Phase transitions in the boson-fermion resonance model in one dimension

Journal Article · Thu Jun 15 04:00:00 EDT 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.73.0· OSTI ID:20787550

Orignac, E; Citro, R ^[1]

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1. Laboratoire de Physique Theorique de l'Ecole Normale Superieure CNRS-UMR8549 24, Rue Lhomond F-75231 Paris Cedex 05 France (France)

We study one-dimensional fermions with photoassociation or with a narrow Fano-Feshbach resonance described by the boson-fermion resonance model. Using the bosonization technique, we derive a low-energy Hamiltonian of the system. We show that at low energy, the order parameters for the Bose condensation and fermion superfluidity become identical, while a spin gap and a gap against the formation of phase slips are formed. As a result of these gaps, charge density wave correlations decay exponentially in contrast with the phases where only bosons or only fermions are present. We find a Luther-Emery point where the phase slips and the spin excitations can be described in terms of pseudofermions. This allows us to provide closed form expressions of the density-density correlations and the spectral functions. The spectral functions of the fermions are gapped, whereas the spectral functions of the bosons remain gapless. The application of a magnetic field results in a loss of coherence between the bosons and the fermion and the disappearance of the gap. Changing the detuning has no effect on the gap until either the fermion or the boson density is reduced to zero. Finally, we discuss the formation of a Mott insulating state in a periodic potential. The relevance of our results for experiments with ultracold atomic gases subject to one-dimensional confinement is also discussed.

• OSTI ID: 20787550
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 73; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
BOSE-EINSTEIN CONDENSATION
BOSON EXPANSION
BOSONS
CHARGE DENSITY
CONFINEMENT
CORRELATIONS
DENSITY
EXCITATION
FERMIONS
GASES
HAMILTONIANS
MAGNETIC FIELDS
ONE-DIMENSIONAL CALCULATIONS
ORDER PARAMETERS
PERIODICITY
PHASE TRANSFORMATIONS
RESONANCE
SLIP
SPECTRAL FUNCTIONS
SPIN
SUPERFLUIDITY