Boson-Fermion coherence in a spherically symmetric harmonic trap

TL;DR

This paper models the coherent photoassociation process of fermionic atoms into bosonic molecules in a harmonic trap, revealing a self-trapping transition and the impact of quantum fluctuations on system dynamics.

Contribution

It introduces a mapping of the fermionic system to the Tavis-Cummings model with pairing, and analyzes the quantum and semiclassical dynamics of atom-molecule coherence.

Findings

Self-trapping transition suppresses atom-molecule oscillations.

Quantum fluctuations dominate near the self-trapping point.

Exact diagonalization reveals ground state and excitation properties.

Abstract

We consider the photoassociation of a low-density gas of quantum-degenerate trapped fermionic atoms into bosonic molecules in a spherically symmetric harmonic potential. For a dilute system and the photoassociation coupling energy small compared to the level separation of the trap, only those fermions in the single shell with Fermi energy are coupled to the bosonic molecular field. Introducing a collective pseudo-spin operator formalism we show that this system can then be mapped onto the Tavis-Cummings Hamiltonian of quantum optics, with an additional pairing interaction. By exact diagonalization of the Hamiltonian, we examine the ground state and low excitations of the Bose-Fermi system, and study the dynamics of the coherent coupling between atoms and molecules. In a semiclassical description of the system, the pairing interaction between fermions is shown to result in a self-trapping transition in the photoassociation, with a sudden suppression of the coherent oscillations between atoms and molecules. We also show that the full quantum dynamics of the system is dominated by quantum fluctuations in the vicinity of the self-trapping solution.