86 research outputs found
Renormalization of the superfluid density in the two-dimensional BCS-BEC crossover
We analyze the theoretical derivation of the beyond-mean-field equation of
state for a two-dimensional gas of dilute, ultracold alkali-metal atoms in the
Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover. We
show that at zero temperature our theory -- considering Gaussian fluctuations
on top of the mean-field equation of state -- is in very good agreement with
experimental data. Subsequently, we investigate the superfluid density at
finite temperature and its renormalization due to the proliferation of
vortex-antivortex pairs. By doing so, we determine the
Berezinskii-Kosterlitz-Thouless (BKT) critical temperature -- at which the
renormalized superfluid density jumps to zero -- as a function of the
inter-atomic potential strength. We find that the Nelson-Kosterlitz criterion
overestimates the BKT temperature with respect to the renormalization group
equations, this effect being particularly relevant in the intermediate regime
of the crossover.Comment: 9 pages, 3 figures, presented to the International Conference
"Electron correlation in superconductors and nanostructures", 17-20 August
2017, Odessa (Ukraine). To be published in the Proceeding
Scattering length of composite bosons in the 3D BCS-BEC crossover
We study the zero-temperature grand potential of a three-dimensional
superfluid made of ultracold fermionic alkali-metal atoms in the BCS-BEC
crossover. In particular, we analyze the zero-point energy of both fermionic
single-particle excitations and bosonic collective excitations. The bosonic
elementary excitations, which are crucial to obtain a reliable equation of
state in the BEC regime, are obtained with a low-momentum expansion up to the
forth order of the quadratic (Gaussian) action of the fluctuating pairing
field. By performing a cutoff regularization and renormalization of Gaussian
fluctuations, we find that the scattering length of composite bosons,
bound states of fermionic pairs, is given by , where is
the scattering length of fermions.Comment: 5 pages; accepted for publication in Phys. Rev.
Gaussian fluctuations in the two-dimensional BCS-BEC crossover: finite temperature properties
The role of fluctuations is enhanced in lower dimensionality systems: in a
two dimensions off-diagonal long-range order is destroyed by the fluctuations
at any finite temperature, drastically modifying the critical properties with
respect to the three-dimensional counterpart. Recently two-dimensional systems
of interacting fermions have been the subject of Montecarlo studies and
experimental investigations, in particular an ultracold gas of attractive
fermions with a widely tunable interaction due to a Feshbach resonance has been
realized and the Berezinskii-Kosterlitz-Thouless transition has been observed.
The present work deals with the theoretical description of an ultracold Fermi
gas: we discuss the role of Gaussian fluctuations of the order parameter in the
equation of state, in particular we take into account the first sound velocity,
showing that the inclusion of order parameter fluctuations is needed in order
to get the correct composite-boson limit in the strong-coupling regime. The
theory is also compared with experimental data. Finally we focus on the
superfluid density in the weak-coupling, intermediate and strong-coupling
regimes at finite temperature, through which the
Berezinskii-Kosterlitz-Thouless critical temperature is obtained.Comment: 7 pages, 3 figures, submitted to the proceedings of the 24th Annual
International Laser Physics Worksho
Vortices and antivortices in two-dimensional ultracold Fermi gases
Vortices are commonly observed in the context of classical hydrodynamics:
from whirlpools after stirring the coffee in a cup to a violent atmospheric
phenomenon such as a tornado, all classical vortices are characterized by an
arbitrary circulation value of the local velocity field. On the other hand the
appearance of vortices with quantized circulation represents one of the
fundamental signatures of macroscopic quantum phenomena. In two-dimensional
superfluids quantized vortices play a key role in determining
finite-temperature properties, as the superfluid phase and the normal state are
separated by a vortex unbinding transition, the Berezinskii-Kosterlitz-Thouless
transition. Very recent experiments with two-dimensional superfluid fermions
motivate the present work: we present theoretical results based on the
renormalization group showing that the universal jump of the superfluid density
and the critical temperature crucially depend on the interaction strength,
providing a strong benchmark for forthcoming investigations.Comment: 17 pages, 2 figure
Finite-temperature quantum fluctuations in two-dimensional Fermi superfluids
In two-dimensional systems with a continuous symmetry the
Mermin-Wagner-Hohenberg theorem precludes spontaneous symmetry breaking and
condensation at finite temperature. The Berezinskii-Kosterlitz-Thouless
critical temperature marks the transition from a superfluid phase characterized
by quasi-condensation and algebraic long-range order to a normal phase, where
vortex proliferation completely destroys superfluidity. As opposed to
conventional off-diagonal long-range order typical of three-dimensional
superfluid systems, algebraic long-range order is driven by quantum and thermal
fluctuations strongly enhanced in reduced dimensionality. Motivated by this
unique scenario and by the very recent experimental realization of trapped
quasi-two-dimensional fermionic clouds, we include one-loop Gaussian
fluctuations in the theoretical description of resonant Fermi superfluids in
two dimensions demonstrating that first sound, second sound and also critical
temperature are strongly renormalized, away from their mean-field values. In
particular, we prove that in the intermediate and strong coupling regimes these
quantities are radically different when Gaussian fluctuations are taken into
account. Our one-loop theory shows good agreement with very recent experimental
data on the Berezinskii-Kosterlitz-Thouless critical temperature [Phys. Rev.
