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arXiv:cond-mat/0612417 · Physical Review A

Dimer states in atomic mixtures

K. Ziegler

Published Jan 30, 2008• 5 citations
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Abstract

A mixture of heavy atoms in a Mott state and light spin-1/2 fermionic atoms is studied in an optical lattice. Inelastic scattering processes between the two atomic species excite the heavy atoms and renormalize the tunneling rate as well as the interaction of the light atoms. An effective Hamiltonian for the latter is derived that describes tunneling of single fermions, tunneling of fermionic pairs, and an exchange of fermionic spins. Low-energy states of this Hamiltonian are a N\'eel state for strong effective repulsion, dimer states for moderate interaction, and a density wave of paired fermions for strong effective attraction.

DOI
10.1103/physreva.77.013623

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A mixture of heavy atoms in a Mott state and light spin-1/2 fermionic atoms is studied in an optical lattice. Inelastic scattering processes between the two atomic species excite the heavy atoms and renormalize the tunneling rate as well as the interaction of the light atoms. An effective Hamiltonian for the latter is derived that describes tunneling of single fermions, tunneling of fermionic pairs, and an exchange of fermionic spins. Low-energy states of this Hamiltonian are a N'eel state for strong effective repulsion, dimer states for moderate interaction, and a density wave of paired fermions for strong effective attraction.
We study a mixture of two light spin-1/2 fermionic atoms and two heavy atoms in a double-well potential. Inelastic scattering processes between both atomic species excite the heavy atoms and renormalize the tunneling rate and the interaction of the light atoms (polaron effect). The effective interaction of the light atoms changes its sign and becomes attractive for strong inelastic scattering. This is accompanied by a crossing of the energy levels from singly occupied sites at weak inelastic scattering to a doubly occupied and an empty site for stronger inelastic scattering. We are able to identify the polaron effect and the level crossing in the quantum dynamics.
We consider collisional properties of weakly bound heteronuclear molecules (dimers) formed in a two-species mixture of atoms with a large mass difference. We focus on dimers containing light fermionic atoms as they manifest collisional stability due to an effective dimer-dimer repulsion originating from the exchange of the light atoms. In order to solve the dimer-dimer scattering problem we develop a theoretical approach, which provides a physically transparent and quantitative description of this four-atom system in terms of three- and two-body observables. We calculate the elastic scattering amplitude and the rates of inelastic processes such as the trimer formation and the relaxation of dimers into deeply bound molecular states. Irrespective of whether the heavy atoms are bosons or fermions, the inelastic rate can be significantly lower than the rate of elastic collisions. Moreover, the measurement of the inelastic rate which is a four-body observable, can be an efficient and precise tool for determining three-body observables such as the three-body parameter, positions of Efimov states, and their lifetimes.
A mixture of spin-polarized light- and heavy-Fermionic atoms on a finite-size two-dimensional optical lattice is considered at various temperatures and values of the coupling between the two atomic species. In the case where the heavy atoms are immobile in comparison to the light atoms, this system can be seen as a correlated binary alloy related to the Falicov-Kimball model. The heavy atoms represent a scattering environment for the light atoms. The distributions of the binary alloy are discussed in terms of strong- and weak-coupling expansions. We further present numerical results for the intermediate interaction regime and for the density of states of the light particles. The numerical approach is based on a combination of a Monte Carlo simulation and an exact diagonalization method. We find that the scattering by the correlated heavy atoms can open a gap in the spectrum of the light atoms, either for strong interaction or small temperatures.
A mixture of spin-1/2 fermionic atoms and molecules of paired fermionic atoms is studied in an optical lattice.The molecules are formed by an attractive nearestneighbor interaction.A functional integral is constructed for this many-body system and analyzed in terms of a mean-field approximation and Gaussian fluctuations.This provides a phase diagram with the two merging Mott insulators and an intermediate superfluid.The Gaussian fluctuations give rise to an induced repulsive dimer-dimer interaction mediated by the unpaired fermions.The effect of an unbalanced distribution of spin-up and spin-down fermions is also discussed.
A mixture of spin-1/2 fermionic atoms and molecules of paired fermionic atoms is studied in an optical lattice. The molecules are formed by an attractive nearest-neighbor interaction. A functional integral is constructed for this many-body system and analyzed in terms of a mean-field approximation and Gaussian fluctuations. This provides a phase diagram with the two merging Mott insulators and an intermediate superfluid. The Gaussian fluctuations give rise to an induced repulsive dimer-dimer interaction mediated by the unpaired fermions. The effect of an unbalanced distribution of spin-up and spin-down fermions is also discussed.
We show that, near a Feshbach resonance, a strong p-wave resonance is present at low energy in atom-dimer scattering for 6^66Li-40^{40}40K fermionic mixtures. This resonance is due to a virtual bound state, in the atom-dimer system, which is present at this low energy. When the mass ratio between the two fermionic elements is increased, this virtual bound state goes to a known real bound state which appears when the mass ratio reaches 8.17. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the equation of state of balanced mixtures at moderate or high temperature. The frequency and the damping of collective modes should also provide a convenient way to evidence this resonance. Finally it should be possible to modify the effective mass of one the fermionic species by making use of an optical lattice. This would allow to study the strong dependence of the resonance as a function of the mass ratio of the two fermionic elements.