Dynamical properties of Fermi gases

Cold atoms are a perfect tool to research spin transport as, unlike solids, they are not encumbered by an ionic lattice and can move essentially freely apart from rare collisions with each other. We developed a simulation of the Boltzmann equation for an interacting Fermi gas in the semiclassical regime. At sufficiently high temperatures it captures all relevant features of the system. Together with Frédéric Chevy and Carlos Lobo we studied the collision of two spin-polarized fermionic clouds in a harmonic trap and explained the observations from an experiment performed at MIT. Surprisingly, for a wide range of parameters the clouds bounce off each other, even though the inter-particle interaction is attractive. We showed that this phenomenon can be understood purely in terms of semiclassical collisions and interpreted the bounce as a consequence of a nonlinear coupling between collective modes which has never before been studied in Fermi gases. We also used the Boltzmann equation simulation in combination with analytical methods to calculate transport coefficients, providing for the first time a rigorous quantitative method to compute the spin drag in trapped gases.

Animated time-evolution of the simulated density profile for the bouncing Fermi clouds. See our paper for the parameter definitions.

We are also collaborating with experimentalists at Laboratoire Kastler Brossel in Paris on a novel approach to study the dynamics of harmonically trapped Weyl fermions. Weyl fermions are massless solutions of the Dirac equation and play an important role in high-energy as well as condensed matter physics. To study how Weyl fermions in a harmonic trap relax after displacement from the trap center we take advantage of a mapping to a collisionless atomic gas in a magnetic quadrupole trap after a momentum kick. This system is experimentally accessible and can be studied using analytical and numerical means. We found several surprising results. First, even without collisions, the system reaches a stationary state due to the dephasing of individual particle trajectories. Second, even though the collisionless system cannot reach thermal equilibrium, the momentum distributions fit closely to a thermal distribution. Most surprisingly, the “temperatures” along different directions are different! The axial and transverse directions of the quadrupole trap decouple despite the non-separability of the potential.