243 research outputs found
Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
We investigate the dynamics of neutral atoms in a 2D optical lattice which
traps two distinct internal states of the atoms in different columns. Two Raman
lasers are used to coherently transfer atoms from one internal state to the
other, thereby causing hopping between the different columns. By adjusting the
laser parameters appropriately we can induce a non vanishing phase of particles
moving along a closed path on the lattice. This phase is proportional to the
enclosed area and we thus simulate a magnetic flux through the lattice. This
setup is described by a Hamiltonian identical to the one for electrons on a
lattice subject to a magnetic field and thus allows us to study this equivalent
situation under very well defined controllable conditions. We consider the
limiting case of huge magnetic fields -- which is not experimentally accessible
for electrons in metals -- where a fractal band structure, the Hofstadter
butterfly, characterizes the system.Comment: 6 pages, RevTe
Attractive ultracold bosons in a necklace optical potential
We study the ground state properties of the Bose-Hubbard model with
attractive interactions on a M-site one-dimensional periodic -- necklace-like
-- lattice, whose experimental realization in terms of ultracold atoms is
promised by a recently proposed optical trapping scheme, as well as by the
control over the atomic interactions and tunneling amplitudes granted by
well-established optical techniques. We compare the properties of the quantum
model to a semiclassical picture based on a number-conserving su(M) coherent
state, which results into a set of modified discrete nonlinear Schroedinger
equations. We show that, owing to the presence of a correction factor ensuing
from number conservation, the ground-state solution to these equations provides
a remarkably satisfactory description of its quantum counterpart not only -- as
expected -- in the weak-interaction, superfluid regime, but even in the deeply
quantum regime of large interactions and possibly small populations. In
particular, we show that in this regime, the delocalized, Schroedinger-cat-like
quantum ground state can be seen as a coherent quantum superposition of the
localized, symmetry-breaking ground-state of the variational approach. We also
show that, depending on the hopping to interaction ratio, three regimes can be
recognized both in the semiclassical and quantum picture of the system.Comment: 11 pages, 7 figures; typos corrected and references added; to appear
in Phys. Rev.
Quantum random walks in optical lattices
We propose an experimental realization of discrete quantum random walks using
neutral atoms trapped in optical lattices. The random walk is taking place in
position space and experimental implementation with present day technology
--even using existing set-ups-- seems feasible. We analyze the influence of
possible imperfections in the experiment and investigate the transition from a
quantum random walk to the classical random walk for increasing errors and
decoherence.Comment: 8 pages, 4 figure
Re-entrance and entanglement in the one-dimensional Bose-Hubbard model
Re-entrance is a novel feature where the phase boundaries of a system exhibit
a succession of transitions between two phases A and B, like A-B-A-B, when just
one parameter is varied monotonically. This type of re-entrance is displayed by
the 1D Bose Hubbard model between its Mott insulator (MI) and superfluid phase
as the hopping amplitude is increased from zero. Here we analyse this
counter-intuitive phenomenon directly in the thermodynamic limit by utilizing
the infinite time-evolving block decimation algorithm to variationally minimize
an infinite matrix product state (MPS) parameterized by a matrix size chi.
Exploiting the direct restriction on the half-chain entanglement imposed by
fixing chi, we determined that re-entrance in the MI lobes only emerges in this
approximate when chi >= 8. This entanglement threshold is found to be
coincident with the ability an infinite MPS to be simultaneously
particle-number symmetric and capture the kinetic energy carried by
particle-hole excitations above the MI. Focussing on the tip of the MI lobe we
then applied, for the first time, a general finite-entanglement scaling
analysis of the infinite order Kosterlitz-Thouless critical point located
there. By analysing chi's up to a very moderate chi = 70 we obtained an
estimate of the KT transition as t_KT = 0.30 +/- 0.01, demonstrating the how a
finite-entanglement approach can provide not only qualitative insight but also
quantitatively accurate predictions.Comment: 12 pages, 8 figure
Quantum Kinetic Theory VI: The Growth of a Bose-Einstein Condensate
A detailed analysis of the growth of a BEC is given, based on quantum kinetic
theory, in which we take account of the evolution of the occupations of lower
trap levels, and of the full Bose-Einstein formula for the occupations of
higher trap levels, as well as the Bose stimulated direct transfer of atoms to
the condensate level introduced by Gardiner et al. We find good agreement with
experiment at higher temperatures, but at lower temperatures the experimentally
observed growth rate is somewhat more rapid. We also confirm the picture of the
``kinetic'' region of evolution, introduced by Kagan et al., for the time up to
the initiation of the condensate. The behavior after initiation essentially
follows our original growth equation, but with a substantially increased rate
coefficient.
