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arXiv:cond-mat/0307035 · Physical Review Letters

Molecular Micromaser

Christopher P. Search, Weiping Zhang, Pierre Meystre

Published Nov 3, 2003• 13 citations
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Abstract

We show that photoassociation of fermionic atoms into bosonic molecules inside an optical lattice can be described using a Jaynes-Cummings Hamiltonian with a nonlinear detuning. Using this equivalence to the Jaynes-Cummings dynamics, we show how one can construct a micromaser for the molecular field in each lattice site.
DOI
10.1103/physrevlett.91.190401

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We propose to subject two Bose-Einstein condensates to a periodic potential, so that one condensate undergoes the Mott-insulator transition to a state with precisely one atom per lattice site. We show that photoassociation of heteronuclear molecules within each lattice site is described by the quantum optical Jaynes-Cummings Hamiltonian. In analogy with studies of this Hamiltonian with cavity fields and trapped ions, we are thus able to engineer quantum optical states of atomic matter wave fields and we are able to reconstruct these states by quantum state tomography.
A micromaser containing a Kerr medium in its cavity has been investigated. We have presented an exact solution to the model Hamiltonian, which, apart from the usual Jaynes-Cummings terms, contains a Kerr term (${\mathit{a}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}2}$a2{\mathit{a}}^{2}a2). We have shown that the Kerr cavity nonlinearity significantly modifies the photon statistics of the micromaser field. Particularly, it is interesting to note that with the introduction of appropriate nonlinearity a micromaser can be made to approach towards a number state with a low number of photons.
We consider atomic mixtures of bosons and two-component fermions in an optical lattice potential. We show that if the bosons are in a Mott-insulator state with precisely one atom per lattice, the photoassociation of bosonic and fermionic atoms into heteronuclear fermionic molecules is described by the Anderson lattice model. We determine the ground-state properties of an inhomogeneous version of that model in the strong atom-molecule coupling regime, including an additional harmonic trap potential. Various spatial structures arise from the interplay between the atom-molecule correlations and the confining potential. Perturbation theory with respect to the tunneling coupling between fermionic atoms shows that antiferromagnetic correlations develop around a spin-singlet core of fermionic atoms and molecules.
We propose the creation of a molecular Bose-Einstein condensate by loading an atomic condensate into an optical lattice and driving it into a Mott insulator with exactly two atoms per site. Molecules in a Mott insulator state are then created under well defined conditions by photoassociation with essentially unit efficiency. Finally, the Mott insulator is melted and a superfluid state of the molecules is created. We study the dynamics of this process and photoassociation of tightly trapped atoms.
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.