387 research outputs found
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
Gaussian quantum Monte Carlo methods for fermions
We introduce a new class of quantum Monte Carlo methods, based on a Gaussian
quantum operator representation of fermionic states. The methods enable
first-principles dynamical or equilibrium calculations in many-body Fermi
systems, and, combined with the existing Gaussian representation for bosons,
provide a unified method of simulating Bose-Fermi systems. As an application,
we calculate finite-temperature properties of the two dimensional Hubbard
model.Comment: 4 pages, 3 figures, Revised version has expanded discussion,
simplified mathematical presentation, and application to 2D Hubbard mode
Correlations of Rydberg excitations in an ultra-cold gas after an echo sequence
We show that Rydberg states in an ultra-cold gas can be excited with strongly
preferred nearest-neighbor distance if densities are well below saturation. The
scheme makes use of an echo sequence in which the first half of a laser pulse
excites Rydberg states while the second half returns atoms to the ground state,
as in the experiment of Raitzsch et al. [Phys. Rev. Lett. 100 (2008) 013002].
Near to the end of the echo sequence, almost any remaining Rydberg atom is
separated from its next-neighbor Rydberg atom by a distance slightly larger
than the instantaneous blockade radius half-way through the pulse. These
correlations lead to large deviations of the atom counting statistics from a
Poissonian distribution. Our results are based on the exact quantum evolution
of samples with small numbers of atoms. We finally demonstrate the utility of
the omega-expansion for the approximate description of correlation dynamics
through an echo sequence.Comment: 8 pages, 6 figure
Covariant spinor representation of and quantization of the spinning relativistic particle
A covariant spinor representation of is constructed for the
quantization of the spinning relativistic particle. It is found that, with
appropriately defined wavefunctions, this representation can be identified with
the state space arising from the canonical extended BFV-BRST quantization of
the spinning particle with admissible gauge fixing conditions after a
contraction procedure. For this model, the cohomological determination of
physical states can thus be obtained purely from the representation theory of
the algebra.Comment: Updated version with references included and covariant form of
equation 1. 23 pages, no figure
Two-dimensional Nanolithography Using Atom Interferometry
We propose a novel scheme for the lithography of arbitrary, two-dimensional
nanostructures via matter-wave interference. The required quantum control is
provided by a pi/2-pi-pi/2 atom interferometer with an integrated atom lens
system. The lens system is developed such that it allows simultaneous control
over atomic wave-packet spatial extent, trajectory, and phase signature. We
demonstrate arbitrary pattern formations with two-dimensional 87Rb wavepackets
through numerical simulations of the scheme in a practical parameter space.
Prospects for experimental realizations of the lithography scheme are also
discussed.Comment: 36 pages, 4 figure
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 renormalization 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. © 2017 American Physical Society
Quantum many-body simulations using Gaussian phase-space representations
Phase-space representations are of increasing importance as a viable and
successful means to study exponentially complex quantum many-body systems from
first principles. This review traces the background of these methods, starting
from the early work of Wigner, Glauber and Sudarshan. We focus on modern
phase-space approaches using non-classical phase-space representations. These
lead to the Gaussian representation, which unifies bosonic and fermionic
phase-space. Examples treated include quantum solitons in optical fibers,
colliding Bose-Einstein condensates, and strongly correlated fermions on
lattices.Comment: Short Review (10 pages); Corrected typo in eq (14); Added a few more
reference
Simulations and Experiments on Polarisation Squeezing in Optical Fibre
We investigate polarisation squeezing of ultrashort pulses in optical fibre,
over a wide range of input energies and fibre lengths. Comparisons are made
between experimental data and quantum dynamical simulations, to find good
quantitative agreement. The numerical calculations, performed using both
truncated Wigner and exact phase-space methods, include nonlinear and
stochastic Raman effects, through coupling to phonons variables. The
simulations reveal that excess phase noise, such as from depolarising GAWBS,
affects squeezing at low input energies, while Raman effects cause a marked
deterioration of squeezing at higher energies and longer fibre lengths. The
optimum fibre length for maximum squeezing is also calculated.Comment: 19 pages, lots of figure
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