Our modelling of growth implicitly gives a model of the spatial shape of the
condensate vapor system as the condensate grows, and thus provides an
alternative to the present phenomenological fitting procedure, based on the sum
of a zero-chemical potential vapor and a Thomas-Fermi shaped condensate. Our
method may give substantially different results for condensate numbers and
temperatures obtained from phenomentological fits, and indicates the need for
more systematic investigation of the growth dynamics of the condensate from a
supersaturated vapor.Comment: TeX source; 29 Pages including 26 PostScript figure
Characterizing the Hofstadter butterfly's outline with Chern numbers
In this work, we report original properties inherent to independent particles
subjected to a magnetic field by emphasizing the existence of regular
structures in the energy spectrum's outline. We show that this fractal curve,
the well-known Hofstadter butterfly's outline, is associated to a specific
sequence of Chern numbers that correspond to the quantized transverse
conductivity. Indeed the topological invariant that characterizes the
fundamental energy band depicts successive stairways as the magnetic flux
varies. Moreover each stairway is shown to be labeled by another Chern number
which measures the charge transported under displacement of the periodic
potential. We put forward the universal character of these properties by
comparing the results obtained for the square and the honeycomb geometries.Comment: Accepted for publication in J. Phys. B (Jan 2009
Extreme State Aggregation Beyond MDPs
We consider a Reinforcement Learning setup where an agent interacts with an
environment in observation-reward-action cycles without any (esp.\ MDP)
assumptions on the environment. State aggregation and more generally feature
reinforcement learning is concerned with mapping histories/raw-states to
reduced/aggregated states. The idea behind both is that the resulting reduced
process (approximately) forms a small stationary finite-state MDP, which can
then be efficiently solved or learnt. We considerably generalize existing
aggregation results by showing that even if the reduced process is not an MDP,
the (q-)value functions and (optimal) policies of an associated MDP with same
state-space size solve the original problem, as long as the solution can
approximately be represented as a function of the reduced states. This implies
an upper bound on the required state space size that holds uniformly for all RL
problems. It may also explain why RL algorithms designed for MDPs sometimes
perform well beyond MDPs.Comment: 28 LaTeX pages. 8 Theorem
Transport of strong-coupling polarons in optical lattices
We study the transport of ultracold impurity atoms immersed in a
Bose-Einstein condensate (BEC) and trapped in a tight optical lattice. Within
the strong-coupling regime, we derive an extended Hubbard model describing the
dynamics of the impurities in terms of polarons, i.e. impurities dressed by a
coherent state of Bogoliubov phonons. Using a generalized master equation based
on this microscopic model we show that inelastic and dissipative phonon
scattering results in (i) a crossover from coherent to incoherent transport of
impurities with increasing BEC temperature and (ii) the emergence of a net
atomic current across a tilted optical lattice. The dependence of the atomic
current on the lattice tilt changes from ohmic conductance to negative
differential conductance within an experimentally accessible parameter regime.
This transition is accurately described by an Esaki-Tsu-type relation with the
effective relaxation time of the impurities as a temperature-dependent
parameter.Comment: 25 pages, 6 figure
Modified spin-wave theory with ordering vector optimization I: frustrated bosons on the spatially anisotropic triangular lattice
We investigate a system of frustrated hardcore bosons, modeled by an XY
antiferromagnet on the spatially anisotropic triangular lattice, using
Takahashi's modified spin-wave (MSW) theory. In particular we implement
ordering vector optimization on the ordered reference state of MSW theory,
which leads to significant improvement of the theory and accounts for quantum
corrections to the classically ordered state. The MSW results at zero
temperature compare favorably to exact diagonalization (ED) and projected
entangled-pair state (PEPS) calculations. The resulting zero-temperature phase
diagram includes a 1D quasi-ordered phase, a 2D Neel ordered phase, and a 2D
spiraling ordered phase. We have strong indications that the various ordered or
quasi-ordered phases are separated by spin-liquid phases with short-range
correlations, in analogy to what has been predicted for the Heisenberg model on
the same lattice. Within MSW theory we also explore the finite-temperature
phase diagram. We find that the zero-temperature long-range-ordered phases turn
into quasi-ordered phases (up to a Berezinskii-Kosterlitz-Thouless
temperature), while zero-temperature quasi-ordered phases become short-range
correlated at finite temperature. These results show that modified spin-wave
theory is very well suited for describing ordered and quasi-ordered phases of
frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at
zero and finite temperatures. While MSW theory, just as other theoretical
methods, cannot describe spin-liquid phases, its breakdown provides a fast
method for singling out Hamiltonians which may feature these intriguing quantum
phases. We thus suggest a tool for guiding our search for interesting systems
whose properties are necessarily studied with a physical quantum simulator.Comment: 40 pages, 16 figure
Spatial fragmentation of a Bose-Einstein condensate in a double-well potential
We present a theoretical study of the ground state of a Bose-Einstein
condensate with repulsive inter-particle interactions in a double-well
potential, using a restricted variational principle. Within such an approach,
there is a transition from a single condensate to a fragmented condensate as
the strength of the central barrier of the potential is increased. We determine
the nature of this transition through approximate analytic as well as numerical
solutions of our model in the regime where the inter-particle interactions can
be treated perturbatively. The degree of fragmentation of the condensate is
characterized by the degrees of first-order and second-order spatial coherence
across the barrier.Comment: 10 pages, 2 figures, submitted to Phys. Rev.
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