MANY-BODY THEORY OF QUANTUM GASES

Bose-Einstein Condensation and Fermi Superfluidity

The research activity of our group is focused on the investigation of degenerate quantum gases by using the methods of statistical mechanics and thermal field theory. We study the thermodynamics of weakly-interacting Bose and Fermi superfluids (alkali-metal atoms like rubidium, sodium and lithium, but also atomic hydrogen) trapped in magnetic or magneto-optical traps. We analyze single-particle and collective elementary excitations by numerically solving both Bologliubov-de Gennes and Popov equations. Moreover, we investigate dynamical properties of Bose-Einstein condensates by using the time-dependent 3D Gross-Pitaevskii equation, which describes the macroscopic wave-function (order parameter) of the Bose condensate.

Recently, we have studied existence, stability and dynamical properties of 3D Bose-condensed bright, grey and dark solitons under transverse or longitudinal confinement. In particular, we have investigated the tunneling of a bright soliton through a Gaussian barrier with the breaking of the soliton like behavior of the condensate and the collision of two bright solitons which shows fringes of interference and long-time transparency. Moreover we have analyzed the periodic motion of a train of bright solitons in a harmonic potential (see also below the color picture obtained by solving the Gross-Pitaevskii equation). We have also investigated the formation of bright soliton trains due to fluctuations of the phase of the complex wavefunction of the Bose-Einstein condensate by using the nonpolynomial nonlinear Schrodinger equation we have recently introduced.

We are studying Bose condensates in toroidal traps, which can be used for atom interferometry. In particular, we are investigating the quantum phase transition from a uniform to a localized ground-state (single-peak bright soliton) for an attractive BEC in a ring. Moreover, we are analyzing the formation and stability of single and multiple bright solitons in a ring. We plan also to study the finite-temperature properties of these solitonic configurations and the interference of Bose-Einstein condensates in a rotating ring.

We are also investigating the dynamics (collective excitations and free expansion) of a two-component Fermi gas in the BCS-BEC crossover and the formation of solitons in atomic mixtures of bosons and fermions. In particular, we are developing a reliable density functional for the unitary Fermi gas (infinite scattering length) at zero and finite teperature.

We are planning to start the analysis of the condensate properties of p-wave Fermi atoms and d-wave superconductors in the BCS-BEC crossover both in two and three dimensions. Moreover, we are working on the many-body quantum tunneling dynamics of spin-polarized fermions in a double-well potential.