110 research outputs found
Correlations in an expanding gas of hard-core bosons
We consider a longitudinal expansion of a one-dimensional gas of hard-core
bosons suddenly released from a trap. We show that the broken translational
invariance in the initial state of the system is encoded in correlations
between the bosonic occupation numbers in the momentum space. The correlations
are protected by the integrability and exhibit no relaxation during the
expansion
Quantum decay of dark solitons in one dimensional Bose systems
Unless protected by the exact integrability, solitons are subject to
dissipative forces, originating from a thermally fluctuating background. At low
enough temperatures background fluctuations should be considered as being
quantized which enables us to calculate finite lifetime of the solitons
. We also find that the coherent nature of the quantum
fluctuations leads to long-range interactions between the solitons mediated by
the superradiation. Our results are of relevance to current experiments with
ultracold atoms, while the approach may be extended to solitons in other media.Comment: 5 pages, 1 figure. Accepted for publication in PRL
Kinetics of mobile impurities and correlation functions in one-dimensional superfluids at finite temperature
We scrutinize the hydrodynamic approach for calculating dynamical
correlations in one-dimensional superfluids near integrability and calculate
the characteristic time scale {\tau} beyond which this approach is valid. For
time scales shorter than {\tau} hydrodynamics fails and we develop an approach
based on kinetics of fermionic quasiparticles described as mobile impurities.
New universal results for the dynamical structure factor relevant to
experiments in ultracold atomic gases are obtained.Comment: 5 pages, 2 figures. Supplemental material included. Version 3: Minor
typos correcte
Castaing's instability in a trapped ultra-cold gas
We consider a trapped ultra-cold gas of (non-condensed) bosons with two
internal states (described by a pseudo spin) and study the stability of a
longitudinal pseudo spin polarization gradient. For this purpose, we
numerically solve a kinetic equation corresponding to a situation close to an
experiment at JILA. It shows the presence of Castaing's instability of
transverse spin polarization fluctuations at long wavelengths. This phenomenon
could be used to create spontaneous transverse spin waves.Comment: 5 pages, 3 figures; equation (8) corrected; submitted to EPJ
Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps
We analyze free expansion of a trapped one-dimensional Bose gas after a
sudden release from the confining trap potential. By using the stationary phase
and local density approximations, we show that the long-time asymptotic density
profile and the momentum distribution of the gas are determined by the initial
distribution of Bethe rapidities (quasimomenta) and hence can be obtained from
the solutions to the Lieb-Liniger equations in the thermodynamic limit. For
expansion from a harmonic trap, and in the limits of very weak and very strong
interactions, we recover the self-similar scaling solutions known from the
hydrodynamic approach. For all other power-law traps and arbitrary interaction
strengths, the expansion is not self-similar and shows strong dependence of the
density profile evolution on the trap anharmonicity. We also characterize
dynamical fermionization of the expanding cloud in terms of correlation
functions describing phase and density fluctuations.Comment: Final published version with modified title and a couple of other
minor changes. 5 pages, 2 figures, and Supplemental Materia
Fluctuational susceptibility of ultracold bosons in the vicinity of condensation
We study the behaviour of ultracold bosonic gas in the critical region above
the Bose-Einstein condensation in the presence of an artificial magnetic field,
. We show that the condensate fluctuations above the critical
temperature cause the fluctuational susceptibility, ,
of a uniform gas to have a stronger power-law divergence than in an analogous
superconducting system. Measuring such a divergence opens new ways of exploring
critical properties of the ultracold gas and an opportunity of an accurate
determination of . We describe a method of measuring
which requires a constant gradient in and suggest a way of
creating such a field in experiment.Comment: 5 pages, 3 figures, 5 pages of Supplement; the text is rewritten and
rearranged, and the figures are modifie
Large amplitude spin waves in ultra-cold gases
We discuss the theory of spin waves in non-degenerate ultra-cold gases, and
compare various methods which can be used to obtain appropriate kinetic
equations. We then study non-hydrodynamic situations, where the amplitude of
spin waves is sufficiently large to bring the system far from local
equilibrium. In the first part of the article, we compare two general methods
which can be used to derive a kinetic equation for a dilute gas of atoms
(bosons or fermions) with two internal states (treated as a pseudo-spin 1/2).
The collisional methods are in the spirit of Boltzmann's original derivation of
his kinetic equation where, at each point of space, the effects of all sorts of
possible binary collisions are added. We discuss two different versions of
collisional methods, the Yvon-Snider approach and the S matrix approach. The
second method uses the notion of mean field, which modifies the drift term of
the kinetic equation, in the line of the Landau theory of transport in quantum
liquids. For a dilute cold gas, it turns out that all these derivations lead to
the same drift terms in the transport equation, but differ in the precise
expression of the collision integral and in higher order gradient terms. In the
second part of the article, the kinetic equation is applied to spin waves in
trapped ultra-cold gases. Numerical simulations are used to illustrate the
strongly non-hydrodynamic character of the spin waves recently observed with
trapped Rb87 atoms. The decay of the phenomenon, which takes place when the
system relaxes back towards equilibrium, is also discussed, with a short
comment on decoherence.Comment: To appear in Eur. Phys. J.
Correlations in an expanding gas of hard-core bosons
We consider a longitudinal expansion of a one-dimensional gas of hard-core
bosons suddenly released from a trap. We show that the broken translational
invariance in the initial state of the system is encoded in correlations
between the bosonic occupation numbers in the momentum space. The correlations
are protected by the integrability and exhibit no relaxation during the
expansion
Exact nonequilibrium dynamics of finite-temperature Tonks-Girardeau gases
Describing finite-temperature nonequilibrium dynamics of interacting
many-particle systems is a notoriously challenging problem in quantum many-body
physics. Here we provide an exact solution to this problem for a system of
strongly interacting bosons in one dimension in the Tonks-Girardeau regime of
infinitely strong repulsive interactions. Using the Fredholm determinant
approach and the Bose-Fermi mapping we show how the problem can be reduced to a
single-particle basis, wherein the finite-temperature effects enter the
solution via an effective "dressing" of the single-particle wavefunctions by
the Fermi-Dirac occupation factors. We demonstrate the utility of our approach
and its computational efficiency in two nontrivial out-of-equilibrium
scenarios: collective breathing mode oscillations in a harmonic trap and
collisional dynamics in the Newton's cradle setting involving real-time
evolution in a periodic Bragg potential.Comment: Final published version in PRA style; moved Supplemental Material
into main text; 6 pages, 3 figure
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