Lett. 115, 010401 (2015)] and on the first sound velocity, giving novel
predictions for the second sound as a function of interaction strength and
temperature, open for experimental verification.Comment: improved version, 8 pages, 4 figures, accepted for publication in
Phys. Rev.
Gauge approach to superfluid density in underdoped cuprates
We prove that a gauge approach based on a composite structure of the hole in
hole-doped cuprates is able to capture analytically many features of the
experimental data on superfluid density in the moderate-underdoping to
nearly-optimal doping region, including critical exponent, the Uemura relation
and near universality of the normalized superfluid density.Comment: 13 pages, 2 figures, accepted for publication in EP
Superfluid density in cuprates: hints on gauge compositeness of the holes
We show that several features (the three-dimensional XY universality for
moderate underdoping, the almost-BCS behaviour for moderate overdoping and the
critical exponent) of the superfluid density in hole-doped cuprates hint at a
composite structure of the holes. This idea can be implemented in a spin-charge
gauge approach to the model and provides indeed good agreement
with available experimental data.Comment: 5 pages, 1 figure, to be published in the proceedings of the
International Conference in Superconductivty and Magnetism ICSM201
Pair condensation of polarized fermions in the BCS-BEC crossover
We investigate a two-component Fermi gas with unequal spin populations along
the BCS-BEC crossover. By using the extended BCS equations and the concept of
off-diagonal-long-range-order we derive a formula for the condensate number of
Cooper pairs as a function of energy gap, average chemical potential, imbalance
chemical potential and temperature. Then we study the zero-temperature
condensate fraction of Cooper pairs by varying interaction strength and
polarization, finding a depletion of the condensate fraction by increasing the
population imbalance. We also consider explicitly the presence of an external
harmonic confinement and we study, within the local-density approximation, the
phase separation between superfluid and normal phase regions of the polarized
fermionic cloud. In particular, we calculate both condensate density profiles
and total density profiles from the inner superfluid core to the normal region
passing for the interface, where a finite jump in the density is a clear
manifestation of this phase-separated regime. Finally, we compare our
theoretical results with the available experimental data on the condensate
fraction of polarized 6Li atoms [Science 311, 492 (2006)]. These experimental
data are in reasonable agreement with our predictions in a suitable range of
polarizations, but only in the BCS side of the crossover up to unitarity.Comment: 13 pages, 3 figures, improved version, added a section on the
interpretation of the results, to be published in J. Phys.
Diagrammatic Monte Carlo approach to angular momentum in quantum many-particle systems
We introduce a Diagrammatic Monte Carlo (DiagMC) approach to angular momentum
properties of quantum many-particle systems possessing a macroscopic number of
degrees of freedom. The treatment is based on a diagrammatic expansion that
merges the usual Feynman diagrams with the angular momentum diagrams known from
atomic and nuclear structure theory, thereby incorporating the non-Abelian
algebra inherent to quantum rotations. Our approach is applicable at arbitrary
coupling, is free of systematic errors and of finite size effects, and
naturally provides access to the impurity Green function. We exemplify the
technique by obtaining an all-coupling solution of the angulon model, however,
the method is quite general and can be applied to a broad variety of systems in
which particles exchange quantum angular momentum with their many-body
environment.Comment: 6+5 pages, 2+2 figures, accepted for publication in Phys. Rev. Let
Beliaev damping of the Goldstone mode in atomic Fermi superfluids
Beliaev damping in a superfluid is the decay of a collective excitation into
two lower frequency collective excitations; it represents the only decay mode
for a bosonic collective excitation in a superfluid at T = 0. The standard
treatment for this decay assumes a linear spectrum, which in turn implies that
the final state momenta must be collinear to the initial state. We extend this
treatment, showing that the inclusion of a gradient term in the Hamiltonian
yields a realistic spectrum for the bosonic excitations; we then derive a
formula for the decay rate of such excitations, and show that even moderate
nonlinearities in the spectrum can yield substantial deviations from the
standard result. We apply our result to an attractive Fermi gas in the BCS-BEC
crossover: here the low-energy bosonic collective excitations are density
oscillations driven by the phase of the pairing order field. These collective
excitations, which are gapless modes as a consequence of the Goldstone
mechanism, have a spectrum which is well established both theoretically and
experimentally, and whose linewidth, we show, is determined at low temperatures
by the Beliaev decay mechanism.Comment: 8 pages, 3 figure
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