Confinement and Superfluidity in one-dimensional Degenerate Fermionic Cold Atoms

TL;DR

This paper explores the phases of one-dimensional degenerate fermionic cold atoms with half-integer spins, revealing two superfluid phases and a phase transition characterized by a $Z_N$ universality class, with implications for experimental detection.

Contribution

It introduces a low-energy theoretical framework for understanding superfluid phases and phase transitions in high-spin fermionic cold atoms in one dimension, including experimental proposals.

Findings

Identification of unconfined BCS pairing and confined molecular superfluid phases.

The phase transition belongs to the $Z_N$ generalized Ising universality class.

Discussion of possible Mott phases at fractional fillings.

Abstract

The physical properties of arbitrary half-integer spins $F = N - 1/2$ fermionic cold atoms trapped in a one-dimensional optical lattice are investigated by means of a low-energy approach. Two different superfluid phases are found for $F \ge 3/2$ depending on whether a discrete symmetry is spontaneously broken or not: an unconfined BCS pairing phase and a confined molecular superfluid instability made of $2N$ fermions. We propose an experimental distinction between these phases for a gas trapped in an annular geometry. The confined-unconfined transition is shown to belong to the $Z_N$ generalized Ising universality class. We discuss on the possible Mott phases at $1/2N$ filling.