28,877 research outputs found
What can ultracold Fermi gases teach us about high superconductors and vice versa?
We review recent developments in the field of ultracold atomic Fermi gases.
As the cold atom system evolves from BCS to Bose-Einstein condensation (BEC),
the behavior of the thermodynamics, and the particle density profiles evolves
smoothly in a way which can be well understood theoretically. In the
interesting "unitary" regime, we show that these and other data necessarily
requires the introduction of a pseudogap in the fermionic spectrum which
exhibits many striking similarities to its counterpart in underdoped high
superconductors. We emphasize these similarities, giving an overview of the
experimental tools and key issues of common interest in both systems.Comment: 4 pages, 6 figures, to appear in a special issue of Physica C for the
M2S-HTSC VIII Conference Proceeding
Establishing Conservation Laws in Pair Correlated Many Body theories: T matrix Approaches
We address conservation laws associated with current, momentum and energy and
show how they can be satisfied within many body theories which focus on pair
correlations. Of interest are two well known t-matrix theories which represent
many body theories which incorporate pairing in the normal state. The first of
these is associated with Nozieres Schmitt-Rink theory, while the second
involves the t-matrix of a BCS-Leggett like state as identified by Kadanoff and
Martin. T-matrix theories begin with an ansatz for the single particle self
energy and are to be distinguished from -derivable theories which
introduce an ansatz for a particular contribution to the thermodynamical
potential. Conservation laws are equivalent to Ward identities which we address
in some detail here. Although -derivable theories are often referred to
as "conserving theories", a consequence of this work is the demonstration that
these two t-matrix approaches similarly can be made to obey all conservation
laws. Moreover, simplifying approximations in -derivable theories,
frequently lead to results which are incompatible with conservation.Comment: 12 pages, 1 figur
A new many-body wave function for BCS-BEC crossover in Fermi gases
We present a new many body formalism for BCS-BEC crossover, which represents
a modification of the BCS-Leggett ground state to include 4-fermion, and higher
correlations. In the BEC regime, we show how our approach contains the
\textit{Petrov et al} 4-fermion behavior and associated scattering length
at short distances, and secondly reduces to composite-boson Bogoliubov
physics at long distances. It reproduces the Lee-Yang term, whose numerical
value is also fixed by . We have also examined the next term beyond the
Lee-Yang correction in a phenomenological fashion, building on cloud size data
and collective mode experiments. However, one has to view this phenomenological
analysis with some caution since experiments are in a state of flux and are
performed close to unitarity.Comment: 5 pages, 2 color figure
Finite Temperature Effects in Ultracold Fermi Gases
This article is written as a Lecture given in the 2006 Varenna Summer School
on "Ultracold Fermi Gases". Here we present a review of BCS--Bose Einstein
condensation (BEC) crossover theory with emphasis on finite temperature
effects. We discuss the role of temperature as it enters a theoretical
formalism which is based on the standard BCS-Leggett ground state. We also
discuss the role of temperature in the context of experiments ranging from
thermometric issues to signatures of superfluidity. Particularly important to
this discussion is the novel normal state associated with the crossover regime,
intermediate between BCS and BEC. The experimental evidence for this unusual
normal state (associated with pre-formed pairs) and its counterpart below
(associated with non-condensed pairs) is presented in the context of different
experiments. We end with a discussion of finite temperature effects in spin
polarized superfluids, where is found to play a crucial role in both theory
and experiment.Comment: Lecture given at the International School of Physics "Enrico Fermi"
-- the 2006 Varenna Summer School on "Ultracold Fermi Gases", 27 pages, 17
figure
Population of closed-channel molecules in trapped Fermi gases with broad Feshbach resonances
We compute the fraction of closed-channel molecules in trapped atomic Fermi
gases, over the entire range of accessible fields and temperatures. We use a
two-channel model of BCS--Bose-Einstein condensation (BEC) crossover theory at
general temperature , and show that this fraction provides a measure of the
dependent pairing gap. Our calculations, containing no free parameters, are
in good quantitative agreement with recent low measurements in Li. We
present readily testable predictions for the dependencies of the closed-channel
fraction on temperature and Fermi momentum.Comment: 4 pages, 3 figures, published in PR
Equilibrating dynamics in quenched Bose gases: characterizing multiple time regimes
We address the physics of equilibration in ultracold atomic gases following a
quench of the interaction parameter. We focus on the momentum distribution of
the excitations, , and observe that larger modes
will equilibrate faster, as has been claimed in recent experimental work. We
identify three time regimes. At short times exhibits
oscillations; these are damped out at intermediate times where the system
appears to be in a false-equilibrium. Finally, at longer times, full
equilibration occurs. This false-equilibrium is associated with the necessarily
slower relaxation of the condensate which sufficiently high -states (of the excitation response) will then quasi-adiabatically follow.
