Small mass- and trap-imbalanced two-component Fermi systems

TL;DR

This paper calculates the energies of small two-component Fermi systems with mass and trap imbalance, providing insights relevant for optical lattice experiments with different atomic species like Li and K.

Contribution

It offers microscopic energy calculations for imbalanced Fermi systems, aiding the understanding of their configurations and interactions in optical lattice setups.

Findings

Energy calculations for N=2 to 6 fermions under imbalance.

Determination of the most favorable configurations for given atom numbers.

Analysis of excitation gaps for systems with up to 13 atoms.

Abstract

Motivated by the prospect of optical lattice experiments with two-component Fermi gases consisting of different atomic species such as Li and K, we calculate the energies for N fermions under harmonic confinement as a function of the mass- and trap-imbalance, i.e., as a function of the ratio between the masses and frequencies of species one and two, using microscopic approaches. Our energies for N=2 through 6 can be used to determine the energetically most favorable configuration for a given number of atoms per species of a deep lattice in which each lattice site is approximately harmonic and in which tunneling between neighboring sites can be neglected. Furthermore, our energies determine one of the input parameters, namely the onsite interaction strength, of the corresponding lattice Hamiltonian. We also determine and interpret the excitation gap for unequal-mass systems with up to N=13 atoms for equal oscillator lengths.