arXiv:cond-mat/0505617 · Physical Review Letters

Confinement and Superfluidity in One-Dimensional Degenerate Fermionic Cold Atoms

P. Lecheminant, E. Boulat, P. Azaria

Published Dec 5, 2005• 102 citations

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 > or = (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 the possible Mott phases at (1/2) filling.

DOI: 10.1103/physrevlett.95.240402

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arXiv:cond-mat/0505617 · Physical Review Letters

Confinement and Superfluidity in One-Dimensional Degenerate Fermionic Cold Atoms

P. Lecheminant, E. Boulat, P. Azaria

Published Dec 5, 2005• 102 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.95.240402

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The phase diagram of spin-

3∕2

fermionic cold atoms trapped in a one-dimensional optical lattice is investigated at quarter filling (one atom per site) by means of large-scale numerical simulations. In full agreement with a recent low-energy approach, we find two phases with confined and deconfined Cooper pairs separated by an Ising quantum phase transition. The leading instability in the confined phase is an atomic-density wave with subdominant quartet superfluid instability made of four fermions. Finally, we reveal the existence of a bond-ordered Mott insulating phase in some part of the repulsive regime.

We study a simple model of

N

-component fermions with contact interactions which describes fermionic atoms with

N=2F+1

hyperfine states loaded into a one-dimensional optical lattice. We show by means of analytical and numerical approaches that, for attractive interaction, a quasi-long-range molecular superfluid phase emerges at low density. In such a phase, the pairing instability is strongly suppressed and the leading instability is formed from bound states made of

N

fermions. At small density, the molecular superfluid phase is generic and exists for a wide range of attractive contact interactions without an

\mathrm{SU}(N)

symmetry between the hyperfine states.

We investigate the zero-temperature phase diagram of two-orbital

\mathrm{SU}(N

) fermionic models at incommensurate filling which are directly relevant to strontium and ytterbium ultracold atoms loading into a one-dimensional optical lattice. Using a low-energy approach that takes into account explicitly the

\mathrm{SU}(N

) symmetry, we find that a spectral gap for the nuclear-spin degrees of freedom is formed for generic interactions. Several phases with one or two gapless modes are then stabilized which describe the competition between different density instabilities. In stark contrast to the

N=2

case, no dominant pairing instabilities emerge and the leading superfluid one is rather formed from bound states of

2N

fermions.

f

, showing an infinite number of level crossings of the lowest states when increasing the trap size. At the

n=1

Mott transition, this gives rise to a modulated TSS: The TSS is still controlled by the trap-size exponent $\ensuremath{\theta}$, but it gets modulated by periodic functions of the trap size. Modulations of the asymptotic power-law behavior is also found in the gapless superfluid region, with additional multiscaling behaviors.