9,051 research outputs found
Quantum turbulence and correlations in Bose-Einstein condensate collisions
We investigate numerically simulated collisions between experimentally
realistic Bose-Einstein condensate wavepackets, within a regime where highly
populated scattering haloes are formed. The theoretical basis for this work is
the truncated Wigner method, for which we present a detailed derivation, paying
particular attention to its validity regime for colliding condensates. This
paper is an extension of our previous Letter [A. A. Norrie, R. J. Ballagh, and
C. W. Gardiner, Phys. Rev. Lett. 94, 040401 (2005)] and we investigate both
single-trajectory solutions, which reveal the presence of quantum turbulence in
the scattering halo, and ensembles of trajectories, which we use to calculate
quantum-mechanical correlation functions of the field
Quantum turbulence in condensate collisions: an application of the classical field method
We apply the classical field method to simulate the production of correlated
atoms during the collision of two Bose-Einstein condensates. Our
non-perturbative method includes the effect of quantum noise, and provides for
the first time a theoretical description of collisions of high density
condensates with very large out-scattered fractions. Quantum correlation
functions for the scattered atoms are calculated from a single simulation, and
show that the correlation between pairs of atoms of opposite momentum is rather
small. We also predict the existence of quantum turbulence in the field of the
scattered atoms--a property which should be straightforwardly measurable.Comment: 5 pages, 3 figures: Rewritten text, replaced figure
Three-body recombination of ultracold Bose gases using the truncated Wigner method
We apply the truncated Wigner method to the process of three-body
recombination in ultracold Bose gases. We find that within the validity regime
of the Wigner truncation for two-body scattering, three-body recombination can
be treated using a set of coupled stochastic differential equations that
include diffusion terms, and can be simulated using known numerical methods. As
an example we investigate the behaviour of a simple homogeneous Bose gas.Comment: Replaced paper same as original; correction to author list on
cond-mat mad
Bogoliubov dynamics of condensate collisions using the positive-P representation
We formulate the time-dependent Bogoliubov dynamics of colliding
Bose-Einstein condensates in terms of a positive-P representation of the
Bogoliubov field. We obtain stochastic evolution equations for the field which
converge to the full Bogoliubov description as the number of realisations
grows. The numerical effort grows linearly with the size of the computational
lattice. We benchmark the efficiency and accuracy of our description against
Wigner distribution and exact positive-P methods. We consider its regime of
applicability, and show that it is the most efficient method in the common
situation - when the total particle number in the system is insufficient for a
truncated Wigner treatment.Comment: 9 pages. 5 figure
Number-Phase Wigner Representation for Efficient Stochastic Simulations
Phase-space representations based on coherent states (P, Q, Wigner) have been
successful in the creation of stochastic differential equations (SDEs) for the
efficient stochastic simulation of high dimensional quantum systems. However
many problems using these techniques remain intractable over long integrations
times. We present a number-phase Wigner representation that can be unraveled
into SDEs. We demonstrate convergence to the correct solution for an anharmonic
oscillator with small dampening for significantly longer than other phase space
representations. This process requires an effective sampling of a non-classical
probability distribution. We describe and demonstrate a method of achieving
this sampling using stochastic weights.Comment: 7 pages, 1 figur
Disruption of reflecting Bose-Einstein condensates due to inter-atomic interactions and quantum noise
We perform fully three-dimensional simulations, using the truncated Wigner
method, to investigate the reflection of Bose-Einstein condensates from abrupt
potential barriers. We show that the inter-atomic interactions can disrupt the
internal structure of a cigar-shaped cloud with a high atom density at low
approach velocities, damping the center-of-mass motion and generating vortices.
Furthermore, by incorporating quantum noise we show that scattering halos form
at high approach velocities, causing an associated condensate depletion. We
compare our results to recent experimental observations.Comment: 5 figure
The stochastic Gross-Pitaevskii equation II
We provide a derivation of a more accurate version of the stochastic
Gross-Pitaevskii equation, as introduced by Gardiner et al. (J. Phys. B
35,1555,(2002). The derivation does not rely on the concept of local energy and
momentum conservation, and is based on a quasi-classical Wigner function
representation of a "high temperature" master equation for a Bose gas, which
includes only modes below an energy cutoff E_R that are sufficiently highly
occupied (the condensate band). The modes above this cutoff (the non-condensate
band) are treated as being essentially thermalized. The interaction between
these two bands, known as growth and scattering processes, provide noise and
damping terms in the equation of motion for the condensate band, which we call
the stochastic Gross-Pitaevskii equation. This approach is distinguished by the
control of the approximations made in its derivation, and by the feasibility of
its numerical implementation.Comment: 24 pages of LaTeX, one figur
Fault-Tolerant Dissipative Preparation of Atomic Quantum Registers with Fermions
We propose a fault tolerant loading scheme to produce an array of fermions in
an optical lattice of the high fidelity required for applications in quantum
information processing and the modelling of strongly correlated systems. A cold
reservoir of Fermions plays a dual role as a source of atoms to be loaded into
the lattice via a Raman process and as a heat bath for sympathetic cooling of
lattice atoms. Atoms are initially transferred into an excited motional state
in each lattice site, and then decay to the motional ground state, creating
particle-hole pairs in the reservoir. Atoms transferred into the ground
motional level are no longer coupled back to the reservoir, and doubly occupied
sites in the motional ground state are prevented by Pauli blocking. This scheme
has strong conceptual connections with optical pumping, and can be extended to
load high-fidelity patterns of atoms.Comment: 12 pages, 7 figures, RevTex
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