Our work bears on the recent literature focus on interaction quench
experiments. We take issue with the fact that theories to date assume that the
oscillatory regime is adequate for addressing experiments.Comment: v2: major rewriting, 6 pages, 3 figure
An Alternative Route to D-wave Superconductivity: the Charge Channel
We demonstrate that a superconducting pairing is naturally
associated with the screened Coulomb interaction
within the plane of high superconductors. This pairing
instability arises (via the dielectric constant) from wave-vector structure in
at , which is associated with 2D
Van Hove and local field effects. Our results, which are independent of the
bandstructure, suggest that direct Coulomb intereactions are significant (when
compared to the spin channel) and will, at the least, enhance any other
underlying mechanism for wave pairing.Comment: 4 pages, postscript file for entire paper, also available at
http://rainbow.uchicago.edu/~ldz/paper/psd09.p
Particle Density Distributions in Fermi Gas Superfluids: Molecular Boson Effects
We show how to describe the behavior associated with the usual
BCS- Bose Einstein condensation (BEC) crossover ground state. We confine our
attention here to the BEC and near-BEC regime where analytical calculations are
possible. At finite , non-condensed fermion pairs must be included, although
they have been generally ignored in the literature. Within this BEC regime we
compute the equations of state for the one and two channel models; these two
cases correspond to whether Feshbach resonance effects are omitted or included.
Differences between these two cases can be traced to differences between the
nature of a Cooper pair and bosonic condensate. Our results are also compared
with the Gross Pitaevskii equations of state for true bosons. Differences found
here are associated with the underlying fermionic character of the system.
Finally, the particle density distribution functions for a trap containing
superfluid fermionic atoms are computed using a Thomas-Fermi approach. The one
and two channel behavior is found to be very different; we find a narrowing of
the density profile as a result of Feshbach resonance effects. Importantly, we
infer that the ratio between bosonic and fermionic scattering lengths depends
on the magnetic detuning and is generally smaller than 2. Future experiments
will be required to determine to what extent this ratio varies with magnetic
fields.Comment: 8 pages, 2 figure, Revtex 4, submitted to PRA; manuscript expanded,
figure adde
Pairing Correlations and the Pseudo-Gap State: Application of the Pairing Approximation Theory
We investigate the pseudogap onset temperature , the superconducting
transition temperature and the general nature of the pseudogap phase
using a diagrammatic BCS-Bose Einstein crossover theory. This decoupling scheme
is based on the pairing approximation of Kadanoff and Martin, further extended
by Patton (KMP). Our consideration of the KMP pairing approximation is driven
by the objective to obtain BCS like behavior at weak coupling, (which does not
necessarily follow for other diagrammatic schemes). The breakdown of the Fermi
liquid state at is investigated within the lowest order theory and is
associated with intermediate values of the coupling. The superconducting
instability is evaluated by introducing mode coupling effects, in which
the long lived pairs are affected by the single particle pseudogap states and
vice versa. Our equations, which turn out to be rather simple as a result
of the KMP scheme, reveal a rich structure as a function of in which the
pseudogap is found to compete with superconductivity. Our results are compared
with alternate theories in the literature.Comment: REVTeX3.1, 15 pages,15 EPS figures (included
Superconductivity from a pseudogapped normal state: a mode coupling approach to precursor superconductivity
We derive a phase diagram for the pseudogap onset temperature
(associated with the breakdown of the Fermi liquid state, due to strong pairing
correlations) and the superconducting instability, , as a function of
variable pairing strength. Our diagrammatic approach to the BCS - Bose-Einstein
cross-over problem self consistently treats the coupling between the single
particle and pair propagators, and leads to a continuous evolution of these
propagators into the standard counterparts. A rich structure is found
in which reflects the way in which the superconducting instability at
is affected by the pseudogap . An important consequence of
Cooper-pair- induced pseudogaps is that the magnitude of is sustained,
even when .Comment: REVTeX3.0; 5 pages, 3 EPS figures (included
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