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arXiv:1211.6613 · Physical Review A

Averaged collision and reaction rates in a two-species gas of ultracold fermions

Alexander Pikovski

Published Jan 31, 2013• 1 citation
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Abstract

Reactive or elastic two-body collisions in an ultracold gas are affected by quantum statistics. In this paper, we study ensemble-averaged collision rates for a two-species fermionic gas. The two species may have different masses, densities, and temperatures. We investigate how averaged collision rates are affected by the presence of Fermi spheres in the initial states; Pauli blocking of final states is not considered. It is shown that, independently on the details of the collision, Fermi-averaged collision rates deviate from Boltzmann-averaged ones, particularly for a gas with strong imbalance of masses or densities.

DOI
10.1103/physreva.87.012713

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•Jan 1, 2012•0 citations
Reactive or elastic two-body collisions in an ultracold gas are affected by quantum statistics. In this paper, we study ensemble-averaged collision rates for a two-species fermionic gas. The two species may have different masses, densities, and temperatures. We investigate how averaged collision rates are affected by the presence of Fermi spheres in the initial states; Pauli blocking of final states is not considered. It is shown that, independently on the details of the collision, Fermi-averaged collision rates deviate from Boltzmann-averaged ones, particularly for a gas with strong imbalance of masses or densities.
We investigate single-particle properties of a strongly interacting ultracold Fermi gas with mass imbalance. Using an extended TTT-matrix theory, we calculate the density of states, as well as the single-particle spectral weight, in the unitarity limit above the superfluid phase transition temperature TcT_{\rm c}Tc​. We show that the momentum regions where pairing fluctuations strongly affect single-particle excitations are different between light fermions and heavy fermions, reflecting the difference of the Pauli blocking effects between them. In addition, we obtain different pseudogap phenomena associated with pairing fluctuations in between the two components. Since the realization of a mass-imbalanced superfluid Fermi gas is an important challenge in this field, our results would contribute to the understanding of physical properties of the hetero-pairing state.
Two-body inelastic collisions arising from chemical reactions are prevalent in ultracold fermionic and bosonic molecular gases. Although recent advancements have achieved quantum degeneracy in these systems, loss dynamics are typically modeled phenomenologically using rate equations that often assume thermalization during chemical reactions. In this study, we employ the inelastic quantum Boltzmann equation to analyze particle loss, temperature evolution, and momentum distributions in single-component Fermi gases from first principles. Our results demonstrate that the conventional particle-number rate equation accurately describes the dynamics in trapped systems but fails to capture the behavior in homogeneous systems. Notably, under pure p-wave inelastic collisions and zero elastic collisions, we find that systems prepared near or above quantum degeneracy remain in a thermal state, whereas systems initialized deep within degeneracy exhibit nonequilibrium dynamics. Our theoretical predictions align well with recent experimental observations in trapped systems, and our claim can be further verified in atomic systems with induced two-body loss in box potentials.
We have produced an interacting quantum degenerate Fermi gas of atoms composed of two spin states of magnetically trapped 40K. The relative Fermi energies are adjusted by controlling the population in each spin state. Thermodynamic measurements reveal a resulting imbalance in the mean energy per particle between the two species, which is a factor of 1.4 at our lowest temperature. This imbalance of energy comes from a suppression of collisions between atoms in the gas due to the Pauli exclusion principle. Through measurements of the thermal relaxation rate we have directly observed this Pauli blocking as a factor of 2 reduction in the effective collision cross section in the quantum degenerate regime.
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 sss-wave scattering with a negative scattering length modeling the $^{40}\mathrm{K}\penalty1000-\hskip0pt^{87}\mathrm{Rb}$ 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.
We study Fermi-liquid properties of a weakly interacting two-dimensional gas of single-component fermionic polar molecules with dipole moments ddd oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean-field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as 1/r31/{r}^{3}1/r3 at large distances rrr, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter kFr∗{k}_{F}{r}_{*}kF​r∗​, where kF{k}_{F}kF​ is the Fermi momentum and ${r}_{*}=m{d}^{2}/{\ensuremath{\hbar}}^{2}$ is the dipole-dipole length, with mmm being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in kFr∗{k}_{F}{r}_{*}kF​r∗​ and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, as it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.
We study Fermi liquid properties of a weakly interacting 2D gas of single-component fermionic polar molecules with dipole moments ddd oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as 1/r31/r^31/r3 at large distances rrr, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter kFr∗k_Fr_*kF​r∗​, where kFk_FkF​ is the Fermi momentum, and r∗=md2/ℏ2r_*=md^2/\hbar^2r∗​=md2/ℏ2 is the dipole-dipole length, with mmm being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in kFr∗k_Fr_*kF​r∗​ and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, like it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.