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Journal of Physics Conference Series

Molecular wavefunction and tunneling properties of a bound pair of Fermi atoms in an optical lattice

Yoji Ohashi

Published Feb 1, 2009• 1 citation
Publisher

Abstract

We investigate tunneling properties of a bound pair of Fermi atoms in an optical lattice. Including a realistic cosine-shape optical lattice potential, we calculate the molecular wavefunction ψ. Starting from the weak-coupling regime, we show how ψ shrinks as one increases the strength of a pairing interaction between atoms. When the molecular size becomes comparable to the lattice constant in the intermediate coupling regime, we find from the spatial structure of ψ that the molecular tunneling between lattice sites is accompanied by virtual dissociation. This phenomenon is shown to be suppressed in the strong-coupling regime due to very strong binding energy. We point out that, while the molecular tunneling accompanied by virtual dissociation can be described by the Hubbard model, it cannot describe the molecular tunneling with no virtual dissociation in the strong-coupling regime.

DOI
10.1088/1742-6596/150/3/032076

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We investigate tunneling properties of a bound pair of Fermi atoms in an optical lattice. Including a realistic cosine-shape optical lattice potential, we calculate the molecular wavefunction ψ. Starting from the weak-coupling regime, we show how ψ shrinks as one increases the strength of a pairing interaction between atoms. When the molecular size becomes comparable to the lattice constant in the intermediate coupling regime, we find from the spatial structure of ψ that the molecular tunneling between lattice sites is accompanied by virtual dissociation. This phenomenon is shown to be suppressed in the strong-coupling regime due to very strong binding energy. We point out that, while the molecular tunneling accompanied by virtual dissociation can be described by the Hubbard model, it cannot describe the molecular tunneling with no virtual dissociation in the strong-coupling regime.
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 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.
The quantum dynamics of an ultracold diatomic molecule tunneling and diffusing in a one-dimensional optical lattice exhibits unusual features. While it is known that the process of quantum tunneling through potential barriers can break up a bound-state molecule into a pair of dissociated atoms, interference and reassociation produce intricate patterns in the time-evolving site-dependent probability distribution for finding atoms and bound-state molecules. We find that the bound-state molecule is unusually resilient against break up at ultralow binding energy Eb{E}_{b}Eb​ (Eb{E}_{b}Eb​ much smaller than the barrier height of the lattice potential). After an initial transient, the bound-state molecule spreads with a width that grows as the square root of time. Surprisingly, the width of the probability of finding dissociated atoms does not increase with time as a power law.
The quantum dynamics of an ultracold diatomic molecule tunneling and diffusing in a one-dimensional optical lattice exhibits unusual features. While it is known that the process of quantum tunneling through potential barriers can break up a bound-state molecule into a pair of dissociated atoms, interference and reassociation produce intricate patterns in the time-evolving site-dependent probability distribution for finding atoms and bound-state molecules. We find that the bound-state molecule is unusually resilient against break up at ultralow binding energy Eb (Eb much smaller than the barrier height of the lattice potential). After an initial transient, the bound-state molecule spreads with a width that grows as the square root of time. Surprisingly, the width of the probability of finding dissociated atoms does not increase with time as a power law.
We study the molecular behavior of two atoms interacting near a Feshbach resonance in the presence of a 1D periodic potential. The critical value of the scattering length needed to produce a molecule and the binding energy at resonance are calculated as a function of the intensity of the periodic potential. Because of the non-separability of the center of mass and relative motion, the binding energy depends on the quasimomentum of the molecule. This has dramatic consequences on the molecular tunneling properties, which become strongly dependent on the scattering length.
We pursue three-body bound states in a one-dimensional tight-binding lattice described by the Bose-Hubbard model with strong on-site interaction. Apart from the simple strongly bound ``trimer'' state corresponding to all three particles occupying the same lattice site, we find two novel kinds of weakly bound trimers with energies below and above the continuum of scattering states of a single-particle (``monomer'') and a bound-particle pair (``dimer''). The corresponding binding mechanism can be inferred from an effective Hamiltonian in the strong-coupling regime which contains an exchange interaction between the monomer and the dimer. In the limit of very strong on-site interaction, the exchange-bound trimers attain a universal value of the binding energy. These phenomena can be observed with cold atoms in optical lattices.