71 research outputs found
Gap equation with pairing correlations beyond mean field and its equivalence to a Hugenholtz-Pines condition for fermion pairs
The equation for the gap parameter represents the main equation of the
pairing theory of superconductivity. Although it is formally defined through a
single-particle property, physically it reflects the pairing correlations
between opposite-spin fermions. Here, we exploit this physical connection and
cast the gap equation in an alternative form which explicitly highlights these
two-particle correlations, by showing that it is equivalent to a
Hugenholtz-Pines condition for fermion pairs. At a formal level, a direct
connection is established in this way between the treatment of the condensate
fraction in condensate systems of fermions and bosons. At a practical level,
the use of this alternative form of the gap equation is expected to make easier
the inclusion of pairing fluctuations beyond mean field. As a proof-of-concept
of the new method, we apply the modified form of the gap equation to the
long-pending problem about the inclusion of the Gorkov-Melik-Barkhudarov
correction across the whole BCS-BEC crossover, from the BCS limit of strongly
overlapping Cooper pairs to the BEC limit of dilute composite bosons, and for
all temperatures in the superfluid phase. Our numerical calculations yield
excellent agreement with the recently determined experimental values of the gap
parameter for an ultra-cold Fermi gas in the intermediate regime between BCS
and BEC, as well as with the available quantum Monte Carlo data in the same
regime.Comment: 24 pages, 13 figure
From superconducting fluctuations to the bosonic limit in the response functions above the critical temperature
We investigate the density, current, and spin response functions above the
critical temperature for a system of three-dimensional fermions interacting via
an attractive short-range potential. In the strong-coupling (bosonic) limit of
this interaction, we identify the dominant diagrammatic contributions for a
``dilute'' system of composite bosons which form as bound-fermion pairs, and
compare them with the usual (Aslamazov-Larkin, Maki-Thompson, and
density-of-states) terms occurring in the theory of superconducting
fluctuations above the critical temperature for a clean system in the
weak-coupling limit. We show that, at the zeroth order in the diluteness
parameter for the composite bosons, the Aslamazov-Larkin term still represents
formally the dominant contribution to the density and current response
functions, while the Maki-Thompson and density-of-states terms are strongly
suppressed. Corrections to the Aslamazov-Larkin term are then considered at the
next order in the diluteness parameter for the composite bosons. The spin
response function is also examined, and it is found to be exponentially
suppressed in the bosonic limit only when appropriate sets of diagrams are
considered simultaneously.Comment: 10 pages, 6 figure
Entanglement between pairing and screening in the Gorkov-Melik-Barkhudarov correction to the critical temperature throughout the BCS-BEC crossover
The theoretical description of the critical temperature Tc of a Fermi
superfluid dates back to the work by Gor'kov and Melik-Barkhudarov (GMB), who
addressed it for a weakly-coupled (dilute) superfluid in the BCS
(weak-coupling) limit of the BCS-BEC crossover. The point made by GMB was that
particle-particle (pairing) excitations, which are responsible for
superfluidity to occur below Tc, and particle-hole excitations, which give rise
to screening also in a normal system, get effectively disentangled from each
other in the BCS limit, thus yielding a reduction by a factor 2.2 of the value
of Tc obtained when neglecting screening effects. Subsequent work on this
topic, aimed at extending the original GMB argument away from the BCS limit
with diagrammatic methods, has kept this disentangling between pairing and
screening throughout the BCS-BEC crossover, without realising that the
conditions for it to be valid are soon violated away from the BCS limit. Here,
we reconsider this problem from a more general perspective and argue that
pairing and screening are intrinsically entangled with each other along the
whole BCS-BEC crossover but for the BCS limit considered by GMB. We perform a
detailed numerical calculation of the GMB diagrammatic contribution extended to
the whole BCS-BEC crossover, where the full wave-vector and frequency
dependence occurring in the repeated in-medium two-particle scattering is duly
taken into account. Our numerical calculations are tested against analytic
results available in both the BCS and BEC limits, and the contribution of the
GMB diagrammatic term to the scattering length of composite bosons in the BEC
limit is highlighted. We calculate Tc throughout the BCS-BEC crossover and find
that it agrees quite well with Quantum Monte Carlo calculations and
experimental data available in the unitarity regime.Comment: 21 pages, 11 figure
Spatial emergence of off-diagonal long-range order throughout the BCS-BEC crossover
In a superfluid system, off-diagonal long-range order is expected to be exhibited in the appropriate reduced
density matrices when the relevant particles (either bosons or fermion pairs) are considered to recede sufficiently
far apart from each other. This concept is usually exploited to identify the value of the condensate density,
without explicit concern, however, as to the spatial range over which this asymptotic condition can effectively be
achieved. Here, based on a diagrammatic approach that includes beyond-mean-field pairing fluctuations in the
broken-symmetry phase at the level of the t-matrix also with the inclusion of the Gorkov-Melik-Barkhudarov
(GMB) correction, we present a systematic study of the two-particle reduced density matrix for a superfluid
fermionic system undergoing the BCS-BEC crossover, when the entities to recede far apart from each other
evolve with continuity from largely overlapping Cooper pairs in the BCS limit to dilute composite bosons in the
BEC limit. By this approach, we not only provide the coupling and temperature dependence of the condensate
density at the level of our diagrammatic approach, which includes the GMB correction, but we also obtain
the evolution of the spatial dependence of the two-particle reduced density matrix, from a power law at low
temperature to an exponential dependence at high temperature in the superfluid phase, when the interparticle
coupling spans the BCS-BEC crossover. Our results put limitations on the minimum spatial extent of a finite-size
system for which superfluid correlations can effectively be established
Strong Fulde-Ferrell Larkin-Ovchinnikov pairing fluctuations in polarized Fermi systems
We calculate the pair susceptibility of an attractive spin-polarized Fermi gas in the normal phase, as a function of the pair momentum. Close to unitarity, we find a strong enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing fluctuations over an extended region of the temperature-polarization phase diagram, which manifests itself as a pronounced peak in the pair-momentum distribution at a finite pair momentum. This peak should be amenable to experimental observation at achievable temperatures in a boxlike trapping potential, as a fingerprint of FFLO pairing. Our calculations rest on a self-consistent t-matrix approach which, for the unitary balanced Fermi gas, has been validated against experimental data for several thermodynamic quantities
Beyond-mean-field description of a trapped unitary Fermi gas with mass and population imbalance
A detailed description is given of the phase diagram for a two-component
unitary Fermi gas with mass and population imbalance, for both homogeneous and
trapped systems. This aims at providing quantitative benchmarks for the
normal-to-superfluid phase transition of a mass-imbalanced Fermi gas in the
temperature-polarization parameter space. A self-consistent t-matrix approach
is adopted, which has already proven to accurately describe the thermodynamic
properties of the mass and population balanced unitary Fermi gas. Our results
provide a guideline for the ongoing experiments on heteronuclear Fermi
mixtures.Comment: 10 pages, 10 figures, final versio
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