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

Nanoscopy of pairs of atoms by fluorescence in a magnetic field

Spontaneous emission spectra of two initially excited closely spaced identical atoms are very sensitive to the strength and the direction of the applied magnetic field. The relevant schemes are considered that ensure the determination of the mutual spatial orientation of the atoms and the distance between them by entirely optical means. A corresponding theoretical description is given accounting for the dipole-dipole interaction between the two atoms in the presence of a magnetic field and for polarizations of the quantum field interacting with magnetic sublevels of the two-atom system

Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids

While it is well-known that the electron-electron (\emph{ee}) interaction cannot affect the resistivity of a Galilean-invariant Fermi liquid (FL), the reverse statement is not necessarily true: the resistivity of a non-Galilean-invariant FL does not necessarily follow a T^2 behavior. The T^2 behavior is guaranteed only if Umklapp processes are allowed; however, if the Fermi surface (FS) is small or the electron-electron interaction is of a very long range, Umklapps are suppressed. In this case, a T^2 term can result only from a combined--but distinct from quantum-interference corrections-- effect of the electron-impurity and \emph{ee} interactions. Whether the T^2 term is present depends on 1) dimensionality (two dimensions (2D) vs three dimensions (3D)), 2) topology (simply- vs multiply-connected), and 3) shape (convex vs concave) of the FS. In particular, the T^2 term is absent for any quadratic (but not necessarily isotropic) spectrum both in 2D and 3D. The T^2 term is also absent for a convex and simply-connected but otherwise arbitrarily anisotropic FS in 2D. The origin of this nullification is approximate integrability of the electron motion on a 2D FS, where the energy and momentum conservation laws do not allow for current relaxation to leading --second--order in T/E_F (E_F is the Fermi energy). If the T^2 term is nullified by the conservation law, the first non-zero term behaves as T^4. The same applies to a quantum-critical metal in the vicinity of a Pomeranchuk instability, with a proviso that the leading (first non-zero) term in the resistivity scales as T^{\frac{D+2}{3}} (T^{\frac{D+8}{3}}). We discuss a number of situations when integrability is weakly broken, e.g., by inter-plane hopping in a quasi-2D metal or by warping of the FS as in the surface states of Bi_2Te_3 family of topological insulators.Comment: Submitted to a special issue of the Lithuanian Journal of Physics dedicated to the memory of Y. B. Levinso

Scattering of massless particles in one-dimensional chiral channel

We present a general formalism describing a propagation of an arbitrary multiparticle wave packet in a one-dimensional multimode chiral channel coupled to an ensemble of emitters which are distributed at arbitrary positions. The formalism is based on a direct and exact resummation of diagrammatic series for the multiparticle scattering matrix. It is complimentary to the Bethe Ansatz and to approaches based on equations of motion, and it reveals a simple and transparent structure of scattering states. In particular, we demonstrate how this formalism works on various examples, including scattering of one- and two-photon states off two- and three-level emitters, off an array of emitters as well as scattering of coherent light. We argue that this formalism can be constructively used for study of scattering of an arbitrary initial photonic state off emitters with arbitrary degree of complexity.Comment: 25 pages, 5 figure

Superfluid transition in quasi-two-dimensional disordered dipolar Fermi gases

We investigate the effect of weak disorder on the superfluid properties of two-component quasi-two-dimensional dipolar Fermi gases. The dipole-dipole interaction amplitude is momentum dependent, which violates the Anderson theorem claiming that the weak disorder has practically no influence on the superfluid transition temperature in the weakly interacting regime. We find that for dipolar fermions the transition temperature in this regime can be strongly increased by the disorder like in the purely two-dimensional case. However, the effect becomes smaller with increasing the intercomponent fermion-fermion interaction, and in the strongly interacting regime the superfluid transition temperature in the weak disorder becomes very close to that in the absence of disorder