Two-body relaxation of spin-polarized fermions in reduced dimensionalities near a p-wave Feshbach resonance

We study inelastic two-body relaxation in a spin-polarized ultracold Fermi gas in the presence of a p-wave Feshbach resonance. It is shown that in reduced dimensionalities, especially in the quasi-one-dimensional case, the enhancement of the inelastic rate constant on approach to the resonance is strongly suppressed compared to three dimensions. This may open promising paths for obtaining novel many-body states.Comment: 14 pages, 12 figure

Two-dimensional dipolar Bose gas with the roton-maxon excitation spectrum

We discuss fluctuations in a dilute two-dimensional Bose-condensed dipolar gas, which has a roton-maxon character of the excitation spectrum. We calculate the density-density correlation function, fluctuation corrections to the chemical potential, compressibility, and the normal (superfluid) fraction. It is shown that the presence of the roton strongly enhances fluctuations of the density, and we establish the validity criterion of the Bogoliubov approach. At T=0 the condensate depletion becomes significant if the roton minimum is sufficiently close to zero. At finite temperatures exceeding the roton energy, the effect of thermal fluctuations is stronger and it may lead to a large normal fraction of the gas and compressibility.Comment: 5 pages, 3 figure

Delocalization of weakly interacting bosons in a 1D quasiperiodic potential

We consider weakly interacting bosons in a 1D quasiperiodic potential (Aubry-Azbel-Harper model) in the regime where all single-particle states are localized. We show that the interparticle interaction may lead to the many-body delocalization and we obtain the finite-temperature phase diagram. Counterintuitively, in a wide range of parameters the delocalization requires stronger cou- pling as the temperature increases. This means that the system of bosons can undergo a transition from a fluid to insulator (glass) state under heating

Superfluidity of identical fermions in an optical lattice: atoms and polar molecules

In this work, we discuss the emergence of $p$-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms, the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the $p$-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic $p$-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological $p_x+ip_y$ superfluid of identical microwave-dressed polar molecules.Comment: 14 pages, 4 figures; prepared for proceedings of the IV International Conference on Quantum Technologies (Moscow, July 12-16, 2017); the present paper summarizes the results of our studies arXiv:1601.03026 and arXiv:1701.0852

Achieving a BCS transition in an atomic Fermi gas

We consider a gas of cold fermionic atoms having two spin components with interactions characterized by their s-wave scattering length $a$. At positive scattering length the atoms form weakly bound bosonic molecules which can be evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative scattering length BCS pairing can take place. It is shown that, by adiabatically tuning the scattering length $a$ from positive to negative values, one may transform the molecular Bose-Einstein condensate into a highly degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature $T/T_F \sim 10^{-2}$. The corresponding critical final value of $k_{F}|a|$ which leads to the BCS transition is found to be about one half, where $k_F$ is the Fermi momentum.Comment: 4 pages, 1 figure. Phys. Rev. Lett. in pres

One-dimensional two-component fermions with contact even-wave repulsion and SU(2) breaking near-resonant odd-wave attraction

We consider a one-dimensional (1D) two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study the effect of an SU(2) symmetry breaking near-resonant odd-wave interaction within one of the components. Starting from the microscopic Hamiltonian, we derive an effective field theory for the spin degrees of freedom using the bosonization technique. It is shown that at a critical value of the odd-wave interaction there is a first-order phase transition from a phase with zero total spin and zero magnetization to the spin-segregated phase where the magnetization locally differs from zero.Comment: 18 pages, 3 fugures; references adde

Collapse and Bose-Einstein condensation in a trapped Bose-gas with negative scattering length

We find that the key features of the evolution and collapse of a trapped Bose condensate with negative scattering length are predetermined by the particle flux from the above-condensate cloud to the condensate and by 3-body recombination of Bose-condensed atoms. The collapse, starting once the number of Bose-condensed atoms reaches the critical value, ceases and turns to expansion when the density of the collapsing cloud becomes so high that the recombination losses dominate over attractive interparticle interaction. As a result, we obtain a sequence of collapses, each of them followed by dynamic oscillations of the condensate. In every collapse the 3-body recombination burns only a part of the condensate, and the number of Bose-condensed atoms always remains finite. However, it can comparatively slowly decrease after the collapse, due to the transfer of the condensate particles to the above-condensate cloud in the course of damping of the condensate oscillations.Comment: 11 pages, 3 figure

Finite size effects for the gap in the excitation spectrum of the one-dimensional Hubbard model

We study finite size effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime one-dimensional Hubbard model with on-site attraction. Two type of corrections to the result of the thermodynamic limit are obtained. Aside from a power law (conformal) correction due to gapless excitations which behaves as $1/N_a$, where $N_a$ is the number of lattice sites, we obtain corrections related to the existence of gapped excitations. First of all, there is an exponential correction which in the weakly interacting regime ($|U|\ll t$) behaves as $\sim \exp (-N_a \Delta_{\infty}/4 t)$ in the extreme limit of $N_a \Delta_{\infty} /t \gg 1$, where $t$ is the hopping amplitude, $U$ is the on-site energy, and $\Delta_{\infty}$ is the gap in the thermodynamic limit. Second, in a finite size system a spin-flip producing unpaired fermions leads to the appearance of solitons with non-zero momenta, which provides an extra (non-exponential) contribution $\delta$. For moderate but still large values of $N_a\Delta_{\infty} /t$, these corrections significantly increase and may become comparable with the $1/N_a$ conformal correction. Moreover, in the case of weak interactions where $\Delta_{\infty}\ll t$, the exponential correction exceeds higher order power law corrections in a wide range of parameters, namely for $N_a\lesssim (8t/\Delta_{\infty})\ln(4t/|U|)$, and so does $\delta$ even in a wider range of $N_a$. For sufficiently small number of particles, which can be of the order of thousands in the weakly interacting regime, the gap is fully dominated by finite size effects.Comment: 17 pages, 5 figure