Abstract We study the thermodynamics of ideal Bose gas as well as the transport properties of non interacting bosons and fermions in a one dimensional quasi-periodic potential, namely Aubry–André (AA) model at finite temperature. For bosons in finite size systems, the effect of quasi-periodic potential on the crossover phenomena corresponding to Bose–Einstein condensation (BEC), superfluidity and localization phenomena at finite temperatures are investigated. From the ground state number fluctuation we calculate the crossover temperature of BEC which exhibits a non monotonic behavior with the strength of AA potential and vanishes at the self-dual critical point following power law. Appropriate rescaling of the crossover temperatures reveals universal behavior which is studied for different quasi-periodicity of the AA model. Finally, we study the temperature and flux dependence of the persistent current of fermions in presence of a quasi-periodic potential to identify the localization at the Fermi energy from the decay of the current.
We show that the chemical potential of a one-dimensional (1D) interacting Bose gas exhibits a nonmonotonic temperature dependence which is peculiar of superfluids. The effect is a direct consequence of the phononic nature of the excitation spectrum at large wavelengths exhibited by 1D Bose gases. For low temperatures
T, we demonstrate that the coefficient in
T2 expansion of the chemical potential is entirely defined by the zero-temperature density dependence of the sound velocity. We calculate that coefficient along the crossover between the Bogoliubov weakly interacting gas and the Tonks-Girardeau gas of impenetrable bosons. Analytic expansions are provided in the asymptotic regimes. The theoretical predictions along the crossover are confirmed by comparison with the exactly solvable Yang-Yang model in which the finite-temperature equation of state is obtained numerically by solving Bethe-ansatz equations. A 1D ring geometry is equivalent to imposing periodic boundary conditions and arising finite-size effects are studied in detail. At
T=0 we calculated various thermodynamic functions, including the inelastic structure factor, as a function of the number of atoms, pointing out the occurrence of important deviations from the thermodynamic limit.
We study the effects of an external periodic potential on the critical velocity of a superfluid Fermi gas in the crossover between the Bardeen-Cooper-Schrieffer (BCS) phase and Bose-Einstein condensation (BEC). We numerically solve the Bogoliubov--de Gennes equations to model a three-dimensional gas of ultracold atoms in the superfluid phase flowing through a one-dimensional optical lattice. We find that when the recoil energy is comparable to the Fermi energy, the presence of the periodic potential reduces the effect of pair-breaking excitations. This behavior is a consequence of the peculiar band structure of the quasiparticle energy spectrum in the lattice. When the lattice height is much larger than the Fermi energy, the periodic potential makes pairs of atoms to be strongly bound, even in the BCS regime, and pair-breaking excitations are further suppressed. We have also found that when the recoil energy is comparable to or larger than the Fermi energy, the critical velocity due to long-wavelength phonon excitations shows a nonmonotonic behavior along the BCS-BEC crossover.
We study the localization properties of weakly interacting Bose gas in a quasiperiodic potential. The Hamiltonian of the non-interacting system reduces to the well known 'Aubry–André model', which shows the localization transition at a critical strength of the potential. In the presence of repulsive interaction we observe multi-site localization and obtain a phase diagram of the dilute Bose gas by computing the superfluid fraction and the inverse participation ratio. We construct a low-dimensional classical Hamiltonian map and show that the onset of localization is manifested by the chaotic phase space dynamics. The level spacing statistics also identify the transition to localized states resembling a Poisson distribution that are ubiquitous for both non-interacting and interacting systems. We also study the quantum fluctuations within the Bogoliubov approximation and compute the quasiparticle energy spectrum. Enhanced quantum fluctuation and multi-site localization phenomenon of non-condensate density are observed above the critical coupling of the potential. We briefly discuss the effect of the trapping potential on the localization of matter wave.
The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the lattice periodicity, the superfluid transition temperature
Tc decreases with pairing strength in the BEC regime, where it approaches asymptotically ${T}_{\mathrm{c}}=\ensuremath{\pi}an/2m$, with
a being the
s-wave scattering length, and
n (
m) the fermion density (mass). In addition, the quasi-two dimensionality leads to fast-growing (absolute value of the) fermionic chemical potential $\ensuremath{\mu}$ and pairing gap $\mathrm{\ensuremath{\Delta}}$, which depends exponentially on the ratio
d/a. Importantly,
Tc at unitarity increases with the lattice constant
d and hopping integral
t. The effect of the van Hove singularity on
Tc is identified. The superfluid density exhibits
T3/2 power laws at low
T, away from the extreme BCS limit. These predictions can be tested in future experiments.
We obtain the thermodynamic properties for a noninteracting Bose gas constrained on multilayers modeled by a periodic Kronig-Penney delta potential in one direction and allowed to be free in the other two directions. We report Bose-Einstein condensation (BEC) critical temperatures, chemical potential, internal energy, specific heat, and entropy for different values of a dimensionless impenetrability $P\ensuremath{\geqslant}0$ between layers. The BEC critical temperature
Tc coincides with the ideal gas BEC critical temperature
T0 when
P=0 and rapidly goes to zero as
P increases to infinity for any finite interlayer separation. The specific heat
CV as a function of absolute temperature
T for finite
P and plane separation
a exhibits one minimum and one or two maxima in addition to the BEC, for temperatures larger than that of BEC
Tc. This highlights the effects due to particle confinement. We then discuss a distinctive dimensional crossover of the system through the specific heat behavior driven by the magnitude of
P. For
T<Tc the crossover is revealed by a change in slope of
logCV(T) and when
T>Tc, it is exhibited by a broad minimum in
CV(T).