81 research outputs found
Quantum copying can increase the practically available information
While it is known that copying a quantum system does not increase the amount
of information obtainable about the originals, it may increase the amount
available in practice, when one is restricted to imperfect measurements. We
present a detection scheme which using imperfect detectors, and possibly noisy
quantum copying machines (that entangle the copies), allows one to extract more
information from an incoming signal, than with the imperfect detectors alone.
The case of single-photon detection with noisy, inefficient detectors and
copiers (single controlled-NOT gates in this case) is investigated in detail.
The improvement in distinguishability between a photon and vacuum is found to
occur for a wide range of parameters, and to be quite robust to random noise.
The properties that a quantum copying device must have to be useful in this
scheme are investigated.Comment: 10 pages, 6 figures, accepted PR
Stochastic gauge: a new technique for quantum simulations
We review progress towards direct simulation of quantum dynamics in many-body
systems, using recently developed stochastic gauge techniques. We consider
master equations, canonical ensemble calculations and reversible quantum
dynamics are compared, as well the general question of strategies for choosing
the gauge.Comment: 11 pages, 2 figures, to be published in Proceedings of the 16th
International Conference on Laser Spectroscopy (ICOLS), Palm Cove, Australia
(2003
Correlations in a BEC collision: First-principles quantum dynamics with 150 000 atoms
The quantum dynamics of colliding Bose-Einstein condensates with 150 000
atoms are simulated directly from the Hamiltonian using the stochastic
positive-P method. Two-body correlations between the scattered atoms and their
velocity distribution are found for experimentally accessible parameters.
Hanbury Brown-Twiss or thermal-like correlations are seen for copropagating
atoms, while number correlations for counterpropagating atoms are even stronger
than thermal correlations at short times. The coherent phase grains grow in
size as the collision progresses with the onset of growth coinciding with the
beginning of stimulated scattering. The method is versatile and usable for a
range of cold atom systems.Comment: 4 pages, 4 figures. v2: Rewording and style changes, minor except for
rewrite of background on the positive-P representation. Original research
unchange
First-principles quantum dynamics in interacting Bose gases I: The positive P representation
The performance of the positive P phase-space representation for exact
many-body quantum dynamics is investigated. Gases of interacting bosons are
considered, where the full quantum equations to simulate are of a
Gross-Pitaevskii form with added Gaussian noise. This method gives tractable
simulations of many-body systems because the number of variables scales
linearly with the spatial lattice size. An expression for the useful simulation
time is obtained, and checked in numerical simulations. The dynamics of first-,
second- and third-order spatial correlations are calculated for a uniform
interacting 1D Bose gas subjected to a change in scattering length. Propagation
of correlations is seen. A comparison is made to other recent methods. The
positive P method is particularly well suited to open systems as no
conservation laws are hard-wired into the calculation. It also differs from
most other recent approaches in that there is no truncation of any kind.Comment: 21 pages, 7 figures, 2 tables, IOP styl
Simulation of complete many-body quantum dynamics using controlled quantum-semiclassical hybrids
A controlled hybridization between full quantum dynamics and semiclassical
approaches (mean-field and truncated Wigner) is implemented for interacting
many-boson systems. It is then demonstrated how simulating the resulting hybrid
evolution equations allows one to obtain the full quantum dynamics for much
longer times than is possible using an exact treatment directly. A collision of
sodium BECs with 1.x10^5 atoms is simulated, in a regime that is difficult to
describe semiclassically. The uncertainty of physical quantities depends on the
statistics of the full quantum prediction. Cutoffs are minimised to a
discretization of the Hamiltonian. The technique presented is quite general and
extension to other systems is considered.Comment: Published version. Broader background and discussion, slightly
shortened, less figures in epaps. Research part unchanged. Article + epaps
(4+4 pages), 8 figure
Tradeoffs for number-squeezing in collisions of Bose-Einstein condensates
We investigate the factors that influence the usefulness of supersonic
collisions of Bose-Einstein condensates as a potential source of entangled
atomic pairs by analyzing the reduction of the number difference fluctuations
between regions of opposite momenta. We show that non-monochromaticity of the
mother clouds is typically the leading limitation on number squeezing, and that
the squeezing becomes less robust to this effect as the density of pairs grows.
We develop a simple model that explains the relationship between density
correlations and the number squeezing, allows one to estimate the squeezing
from properties of the correlation peaks, and shows how the multi-mode nature
of the scattering must be taken into account to understand the behavior of the
pairing. We analyze the impact of the Bose enhancement on the number squeezing,
by introducing a simplified low-gain model. We conclude that as far as
squeezing is concerned the preferable configuration occurs when atoms are
scattered not uniformly but rather into two well separated regions.Comment: 13 pages, 13 figures, final versio
Gauge P-representations for quantum-dynamical problems: Removal of boundary terms
P representation techniques, which have been very successful in quantum
optics and in other fields, are also useful for general bosonic quantum
dynamical many-body calculations such as Bose-Einstein condensation. We
introduce a representation called the gauge P representation which greatly
widens the range of tractable problems. Our treatment results in an infinite
set of possible time-evolution equations, depending on arbitrary gauge
functions that can be optimized for a given quantum system. In some cases,
previous methods can give erroneous results, due to the usual assumption of
vanishing boundary conditions being invalid for those particular systems.
Solutions are given to this boundary-term problem for all the cases where it is
known to occur: two-photon absorption and the single-mode laser. We also
provide some brief guidelines on how to apply the stochastic gauge method to
other systems in general, quantify the freedom of choice in the resulting
equations, and make a comparison to related recent developments.Comment: 17 pages, 5 figures. v2: Some changes in Appendix 1. Typos correcte
Quantum dynamics of long-range interacting systems using the positive-P and gauge-P representations
We provide the necessary framework for carrying out stochastic positive-P and
gauge-P simulations of bosonic systems with long range interactions. In these
approaches, the quantum evolution is sampled by trajectories in phase space,
allowing calculation of correlations without truncation of the Hilbert space or
other approximations to the quantum state. The main drawback is that the
simulation time is limited by noise arising from interactions.
We show that the long-range character of these interactions does not further
increase the limitations of these methods, in contrast to the situation for
alternatives such as the density matrix renormalisation group. Furthermore,
stochastic gauge techniques can also successfully extend simulation times in
the long-range-interaction case, by making using of parameters that affect the
noise properties of trajectories, without affecting physical observables.
We derive essential results that significantly aid the use of these methods:
estimates of the available simulation time, optimized stochastic gauges, a
general form of the characteristic stochastic variance and adaptations for very
large systems. Testing the performance of particular drift and diffusion gauges
for nonlocal interactions, we find that, for small to medium systems, drift
gauges are beneficial, whereas for sufficiently large systems, it is optimal to
use only a diffusion gauge.
The methods are illustrated with direct numerical simulations of interaction
quenches in extended Bose-Hubbard lattice systems and the excitation of Rydberg
states in a Bose-Einstein condensate, also without the need for the typical
frozen gas approximation. We demonstrate that gauges can indeed lengthen the
useful simulation time.Comment: 19 pages, 11 appendix, 3 figure
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