951 research outputs found
Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems
We prove the absence of a direct quantum phase transition between a
superfluid and a Mott insulator in a bosonic system with generic, bounded
disorder. We also prove compressibility of the system on the
superfluid--insulator critical line and in its neighborhood. These conclusions
follow from a general {\it theorem of inclusions} which states that for any
transition in a disordered system one can always find rare regions of the
competing phase on either side of the transition line. Quantum Monte Carlo
simulations for the disordered Bose-Hubbard model show an even stronger result,
important for the nature of the Mott insulator to Bose glass phase transition:
The critical disorder bound, , corresponding to the onset of
disorder-induced superfluidity, satisfies the relation , with the half-width of the Mott gap in the pure system.Comment: 4 pages, 3 figures; replaced with resubmitted versio
Measuring the equation of state of trapped ultracold bosonic systems in an optical lattice with in-situ density imaging
We analyze quantitatively how imaging techniques with single-site resolution
allow to measure thermodynamical properties that cannot be inferred from
time-of-light images for the trapped Bose-Hubbard model. If the normal state
extends over a sufficiently large range, the chemical potential and the
temperature can be extracted from a single shot, provided the sample is in
thermodynamic equilibrium. When the normal state is too narrow, temperature is
low but can still be extracted using the fluctuation-dissipation theorem over
the entire trap range as long as the local density approximation remains valid,
as was recently suggested by Qi Zhou and Tin-Lun Ho [arXiv:0908.3015]. However,
for typical present-day experiments, the number of samples needed is of the
order of 1000 in order to get the temperature at least accurate, but it
is possible to reduce the variance by 2 orders of magnitude if the
density-density correlation length is short, which is the case for the
Bose-Hubbard model. Our results provide further evidence that cold gases in an
optical lattices can be viewed as quantum analog computers.Comment: 8 pages, 10 figure
Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
Motivated by recent experiments, we study the relaxation dynamics and
thermalization in the one-dimensional Bose-Hubbard model induced by a global
interaction quench. Specifically, we start from an initial state that has
exactly one boson per site and is the ground state of a system with infinitely
strong repulsive interactions at unit filling. Using exact diagonalization and
the density matrix renormalization group method, we compute the time dependence
of such observables as the multiple occupancy and the momentum distribution
function. Typically, the relaxation to stationary values occurs over just a few
tunneling times. The stationary values are identical to the so-called diagonal
ensemble on the system sizes accessible to our numerical methods and we further
observe that the micro-canonical ensemble describes the steady state of many
observables reasonably well for small and intermediate interaction strength.
The expectation values of observables in the canonical ensemble agree
quantitatively with the time averages obtained from the quench at small
interaction strengths, and qualitatively provide a good description of
steady-state values even in parameter regimes where the micro-canonical
ensemble is not applicable due to finite-size effects. We discuss our numerical
results in the framework of the eigenstate thermalization hypothesis. Moreover,
we also observe that the diagonal and the canonical ensemble are practically
identical for our initial conditions already on the level of their respective
energy distributions for small interaction strengths. Finally, we discuss
implications of our results for the interpretation of a recent sudden expansion
experiment [Phys. Rev. Lett. 110, 205301 (2013)], in which the same interaction
quench was realized.Comment: 19 pages, 22 figure
Dynamical critical exponent of the Jaynes-Cummings-Hubbard model
An array of high-Q electromagnetic resonators coupled to qubits gives rise to
the Jaynes-Cummings-Hubbard model describing a superfluid to Mott insulator
transition of lattice polaritons. From mean-field and strong coupling
expansions, the critical properties of the model are expected to be identical
to the scalar Bose-Hubbard model. A recent Monte Carlo study of the superfluid
density on the square lattice suggested that this does not hold for the
fixed-density transition through the Mott lobe tip. Instead, mean-field
behavior with a dynamical critical exponent z=2 was found. We perform
large-scale quantum Monte Carlo simulations to investigate the critical
behavior of the superfluid density and the compressibility. We find z=1 at the
tip of the insulating lobe. Hence the transition falls in the 3D XY
universality class, analogous to the Bose-Hubbard model.Comment: 4 pages, 4 figures. To appear as a Rapid Communication in Phys. Rev.
Criticality in Trapped Atomic Systems
We discuss generic limits posed by the trap in atomic systems on the accurate
determination of critical parameters for second-order phase transitions, from
which we deduce optimal protocols to extract them. We show that under current
experimental conditions the in-situ density profiles are barely suitable for an
accurate study of critical points in the strongly correlated regime. Contrary
to recent claims, the proper analysis of time-of-fight images yields critical
parameters accurately.Comment: 4 pages, 3 figures; added reference
Comment on "Direct Mapping of the Finite Temperature Phase Diagram of Strongly Correlated Quantum Models" by Q. Zhou, Y. Kato, N. Kawashima, and N. Trivedi, Phys. Rev. Lett. 103, 085701 (2009)
In their Letter, Zhou, Kato, Kawashima, and Trivedi claim that
finite-temperature critical points of strongly correlated quantum models
emulated by optical lattice experiments can generically be deduced from kinks
in the derivative of the density profile of atoms in the trap with respect to
the external potential, . In this comment we demonstrate
that the authors failed to achieve their goal: to show that under realistic
experimental conditions critical densities can be extracted from
density profiles with controllable accuracy.Comment: 1 page, 1 figur
Consequences of the Pauli exclusion principle for the Bose-Einstein condensation of atoms and excitons
The bosonic atoms used in present day experiments on Bose-Einstein
condensation are made up of fermionic electrons and nucleons. In this Letter we
demonstrate how the Pauli exclusion principle for these constituents puts an
upper limit on the Bose-Einstein-condensed fraction. Detailed numerical results
are presented for hydrogen atoms in a cubic volume and for excitons in
semiconductors and semiconductor bilayer systems. The resulting condensate
depletion scales differently from what one expects for bosons with a repulsive
hard-core interaction. At high densities, Pauli exclusion results in
significantly more condensate depletion. These results also shed a new light on
the low condensed fraction in liquid helium II.Comment: 4 pages, 2 figures, revised version, now includes a direct comparison
with hard-sphere QMC results, submitted to Phys. Rev. Let
Disorder-induced superfluidity
We use quantum Monte Carlo simulations to study the phase diagram of
hard-core bosons with short-ranged {\it attractive} interactions, in the
presence of uniform diagonal disorder. It is shown that moderate disorder
stabilizes a glassy superfluid phase in a range of values of the attractive
interaction for which the system is a Mott insulator, in the absence of
disorder. A transition to an insulating Bose glass phase occurs as the strength
of the disorder or interactions increases.Comment: 5 pages, 6 figure
Discerning Incompressible and Compressible Phases of Cold Atoms in Optical Lattices
Experiments with cold atoms trapped in optical lattices offer the potential
to realize a variety of novel phases but suffer from severe spatial
inhomogeneity that can obscure signatures of new phases of matter and phase
boundaries. We use a high temperature series expansion to show that
compressibility in the core of a trapped Fermi-Hubbard system is related to
measurements of changes in double occupancy. This core compressibility filters
out edge effects, offering a direct probe of compressibility independent of
inhomogeneity. A comparison with experiments is made
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