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Functional-integral representation of atomic mixtures

Oleksandr Fialko, K. Ziegler

Published Jan 1, 2008• 0 citations
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Abstract

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.

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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 study an atomic Bose-Fermi mixture with unpolarized fermions in an optical lattice. We obtain the Mott ground states of such a system in the limit of the deep optical lattice and discuss the effect of quantum fluctuations on these states. We also study the superfluid-insulator transitions of bosons and metal-insulator transition of fermions in such a mixture within a slave-rotor mean-field approximation, and obtain the corresponding phase diagram. We discuss experimental implications of our results.
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.
In the strong-coupling Bose-Einstein condensation (BEC) region where a Feshbach resonance gives rise to tightly bound dimer molecules, we show that a spin-polarized Fermi superfluid reduces to a simple Bose-Fermi mixture of Bose-condensed dimers and the leftover unpaired fermions. Using a many-body functional integral formalism, the Gaussian fluctuations give rise to an induced dimer-dimer interaction mediated by the unpaired fermions, with the dimer-fermion vertex being given by the (mean-field) Born approximation. Treating the pairing fluctuations to quartic order, we show how the action for a spin-polarized Fermi superfluid reduces to one for a Bose-Fermi mixture. This Bose-Fermi action includes an expression for the effective dimer-unpaired fermion interaction in a spin-polarized Fermi superfluid beyond the Born approximation, in the BEC limit. In the low-density limit, we show how this dimer-fermion interaction gives the sss-wave scattering length aBF=1.18aF{a}_{\mathit{BF}}=1.18{a}_{F}aBF​=1.18aF​ (aF{a}_{F}aF​ is the sss-wave fermion scattering length), a result first derived by Skorniakov and Ter-Martirosian in 1957 for three interacting fermions.
The formation and dissociation of bosonic molecules in an optical lattice, formed by spin-1/2 fermionic atoms, is considered in the presence of an attractive nearest-neighbor interaction. A mean-field approximation reveals three different phases at zero temperature: an empty, a condensate and a Mott-insulating phase. The density of fermionic atoms and the density of bosonic molecules indicate a characteristic behavior with respect to the interaction strength that distinguishes between a dilute and a dense regime. In particular, the attractive interaction favors the formation of molecules in the dilute regime and the dissociation of atoms in the dense regime.
We study a behaviour of mixture of two species of ultracold bosons trapped in optical lattice.Using mean-field approximation, we determine the phase diagram of the system for wide range of parameters.We observe that each of the groups of atoms can condense into superfluid state or localize and form the Mott insulator, which yields that the whole system is either superfluid, the Mott insulator, or a mixed state.It appears that introduction of interaction between different kinds of atoms can strongly renormalise the phase diagram.It can alter the critical behaviour modifying multi-criticality of crossing points and order of phase transitions between mixed and superfluid states.