Person:

Babadi, Mehrtash

We theoretically analyze a quasi-two-dimensional system of fermionic polar molecules in a harmonic transverse confining potential. The renormalized energy bands are calculated by solving the Hartree-Fock equation numerically for various trap and dipolar interaction strengths. The inter-subband excitations of the system are studied in the conserving time-dependent Hartree-Fock (TDHF) approximation from the perspective of lattice modulation spectroscopy experiments. We find that the excitation spectrum consists of both inter-subband particle-hole excitation continuums and anti-bound excitons, arising from the anisotropic nature of dipolar interactions. The excitonic modes capture the majority of the spectral weight. We also evaluate the inter-subband transition rates in order to investigate the nature of the excitonic modes and find that they are anti-bound states formed from particle-hole excitations arising from several subbands. Our results indicate that the excitonic effects are present for interaction strengths and temperatures accessible in current experiments with polar molecules.

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.

We show by a meta-analysis of the available Quantum Monte Carlo (QMC) results that two-dimensional fermions with repulsive interactions exhibit universal behavior in the strongly correlated regime, and that their freezing transition can be described using a quantum generalization of the classical Hansen-Verlet freezing criterion. We calculate the liquid-state energy and the freezing point of the 2D dipolar Fermi gas (2DDFG) using a variational method by taking ground-state wave functions of 2D electron gas (2DEG) as trial states. A comparison with the recent fixed-node diffusion Monte Carlo analysis of the 2DDFG shows that our simple variational technique captures more than 95% of the correlation energy, and predicts the freezing transition within the uncertainty bounds of QMC. Finally, we utilize the ground-state wave functions of 2DDFG as trial states and provide a variational account of the effects of finite 2D confinement width. Our results indicate significant beyond mean-field effects. We calculate the frequency of collective monopole oscillations of the quasi-2D dipolar gas as an experimental demonstration of correlation effects.

The rapid progress of the field of ultracold atoms during the past two decades has set new milestones in our control over matter. By cooling dilute atomic gases and molecules to nano-Kelvin temperatures, novel quantum mechanical states of matter can be realized and studied on a table-top experimental setup while bulk matter can be tailored to faithfully simulate abstract theoretical models. Two of such models which have witnessed significant experimental and theoretical attention are (1) the two-component Fermi gas with resonant $s$-wave interactions, and (2) the single-component Fermi gas with dipole-dipole interactions. This thesis is devoted to studying the non-equilibrium collective dynamics of these systems using the general framework of quantum kinetic theory.