Dimensional crossover of Fermi polaron in quasi-low-dimensional traps

Abstract

We study the polaron problem of an impurity immersed in the background of a Fermi sea confined in one-dimensional or two-dimensional isotropic traps. By changing the trapping potential from loose to tight, a dimensional crossover from anisotropically trapped three-dimensional to quasi-two-dimensional (quasi-2D) or quasi-one-dimensional (quasi-1D) configurations is investigated by calculating the ground-state energy in a wide range of interaction strength. We adopt a low-dimensional effective Hamiltonian in the form of a two-channel model, where the excited levels in the confined directions are described phenomenologically by a dressed molecule, and use the variational approach up to one pair of particle-hole fluctuations to calculate the energies of polaron and molecule states. We map out the phase diagrams for both quasi-1D and quasi-2D configurations and different mass ratios, and conclude that the polaron phase is preferable with tighter confinement and lighter impurity mass in lower dimensions. We also find that owing to the significant population of excited levels by strong interaction, a strictly low-dimensional system with all particles residing in the ground state of the trap can never work when study polaron-molecule transition, even in the tightly confined limit. This discrepancy has been observed in an experiment of quasi-2D gases of 40K atoms and is well explained by our calculation.