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

Scattering properties of weakly bound dimers of fermionic atoms

We consider weakly bound diatomic molecules (dimers) formed in a two-component atomic Fermi gas with a large positive scattering length for the interspecies interaction. We develop a theoretical approach for calculating atom-dimer and dimer-dimer elastic scattering and for analyzing the inelastic collisional relaxation of the molecules into deep bound states. This approach is based on the single-channel zero range approximation, and we find that it is applicable in the vicinity of a wide two-body Feshbach resonance. Our results draw prospects for various interesting manipulations of weakly bound dimers of fermionic atoms.Comment: extended version of cond-mat/030901

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

Zero sound in a two-dimensional dipolar Fermi gas

We study zero sound in a weakly interacting 2D gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean field and many-body (beyond mean field) effects, and the anisotropy of the sound velocity is the same as the one of the Fermi velocity. The damping of zero sound modes can be much slower than that of quasiparticle excitations of the same energy. One thus has wide possibilities for the observation of zero sound modes in experiments with 2D fermionic dipoles, although the zero sound peak in the structure function is very close to the particle-hole continuum.Comment: 15 pages, 2 figure

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

Stable dilute supersolid of two-dimensional dipolar bosons

We consider two-dimensional bosonic dipoles oriented perpendicularly to the plane. On top of the usual two-body contact and long-range dipolar interactions we add a contact three-body repulsion as expected, in particular, for dipoles in the bilayer geometry with tunneling. The three-body repulsion is crucial for stabilizing the system, and we show that our model allows for stable continuous space supersolid states in the dilute regime and calculate the zero-temperature phase diagram.Comment: revised version, 5 pages, 2 figures, with 3 pages supplementary materia

Dynamics of dark solitons in elongated Bose-Einstein condensates

We find two types of moving dark soliton textures in elongated Bose-Einstein condensates: non-stationary kinks and proper dark solitons. The former have a curved notch region and rapidly decay by emitting phonons and/or proper dark solitons. The proper moving solitons are characterized by a flat notch region and we obtain the diagram of their dynamical stability. At finite temperatures the dynamically stable solitons decay due to the thermodynamic instability. We develop a theory of their dissipative dynamics and explain experimental data.Comment: ~ 5 pages, 1 figur