371 research outputs found
Few-Body Route to One-Dimensional Quantum Liquids
Gapless many-body quantum systems in one spatial dimension are universally
described by the Luttinger liquid effective theory at low energies.
Essentially, only two parameters enter the effective low-energy description,
namely the speed of sound and the Luttinger parameter. These are highly system
dependent and their calculation requires accurate non-perturbative solutions of
the many-body problem. Here, we present a simple method that only uses
collisional information to extract the low-energy properties of these systems.
Our results are in remarkable agreement with available results for integrable
models and from large scale Monte Carlo simulations of one-dimensional helium
and hydrogen isotopes. Moreover, we estimate theoretically the critical point
for spinodal decomposition in one-dimensional helium-4, and show that the
exponent governing the divergence of the Luttinger parameter near the critical
point is exactly 1/2, in excellent agreement with Monte Carlo simulations.Comment: 8 pages, 6 figures, including supplementary materia
Universality and tails of long range interactions in one dimension
Long-range interactions and, in particular, two-body potentials with
power-law long-distance tails are ubiquitous in nature. For two bosons or
fermions in one spatial dimension, the latter case being formally equivalent to
three-dimensional -wave scattering, we show how generic asymptotic
interaction tails can be accounted for in the long-distance limit of scattering
wave functions. This is made possible by introducing a generalisation of the
collisional phase shifts to include space dependence. We show that this
distance dependence is universal, in that it does not depend on short-distance
details of the interaction. The energy dependence is also universal, and is
fully determined by the asymptotic tails of the two-body potential. As an
important application of our findings, we describe how to eliminate finite-size
effects with long-range potentials in the calculation of scattering phase
shifts from exact diagonalisation. We show that even with moderately small
system sizes it is possible to accurately extract phase shifts that would
otherwise be plagued with finite-size errors. We also consider multi-channel
scattering, focusing on the estimation of open channel asymptotic interaction
strengths via finite-size analysis.Comment: 7 pages, 3 figure
Vortex sorter for Bose-Einstein condensates
We have designed interferometers that sort Bose-Einstein condensates into
their vortex components. The Bose-Einstein condensates in the two arms of the
interferometer are rotated with respect to each other through fixed angles;
different vortex components then exit the interferometer in different
directions. The method we use to rotate the Bose-Einstein condensates involves
asymmetric phase imprinting and is itself new. We have modelled rotation
through fixed angles and sorting into vortex components with even and odd
values of the topological charge of 2-dimensional Bose-Einstein condensates in
a number of states (pure or superposition vortex states for different values of
the scattering length). Our scheme may have applications for quantum
information processing.Comment: 4 pages, high resolution figures can be obtained from the author
Theory of elementary excitations in unstable Bose-Einstein condensates
Like classical fluids, quantum gases may suffer from hydrodynamic instabilities. Our paper develops a quantum version of the classical stability analysis in fluids, the Bogoliubov theory of elementary excitations in unstable Bose-Einstein condensates. In unstable condensates the excitation modes have complex frequencies. We derive the normalization conditions for unstable modes such that they can serve in a mode decomposition of the noncondensed component. Furthermore, we develop approximative techniques to determine the spectrum and the mode functions. Finally, we apply our theory to sonic horizons - sonic black and white holes. For sonic white holes the spectrum of unstable modes turns out to be intrinsically discrete, whereas black holes may be stable
Driven Topological Systems in the Classical Limit
Periodically-driven quantum systems can exhibit topologically non-trivial
behaviour, even when their quasi-energy bands have zero Chern numbers. Much
work has been conducted on non-interacting quantum-mechanical models where this
kind of behaviour is present. However, the inclusion of interactions in
out-of-equilibrium quantum systems can prove to be quite challenging. On the
other hand, the classical counterpart of hard-core interactions can be
simulated efficiently via constrained random walks. The non-interacting model
proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013)], has a special point
for which the system is equivalent to a classical random walk. We consider the
classical counterpart of this model, which is exact at a special point even
when hard-core interactions are present, and show how these quantitatively
affect the edge currents in a strip geometry. We find that the interacting
classical system is well described by a mean-field theory. Using this we
simulate the dynamics of the classical system, which show that the interactions
play the role of Markovian, or time dependent disorder. By comparing the
evolution of classical and quantum edge currents in small lattices, we find
regimes where the classical limit considered gives good insight into the
quantum problem.Comment: 15 pages, 15 figures, new content on the quantum mode
Constructive role of dissipation for driven coupled bosonic modes
We theoretically investigate a system of two coupled bosonic modes subject to
both dissipation and external driving. We show that in the steady state the
degree of entanglement between the coupled bosonic modes can be enhanced by
dissipation. The non-monotonic dependence of entanglement on the decay rates is
observed when the bosonic modes are asymmetrically coupled to their local
baths. This counterintuitive result opens a new way to better understand the
interplay between noise and coherence in continuous variable systems driven
away from equilibrium.Comment: 4.5 pages. Published version (with minor modifications
Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
We show that the adiabatic motion of ultracold, multilevel atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atom-laser interaction exist. A pair of such degenerate dark states emerges, e.g., if laser fields couple three internal states of an atom to a fourth common one under pairwise two-photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component
Markovian evolution of strongly coupled harmonic oscillators
We investigate how to model Markovian evolution of coupled harmonic
oscillators, each of them interacting with a local environment. When the
coupling between the oscillators is weak, dissipation may be modeled using
local Lindblad terms for each of the oscillators in the master equation, as is
commonly done. When the coupling between oscillators is strong, this model may
become invalid. We derive a master equation for two coupled harmonic
oscillators which are subject to individual heat baths modeled by a collection
of harmonic oscillators, and show that this master equation in general contains
non-local Lindblad terms. We compare the resulting time evolution with that
obtained for dissipation through local Lindblad terms for each individual
oscillator, and show that the evolution is different in the two cases. In
particular, the two descriptions give different predictions for the steady
state and for the entanglement between strongly coupled oscillators. This shows
that when describing strongly coupled harmonic oscillators, one must take great
care in how dissipation is modeled, and that a description using local Lindblad
terms may fail. This may be particularly relevant when attempting to generate
entangled states of strongly coupled quantum systems.Comment: 11 pages, 4 figures, significantly revised and close to the published
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