185 research outputs found
Mott transition of fermionic atoms in a three-dimensional optical trap
We study theoretically the Mott metal-insulator transition for a system of
fermionic atoms confined in a three-dimensional optical lattice and a harmonic
trap. We describe an inhomogeneous system of several thousand sites using an
adaptation of dynamical mean field theory solved efficiently with the numerical
renormalization group method. Above a critical value of the on-site
interaction, a Mott-insulating phase appears in the system. We investigate
signatures of the Mott phase in the density profile and in time-of-flight
experiments.Comment: 4 pages and 5 figure
Kondo proximity effect: How does a metal penetrate into a Mott insulator?
We consider a heterostructure of a metal and a paramagnetic Mott insulator
using an adaptation of dynamical mean field theory to describe inhomogeneous
systems. The metal can penetrate into the insulator via the Kondo effect. We
investigate the scaling properties of the metal-insulator interface close to
the critical point of the Mott insulator. At criticality, the quasiparticle
weight decays as 1/x^2 with distance x from the metal within our mean field
theory. Our numerical results (using the numerical renormalization group as an
impurity solver) show that the prefactor of this power law is extremely small.Comment: 4 pages, 3 figure
On Optimal Harvesting in Stochastic Environments: Optimal Policies in a Relaxed Model
This paper examines the objective of optimally harvesting a single species in
a stochastic environment. This problem has previously been analyzed in Alvarez
(2000) using dynamic programming techniques and, due to the natural payoff
structure of the price rate function (the price decreases as the population
increases), no optimal harvesting policy exists. This paper establishes a
relaxed formulation of the harvesting model in such a manner that existence of
an optimal relaxed harvesting policy can not only be proven but also
identified. The analysis embeds the harvesting problem in an
infinite-dimensional linear program over a space of occupation measures in
which the initial position enters as a parameter and then analyzes an auxiliary
problem having fewer constraints. In this manner upper bounds are determined
for the optimal value (with the given initial position); these bounds depend on
the relation of the initial population size to a specific target size. The more
interesting case occurs when the initial population exceeds this target size; a
new argument is required to obtain a sharp upper bound. Though the initial
population size only enters as a parameter, the value is determined in a
closed-form functional expression of this parameter.Comment: Key Words: Singular stochastic control, linear programming, relaxed
contro
Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice
The fermionic Hubbard model plays a fundamental role in the description of
strongly correlated materials. Here we report on the realization of this
Hamiltonian using a repulsively interacting spin mixture of ultracold K
atoms in a 3D optical lattice. We have implemented a new method to directly
measure the compressibility of the quantum gas in the trap using in-situ
imaging and independent control of external confinement and lattice depth.
Together with a comparison to ab-initio Dynamical Mean Field Theory
calculations, we show how the system evolves for increasing confinement from a
compressible dilute metal over a strongly-interacting Fermi liquid into a band
insulating state. For strong interactions, we find evidence for an emergent
incompressible Mott insulating phase.Comment: 21 pages, 5 figures and additional supporting materia
Ground State Properties of an Asymmetric Hubbard Model for Unbalanced Ultracold Fermionic Quantum Gases
In order to describe unbalanced ultracold fermionic quantum gases on optical
lattices in a harmonic trap, we investigate an attractive () asymmetric
() Hubbard model with a Zeeman-like magnetic
field. In view of the model's spatial inhomogeneity, we focus in this paper on
the solution at Hartree-Fock level. The Hartree-Fock Hamiltonian is
diagonalized with particular emphasis on superfluid phases. For the special
case of spin-independent hopping we analytically determine the number of
solutions of the resulting self-consistency equations and the nature of the
possible ground states at weak coupling. Numerical results for unbalanced
Fermi-mixtures are presented within the local density approximation. In
particular, we find a fascinating shell structure, involving normal and
superfluid phases. For the general case of spin-dependent hopping we calculate
the density of states and the possible superfluid phases in the ground state.
In particular, we find a new magnetized superfluid phase.Comment: 9 pages, 5 figure
The Euler-Maruyama approximation for the absorption time of the CEV diffusion
A standard convergence analysis of the simulation schemes for the hitting
times of diffusions typically requires non-degeneracy of their coefficients on
the boundary, which excludes the possibility of absorption. In this paper we
consider the CEV diffusion from the mathematical finance and show how a weakly
consistent approximation for the absorption time can be constructed, using the
Euler-Maruyama scheme
A Mott insulator of fermionic atoms in an optical lattice
In a solid material strong interactions between the electrons can lead to
surprising properties. A prime example is the Mott insulator, where the
suppression of conductivity is a result of interactions and not the consequence
of a filled Bloch band. The proximity to the Mott insulating phase in fermionic
systems is the origin for many intriguing phenomena in condensed matter
physics, most notably high-temperature superconductivity. Therefore it is
highly desirable to use the novel experimental tools developed in atomic
physics to access this regime. Indeed, the Hubbard model, which encompasses the
essential physics of the Mott insulator, also applies to quantum gases trapped
in an optical lattice. However, the Mott insulating regime has so far been
reached only with a gas of bosons, lacking the rich and peculiar nature of
fermions. Here we report on the formation of a Mott insulator of a repulsively
interacting two-component Fermi gas in an optical lattice. It is signalled by
three features: a drastic suppression of doubly occupied lattice sites, a
strong reduction of the compressibility inferred from the response of double
occupancy to atom number increase, and the appearance of a gapped mode in the
excitation spectrum. Direct control of the interaction strength allows us to
compare the Mott insulating and the non-interacting regime without changing
tunnel-coupling or confinement. Our results pave the way for further studies of
the Mott insulator, including spin ordering and ultimately the question of
d-wave superfluidity.Comment: 6 pages, 4 figure
Supersolid state of ultracold fermions in an optical lattice
We study ultracold fermionic atoms trapped in an optical lattice with
harmonic confinement by means of the dynamical mean-field approximation. It is
demonstrated that a supersolid state, where an s-wave superfluid coexists with
a density-wave state with a checkerboard pattern, is stabilized by attractive
onsite interactions on a square lattice. Our new finding here is that a
confining potential plays an invaluable role in stabilizing the supersolid
state. We establish a rich phase diagram at low temperatures, which clearly
shows how the insulator, the density wave and the superfluid compete with each
other to produce an intriguing domain structure. Our results shed light on the
possibility of the supersolid state in fermionic optical lattice systems.Comment: 5 pages, 4 figure
Dynamical Mean-Field Theory
The dynamical mean-field theory (DMFT) is a widely applicable approximation
scheme for the investigation of correlated quantum many-particle systems on a
lattice, e.g., electrons in solids and cold atoms in optical lattices. In
particular, the combination of the DMFT with conventional methods for the
calculation of electronic band structures has led to a powerful numerical
approach which allows one to explore the properties of correlated materials. In
this introductory article we discuss the foundations of the DMFT, derive the
underlying self-consistency equations, and present several applications which
have provided important insights into the properties of correlated matter.Comment: Chapter in "Theoretical Methods for Strongly Correlated Systems",
edited by A. Avella and F. Mancini, Springer (2011), 31 pages, 5 figure
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