1,347 research outputs found
Universal Thermometry for Quantum Simulation
Quantum simulation is a highly ambitious program in cold atom research
currently being pursued in laboratories worldwide. The goal is to use cold
atoms in optical lattice to simulate models for unsolved strongly correlated
systems, so as to deduce their properties directly from experimental data. An
important step in this effort is to determine the temperature of the system,
which is essential for deducing all thermodynamic functions. This step,
however, remains difficult for lattice systems at the moment. Here, we propose
a method based on a generalized fluctuation-dissipation theorem. It does not
reply on numerical simulations and is a universal thermometry for all quantum
gases systems including mixtures and spinor gases. It is also unaffected by
photon shot noise.Comment: 4 pages, 3 figures, title, abstract and introduction modifie
Signature of Quantum Criticality in the Density Profiles of Cold Atom Systems
In recent years, there is considerable experimental effort using cold atoms
to study strongly correlated many-body systems. One class of phenomena of
particularly interests is quantum critical (QC) phenomena. While prevalent in
many materials, these phenomena are notoriously difficult theoretical problems
due to the vanishing of energy scales in QC region. So far, there are no
systematic ways to deduce QC behavior of bulk systems from the data of trapped
atomic gases. Here, we present a simple algorithm to use the experimental
density profile to determine the T=0 phase boundary of bulk systems, as well as
the scaling functions in QC regime. We also present another scheme for removing
finite size effects of the trap. We demonstrate the validity of our schemes
using exactly soluble models.Comment: 4 pages, 5 figure
A Unified Elementary Approach to the Dyson, Morris, Aomoto, and Forrester Constant Term Identities
We introduce an elementary method to give unified proofs of the Dyson,
Morris, and Aomoto identities for constant terms of Laurent polynomials. These
identities can be expressed as equalities of polynomials and thus can be proved
by verifying them for sufficiently many values, usually at negative integers
where they vanish. Our method also proves some special cases of the Forrester
conjecture.Comment: 20 page
Criterion for bosonic superfluidity in an optical lattice
We show that the current method of determining superfluidity in optical
lattices based on a visibly sharp bosonic momentum distribution
can be misleading, for even a normal Bose gas can have a similarly sharp
. We show that superfluidity in a homogeneous system can be
detected from the so-called visibility of that must
be 1 within , where is the number of bosons. We also show that
the T=0 visibility of trapped lattice bosons is far higher than what is
obtained in some current experiments, suggesting strong temperature effects and
that these states can be normal. These normal states allow one to explore the
physics in the quantum critical region.Comment: 4 pages, 2 figures; published versio
Squeezing Out the Entropy of Fermions in Optical Lattices
At present, there is considerable interest in using atomic fermions in
optical lattices to emulate the mathematical models that have been used to
study strongly correlated electronic systems. Some of these models, such as the
two dimensional fermion Hubbard model, are notoriously difficult to solve, and
their key properties remain controversial despite decades of studies. It is
hoped that the emulation experiments will shed light on some of these long
standing problems. A successful emulation, however, requires reaching
temperatures as low as K and beyond, with entropy per particle far
lower than what can be achieved today. Achieving such low entropy states is an
essential step and a grand challenge of the whole emulation enterprise. In this
paper, we point out a method to literally squeeze the entropy out from a Fermi
gas into a surrounding Bose-Einstein condensed gas (BEC), which acts as a heat
reservoir. This method allows one to reduce the entropy per particle of a
lattice Fermi gas to a few percent of the lowest value obtainable today.Comment: 6 pages, 3 figures. This paper has appeared in the Early Edition of
Proceeding of National Academy on April 13, 2009. Please see
http://www.pnas.org/cgi/doi/10.1073/pnas.080986210
A family of q-Dyson style constant term identities
AbstractBy generalizing Gessel–Xin's Laurent series method for proving the Zeilberger–Bressoud q-Dyson Theorem, we establish a family of q-Dyson style constant term identities. These identities give explicit formulas for certain coefficients of the q-Dyson product, including three conjectures of Sills' as special cases and generalizing Stembridge's first layer formulas for characters of SL(n,C)
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