Boson-fermion coherence in a spherically symmetric harmonic trap

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 BoseFermi 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.

Universality in nonadiabatic behavior of classical actions in nonlinear models of Bose-Einstein condensates

“…The phenomenon is very important for BEC physics: we consider here nonlinear two-mode models related to tunnelling between coupled BEC in a double well [23], nonlinear Landau-Zener tunnelling [24,25], Feshbach resonance passage in atom-molecule systems [26,27,28]. Nonlinear two-mode models were extensively studied previously (sometimes beyond the mean-field approxima- * Electronic address: alx˙it@yahoo.com tion, [23,24,25,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]), and destruction of adiabaticity was discussed already in [24,25,26], still there are regimes of motion that were not analyzed in these papers from the point of view of nonadiabatic behaviour, that is, when initial populations of both modes are not zero (or very small), but finite. We presented some of our results on that theme in [27,28]; nevertheless destruction of adiabatic invariance has not been studied systematically in BEC-related models yet.…”

Adiabatic passage through a Feshbach resonance in a degenerate quantum gas

“…The bosonic photoassociation problem was addressed by Ishkhanyan et al [18]; this is simply the bosonic analogue of the fermionic pairing we addressed in this paper. Given the mapping between the bosonic disassociation to fermionic association [14][15][16], it is not surprising that Ishkhanyan et al obtained a linear power law result. However the semiclassical approximation method they used to solve the problem required them to assume that the system starts as all atoms at large negative detuning.…”

“…In these definitions, the sign of the operator J z has been reversed relative to equation (2), and therefore this maps fermionic association to bosonic dissociation. This provides another perspective on the recently observed mapping between the two systems [14][15][16].…”

“…Employing the degenerate model with k ¼ for all k [14][15][16], it is convenient to define the model in terms of the following lowering and raising operators [15,17]:…”

“…The sweep rate in the above experiment is considered to be adiabatic with respect to both the many-body state as well as the single-particle timescales, allowing us to consider the collisionless regime in which inelastic collisions can be ignored. At low temperatures we assume a single bosonic mode Hamiltonian [10][11][12][13][14][15][16] because of the Cooper instability which singles out the zero momentum mode of the molecules produced. Thus, we take the Hamiltonian to be…”