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Revista Mexicana de Física

Exactly-solvable generalization of the jaynes-Cummings model and its application to atom-molecule systems

Stuart Pittel, J. Dukelsky, G.G. Dussel

Published Dec 1, 2004• 0 citations
Publisher

Abstract

5 pags., 3 figs. -- The work reported here is based on a talk presented by one of the authors (SP) at the XXVIIth Symposium on Nuclear Physics held in Taxco, Mexico, from 5-8 January 2004. -- PACS: 02.30.Ik; 03.75.-b; 34.50.-s; 42.50.Pq
DOI
10.13039/501100005363

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We formulate and exactly solve a model for coherent association and dissociation of fermionic heteronuclear dimers in the deep-lattice Mott regime. Starting from the onsite three-component atom--molecule Hamiltonian, we show how the single-site model maps to the paradigmatic Jaynes--Cummings Hamiltonian from quantum optics. In this mapping, the fermionic molecular/free-atom sector forms an effective two-level system, while the bosonic atomic mode plays the role of the oscillator degree of freedom. We fix the conserved number of fermionic constituent atoms to one but allow an arbitrary conserved number NNN of bosonic constituent atoms. The accessible doublet is then ∣e,N−1⟩↔∣g,N⟩|e,N-1\rangle\leftrightarrow|g,N\rangle∣e,N−1⟩↔∣g,N⟩, and the coherent conversion coupling is bosonically enhanced to χNχ\sqrt{N}χN​. Exact analytic expressions are derived for molecular dissociation, atom-pair association, mode populations, and boson--fermion correlation dynamics. The model provides a transparent matter-wave realization of Jaynes--Cummings physics in a heteronuclear Bose--Fermi system and an exactly solvable setting for understanding coherent atom--molecule conversion and bosonic enhancement in lattice systems.