinear dynamics for vortex lattice formation in a rotating Bose-Einstein condensate
We study the response of a trapped Bose-Einstein condensate to a sudden
turn-on of a rotating drive by solving the two-dimensional Gross-Pitaevskii
equation. A weakly anisotropic rotating potential excites a quadrupole shape
oscillation and its time evolution is analyzed by the quasiparticle projection
method. A simple recurrence oscillation of surface mode populations is broken
in the quadrupole resonance region that depends on the trap anisotropy, causing
stochastization of the dynamics. In the presence of the phenomenological
dissipation, an initially irrotational condensate is found to undergo damped
elliptic deformation followed by unstable surface ripple excitations, some of
which develop into quantized vortices that eventually form a lattice. Recent
experimental results on the vortex nucleation should be explained not only by
the dynamical instability but also by the Landau instability; the latter is
necessary for the vortices to penetrate into the condensate.Comment: RevTex4, This preprint includes no figures. You can download the
complete article and figures at
http://matter.sci.osaka-cu.ac.jp/bsr/cond-mat.htm
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