50 research outputs found
Superfluidity of identical fermions in an optical lattice: atoms and polar molecules
In this work, we discuss the emergence of -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 -wave superfluidity. However, we show that for a moderate
lattice depth there is still a possibility to create atomic -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 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
One-dimensional Anderson Localization: Devil's staircase of Statistical Anomalies
The statistics of wavefunctions in the one-dimensional (1d) Anderson model of
localization is considered. It is shown that at any energy that corresponds to
a rational filling factor f=p/q there is a statistical anomaly which is seen in
expansion of the generating function (GF) to the order (q-2) in the disorder
parameter. We study in detail the principle anomaly at that appears in
the leading order. The transfer-matrix equation of the Fokker-Planck type with
a two-dimensional internal space is derived for GF. It is shown that the
zero-mode variant of this equation is integrable and a solution for the
generating function is found in the thermodynamic limit.Comment: 4 pages RevTex, 1 pictur
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