195 research outputs found
Dynamics of evaporative cooling in magnetically trapped atomic hydrogen
We study the evaporative cooling of magnetically trapped atomic hydrogen on
the basis of the kinetic theory of a Bose gas. The dynamics of trapped atoms is
described by the coupled differential equations, considering both the
evaporation and dipolar spin relaxation processes. The numerical time-evolution
calculations quantitatively agree with the recent experiment of Bose-Einstein
condensation with atomic hydrogen. It is demonstrated that the balance between
evaporative cooling and heating due to dipolar relaxation limits the number of
condensates to 9x10^8 and the corresponding condensate fraction to a small
value of 4% as observed experimentally.Comment: 5 pages, REVTeX, 3 eps figures, Phys. Rev. A in pres
Quantum Kinetic Theory V: Quantum kinetic master equation for mutual interaction of condensate and noncondensate
A detailed quantum kinetic master equation is developed which couples the
kinetics of a trapped condensate to the vapor of non-condensed particles. This
generalizes previous work which treated the vapor as being undepleted.Comment: RevTeX, 26 pages and 5 eps figure
Quantum Kinetic Theory III: Quantum kinetic master equation for strongly condensed trapped systems
We extend quantum kinetic theory to deal with a strongly Bose-condensed
atomic vapor in a trap. The method assumes that the majority of the vapor is
not condensed, and acts as a bath of heat and atoms for the condensate. The
condensate is described by the particle number conserving Bogoliubov method
developed by one of the authors. We derive equations which describe the
fluctuations of particle number and phase, and the growth of the Bose-Einstein
condensate. The equilibrium state of the condensate is a mixture of states with
different numbers of particles and quasiparticles. It is not a quantum
superposition of states with different numbers of particles---nevertheless, the
stationary state exhibits the property of off-diagonal long range order, to the
extent that this concept makes sense in a tightly trapped condensate.Comment: 3 figures submitted to Physical Review
Exciting, Cooling And Vortex Trapping In A Bose-Condensed Gas
A straight forward numerical technique, based on the Gross-Pitaevskii
equation, is used to generate a self-consistent description of
thermally-excited states of a dilute boson gas. The process of evaporative
cooling is then modelled by following the time evolution of the system using
the same equation. It is shown that the subsequent rethermalisation of the
thermally-excited state produces a cooler coherent condensate. Other results
presented show that trapping vortex states with the ground state may be
possible in a two-dimensional experimental environment.Comment: 9 pages, 7 figures. It's worth the wait! To be published in Physical
Review A, 1st February 199
Nonergodic Behavior of Interacting Bosons in Harmonic Traps
We study the time evolution of a system of interacting bosons in a harmonic
trap. In the low-energy regime, the quantum system is not ergodic and displays
rather large fluctuations of the ground state occupation number. In the high
energy regime of classical physics we find nonergodic behavior for modest
numbers of trapped particles. We give two conditions that assure the ergodic
behavior of the quantum system even below the condensation temperature.Comment: 11 pages, 3 PS-figures, uses psfig.st
Time evolution of condensed state of interacting bosons with reduced number fluctuation in a leaky box
We study the time evolution of the Bose-Einstein condensate of interacting
bosons confined in a leaky box, when its number fluctuation is initially (t=0)
suppressed. We take account of quantum fluctuations of all modes, including k =
0. We identify a ``natural coordinate'' b_0 of the interacting bosons, by which
many physical properties can be simply described. Using b_0, we successfully
define the cosine and sine operators for interacting many bosons. The
wavefunction, which we call the ``number state of interacting bosons'' (NSIB),
of the ground state that has a definite number N of interacting bosons can be
represented simply as a number state of b_0. We evaluate the time evolution of
the reduced density operator \rho(t) of the bosons in the box with a finite
leakage flux J, in the early time stage for which Jt << N. It is shown that
\rho(t) evolves from a single NSIB at t = 0, into a classical mixture of NSIBs
of various values of N at t > 0. We define a new state called the
``number-phase squeezed state of interacting bosons'' (NPIB). It is shown that
\rho(t) for t>0 can be rewritten as the phase-randomized mixture (PRM) of
NPIBs. It is also shown that the off-diagonal long-range order (ODLRO) and the
order parameter defined by it do not distinguish the NSIB and NPIB. On the
other hand, the other order parameter \Psi, defined as the expectation value of
the boson operator, has different values among these states. For each element
of the PRM of NPIBs, we show that \Psi evolves from zero to a finite value very
quickly. Namely, after the leakage of only two or three bosons, each element
acquires a full, stable and definite (non-fluctuating) value of \Psi.Comment: 25 pages including 3 figures. To appear in Phys. Rev. A (1999). The
title is changed to stress the time evolution. Sections II, III and IV of the
previous manuscript have been combined into one section. The introduction and
summary of the previous manuscript have been combined into the Introduction
and Summary. The names and abbreviations of quantum states are changed to
stress that they are for interacting many bosons. More references are cite
A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is
generalized to apply to a gas with an exact large number of particles.
This generalization yields a description of the Schr\"odinger picture field
operators as the product of an annihilation operator for the total number
of particles and the sum of a ``condensate wavefunction'' and a phonon
field operator in the form when the field operator acts on the N particle subspace. It
is then possible to expand the Hamiltonian in decreasing powers of ,
an thus obtain solutions for eigenvalues and eigenstates as an asymptotic
expansion of the same kind. It is also possible to compute all matrix elements
of field operators between states of different N.Comment: RevTeX, 11 page
Condensate fluctuations in finite Bose-Einstein condensates at finite temperature
A Langevin equation for the complex amplitude of a single-mode Bose-Einstein
condensate is derived. The equation is first formulated phenomenologically,
defining three transport parameters. It is then also derived microscopically.
Expressions for the transport parameters in the form of Green-Kubo formulas are
thereby derived and evaluated for simple trap geometries, a cubic box with
cyclic boundary conditions and an isotropic parabolic trap. The number
fluctuations in the condensate, their correlation time, and the
temperature-dependent collapse-time of the order parameter as well as its
phase-diffusion coefficient are calculated.Comment: 29 pages, Revtex, to appear in Phys.Rev.
Input-output theory for fermions in an atom cavity
We generalize the quantum optical input-output theory developed for optical
cavities to ultracold fermionic atoms confined in a trapping potential, which
forms an "atom cavity". In order to account for the Pauli exclusion principle,
quantum Langevin equations for all cavity modes are derived. The dissipative
part of these multi-mode Langevin equations includes a coupling between cavity
modes. We also derive a set of boundary conditions for the Fermi field that
relate the output fields to the input fields and the field radiated by the
cavity. Starting from a constant uniform current of fermions incident on one
side of the cavity, we use the boundary conditions to calculate the occupation
numbers and current density for the fermions that are reflected and transmitted
by the cavity
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