Speaker
Prof.
Jorge Dukelsky
(Instituto de Estructura de la Materia. CSIC.)
Description
The exact solution of the SU(2) pairing Hamiltonian with
non-degenerate single particle orbits was introduced by
Richardson in the early sixties, although it was
recovered in the last decade in an effort to describe the
disappearance of superconductivity in ultrasmall grains.
Since then it has been widely applied to mesoscopic
systems where finite size effects play an important role.
Lately we have extended this family of exactly solvable
models to higher rank algebras to describe pairing
between multi-component fermion systems like three
and four color atomic gases.
In this talk I will review some of the achievements in the
application of the exactly solvable Richardson models to
cold atomic gases.
I will start with the description of the BCS-BEC crossover
view from the exact Richardson wavefunction which
defines uniquely the structure of the Cooper pairs from
extended resonances in the BCS regime to tightly bound
molecules in the BEC regime. Another recent
development is associated to the implementation of the
hyperbolic family of the SU(2) Richardson model to
describe p-wave pairing. Using this new tool we study
the quantum phase diagram of a spinless Fermi gas in a
2D optical lattice with px + i py pairing interaction
symmetry. Unlike the case of s-wave pairing, which has
a smooth a crossover between BCS and BEC, p-wave
pairing displays a quantum phase transition separating
two gapped superfluid phases known as weak-pairing
and strong-pairing. We use the exact solution as well as
mean-field to characterize the quantum phase transition
and the properties of the two phases.
Finally, as an example of the higher rank Richardson
models, I will introduce the exact solution of an SO(6)
Richardson model that describes pairing between three
component atomic fermions. The study of this new
exactly solvable model allowed us to unveil a complex
structure of breached pairing phases. We find two
competing superfluid phases at weak and intermediate
couplings, each with two-color pair condensates that can
be distinguished with density profile measurements.
Primary author
Prof.
Jorge Dukelsky
(Instituto de Estructura de la Materia. CSIC.)
