Effects of collisions against thermal impurities in the dynamics of a trapped fermion gas

Abstract

We present a theoretical study of the dynamical behavior of a gas made of ultracold fermionic atoms, which during their motions can collide with a much smaller number of thermal bosonic impurities. The atoms are confined inside harmonic traps and the interactions between the two species are treated as due to s-wave scattering with a negative scattering length modeling the 40 K-87 Rb fermion-boson system. We set the fermions into motion by giving a small shift to their trap center and examine two alternative types of initial conditions, referring to (i) a close-to-equilibrium situation in which the two species are at the same temperature (well below the Fermi temperature and well above the Bose-Einstein condensation temperature); and (ii) a far-from-equilibrium case in which the impurities are given a Boltzmann distribution of momenta while the fermions are at very low temperatures. The dynamics of the gas is evaluated by the numerical solution of the Vlasov-Landau equations for the one-body distribution functions, supported by some analytical results on the collisional properties of a fermion gas. We find that the trapped gaseous mixture is close to the collisionless regime for values of the parameters corresponding to current experiments, but can be driven towards a collisional regime even without increasing the strength of the interactions, either by going over to heavier impurity masses or by matching the width of the momentum distribution of the impurities to the Fermi momentum of the fermion gas.

Direct simulation Monte Carlo method for cold-atom dynamics: Classical Boltzmann equation in the quantum collision regime

“…Some applications of such calculations include the work of Wu and co-workers [13][14][15] on evaporative cooling and expansion dynamics, Jackson and co-workers [16][17][18][19][20] on bosonic collective-mode dynamics (coupled to a superfluid by the Zaremba-Nikuni-Griffin (ZNG) formalism [21]), the work of Urban and Schuck [22], Urban [23,24], and Lepers et al [25] in formulating fermion dynamics (see also Refs. [26][27][28][29]), and Barletta et al [30] and Barletta [31] in describing sympathetically cooled molecular gases.…”

Collective Excitations in Bose–Fermi Mixtures

“…where the single-particle energies are given by ε B,F = p 2 /2m [13][14][15][16]. The static equilibrium solution is given by the Bose-Einstein and Fermi-Dirac distribution functions f 0 B,F = [e (ε 0 B,F −µ B,F )/k B T ∓ 1] −1 .…”

Nonequilibrium enhancement of Cooper pairing in cold fermion systems

“…In our system, this lifetime will be dominated by the inelastic collision time between bosons and fermions. We may estimate this time as in [24,25] by means of a 1/τ 0 = nσv approximation where n is the boson density at the center of the trap, σ is the constant low temperature cross-section for boson-fermion scattering, and v is the average relative velocity associated with the collisions between bosons and fermions. Note that there exist other contributions to the collision integral, in particular those coming from fermion collisions.…”