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arXiv:cond-mat/0603469 · Physical Review A

Dissociation dynamics of resonantly coupled Bose-Fermi mixtures in an optical lattice

Takahiko Miyakawa, Pierre Meystre

Published Oct 23, 2006• 8 citations
arXivHTMLPDF

Abstract

We consider the photodissociation of ground-state bosonic molecules trapped in an optical lattice potential into a two-component gas of fermionic atoms. The system is assumed to be described by a single-band resonantly coupled Bose-Fermi Hubbard model. We show that in the strong fermion-fermion interaction limit the dissociation dynamics is governed by a spin-boson lattice Hamiltonian. In the framework of a mean-field analysis based on a generalized Gutzwiller ansatz, we then examine the crossover of the dissociation from a regime of independent single-site dynamics to a regime of cooperative dynamics as the molecular tunneling increases. We also show that in the limits of weak and strong intersite tunneling the mean-field solutions agree well with the results from the quantum optical Jaynes-Cummings and Tavis-Cummings models, respectively. Finally, we identify two types of self-trapping transitions, a coherent and an incoherent one, depending on the ratio of the repulsive molecule-molecule interaction strength to molecular tunneling.

DOI
10.1103/physreva.74.043615

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We investigate the tunneling properties of a bound pair of Fermi atoms in an optical lattice, comparing with results obtained in an attractive Hubbard model. In the strong-coupling regime of the Hubbard model, it has been predicted that the motion of a bound pair between lattice sites is accompanied by virtual dissociation. To explore the possibility of this interesting phenomenon in an optical lattice, we calculate the molecular wave function in a cosine-shaped periodic potential. We show that the molecular tunneling accompanied by dissociation occurs in the intermediate-coupling regime of the optical-lattice system. In the strong-coupling regime, in contrast to the prediction in the Hubbard model, the bound pair is shown to tunnel through the lattice potential without dissociation. As a result, the magnitude of the molecular band mass MMM remains finite even in the strong-coupling limit, which is in contrast to the diverging molecular mass in the case of the Hubbard model. Including this finite value of the molecular band mass, we evaluate the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​ in the Bose-Einstein-condensate limit of the optical-lattice system, where the Hubbard model gives Tc=0{T}_{\mathrm{c}}=0Tc​=0 due to the diverging molecular mass.
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 pseudospin 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.
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.
We investigate properties of an ultracold, two-component bosonic gas in a square optical lattice at unit filling. In addition to density-density interactions, the atoms are subject to coherent light-matter interactions that couple different internal states. We examine the influence of this coherent coupling on the system and its quantum phases by using Gutzwiller mean-field theory as well as bosonic dynamical mean-field theory. We find that the interplay of strong interspecies repulsion and coherent coupling affects the Mott insulator to superfluid transition and shifts the tip of the Mott lobe toward higher values of the tunneling amplitude. In the strongly interacting Mott regime, the resulting Bose-Hubbard model can be mapped onto an effective spin Hamiltonian that offers additional insights into the observed phenomena.
We discuss the theory of mixtures of bosonic and fermionic atoms in periodic potentials at zero temperature. We derive a general Bose-Fermi Hubbard Hamiltonian in a one-dimensional optical lattice with a superimposed harmonic trapping potential. We study the conditions for linear stability of the mixture and derive a mean-field criterion for the onset of a bosonic superfluid transition. We investigate the ground-state properties of the mixture in the Gutzwiller formulation of mean-field theory, and present numerical studies of finite systems. The bosonic and fermionic density distributions and the onset of quantum phase transitions to demixing and to a bosonic Mott-insulator are studied as a function of the lattice potential strength. The existence is predicted of a disordered phase for mixtures loaded in very deep lattices. Such a disordered phase possessing many degenerate or quasidegenerate ground states is related to a breaking of the mirror symmetry in the lattice.
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.