50 research outputs found
Stochastic Mean-Field Theory for the Disordered Bose-Hubbard Model
We investigate the effect of diagonal disorder on bosons in an optical
lattice described by an Anderson-Hubbard model at zero temperature. It is known
that within Gutzwiller mean-field theory spatially resolved calculations suffer
particularly from finite system sizes in the disordered case, while arithmetic
averaging of the order parameter cannot describe the Bose glass phase for
finite hopping . Here we present and apply a new \emph{stochastic}
mean-field theory which captures localization due to disorder, includes
non-trivial dimensional effects beyond the mean-field scaling level and is
applicable in the thermodynamic limit. In contrast to fermionic systems, we
find the existence of a critical hopping strength, above which the system
remains superfluid for arbitrarily strong disorder.Comment: 6 pages, 6 figure
Some remarks on the coherent-state variational approach to nonlinear boson models
The mean-field pictures based on the standard time-dependent variational
approach have widely been used in the study of nonlinear many-boson systems
such as the Bose-Hubbard model. The mean-field schemes relevant to
Gutzwiller-like trial states , number-preserving states and
Glauber-like trial states are compared to evidence the specific
properties of such schemes. After deriving the Hamiltonian picture relevant to
from that based on , the latter is shown to exhibit a Poisson
algebra equipped with a Weyl-Heisenberg subalgebra which preludes to the
-based picture. Then states are shown to be a superposition of -boson states and the similarities/differences of the -based and
-based pictures are discussed. Finally, after proving that the simple,
symmetric state indeed corresponds to a SU(M) coherent state, a dual
version of states and in terms of momentum-mode operators is
discussed together with some applications.Comment: 16 page
Glassy features of a Bose Glass
We study a two-dimensional Bose-Hubbard model at a zero temperature with
random local potentials in the presence of either uniform or binary disorder.
Many low-energy metastable configurations are found with virtually the same
energy as the ground state. These are characterized by the same blotchy pattern
of the, in principle, complex nonzero local order parameter as the ground
state. Yet, unlike the ground state, each island exhibits an overall random
independent phase. The different phases in different coherent islands could
provide a further explanation for the lack of coherence observed in experiments
on Bose glasses.Comment: 14 pages, 4 figures
Atomic Bose-Fermi mixtures in an optical lattice
A mixture of ultracold bosons and fermions placed in an optical lattice
constitutes a novel kind of quantum gas, and leads to phenomena, which so far
have been discussed neither in atomic physics, nor in condensed matter physics.
We discuss the phase diagram at low temperatures, and in the limit of strong
atom-atom interactions, and predict the existence of quantum phases that
involve pairing of fermions with one or more bosons, or, respectively, bosonic
holes. The resulting composite fermions may form, depending on the system
parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an
insulator with fermionic domains. We discuss the feasibility for observing such
phases in current experiments.Comment: 4 pages, 1 eps figure, misprints correcte
Ultracold atoms in optical lattices
Bosonic atoms trapped in an optical lattice at very low temperatures, can be
modeled by the Bose-Hubbard model. In this paper, we propose a slave-boson
approach for dealing with the Bose-Hubbard model, which enables us to
analytically describe the physics of this model at nonzero temperatures. With
our approach the phase diagram for this model at nonzero temperatures can be
quantified.Comment: 29 pages, 10 figure
Quantum Hall states for in optical lattices
We examine the quantum Hall (QH) states of the optical lattices with square
geometry using Bose-Hubbard model (BHM) in presence of artificial gauge field.
In particular, we focus on the QH states for the flux value of .
For this, we use cluster Gutzwiller mean-field (CGMF) theory with cluster sizes
of and . We obtain QH states at fillings with the cluster size and with cluster. Our results show that the geometry
of the QH states are sensitive to the cluster sizes. For all the values of
, the competing superfluid (SF) state is the ground state and QH state is
the metastable state.Comment: 6 pages, 4 figures. This is a pre-submission version of the
manuscript. The published version is available online in "Quantum Collisions
and Confinement of Atomic and Molecular Species, and Photons, Springer
Proceedings in Physics 230, pp 211--221 (2019)". The final authenticated
version is available online at : https://doi.org/10.1007/978-981-13-9969-5_2
Mean-field phase diagram of disordered bosons in a lattice at non-zero temperature
Bosons in a periodic lattice with on-site disorder at low but non-zero
temperature are considered within a mean-field theory. The criteria used for
the definition of the superfluid, Mott insulator and Bose glass are analysed.
Since the compressibility does never vanish at non-zero temperature, it can not
be used as a general criterium. We show that the phases are unambiguously
distinguished by the superfluid density and the density of states of the
low-energy exitations. The phase diagram of the system is calculated. It is
shown that even a tiny temperature leads to a significant shift of the boundary
between the Bose glass and superfluid
Simulation of gauge transformations on systems of ultracold atoms
We show that gauge transformations can be simulated on systems of ultracold
atoms. We discuss observables that are invariant under these gauge
transformations and compute them using a tensor network ansatz that escapes the
phase problem. We determine that the Mott-insulator-to-superfluid critical
point is monotonically shifted as the induced magnetic flux increases. This
result is stable against the inclusion of a small amount of entanglement in the
variational ansatz.Comment: 14 pages, 6 figure
Vortex Pinning and the Non-Hermitian Mott Transition
The boson Hubbard model has been extensively studied as a model of the zero
temperature superfluid/insulator transition in Helium-4 on periodic substrates.
It can also serve as a model for vortex lines in superconductors with a
magnetic field parallel to a periodic array of columnar pins, due to a formal
analogy between the vortex lines and the statistical mechanics of quantum
bosons. When the magnetic field has a component perpendicular to the pins, this
analogy yields a non-Hermitian boson Hubbard model. At integer filling, we find
that for small transverse fields, the insulating phase is preserved, and the
transverse field is exponentially screened away from the boundaries of the
superconductor. At larger transverse fields, a ``superfluid'' phase of tilted,
entangled vortices appears. The universality class of the transition is found
to be that of vortex lines entering the Meissner phase at H_{c1}, with the
additional feature that the direction of the tilted vortices at the transition
bears a non-trivial relationship to the direction of the applied magnetic
field. The properties of the Mott Insulator and flux liquid phases with tilt
are also discussed.Comment: 20 pages, 12 figures included in text; to appear in Physical Review
Cooling in strongly correlated optical lattices: prospects and challenges
Optical lattices have emerged as ideal simulators for Hubbard models of
strongly correlated materials, such as the high-temperature superconducting
cuprates. In optical lattice experiments, microscopic parameters such as the
interaction strength between particles are well known and easily tunable.
Unfortunately, this benefit of using optical lattices to study Hubbard models
come with one clear disadvantage: the energy scales in atomic systems are
typically nanoKelvin compared with Kelvin in solids, with a correspondingly
miniscule temperature scale required to observe exotic phases such as d-wave
superconductivity. The ultra-low temperatures necessary to reach the regime in
which optical lattice simulation can have an impact-the domain in which our
theoretical understanding fails-have been a barrier to progress in this field.
To move forward, a concerted effort to develop new techniques for cooling and,
by extension, techniques to measure even lower temperatures. This article will
be devoted to discussing the concepts of cooling and thermometry, fundamental
sources of heat in optical lattice experiments, and a review of proposed and
implemented thermometry and cooling techniques.Comment: in review with Reports on Progress in Physic