arXiv:0907.1533 · Physical Review Letters

Luttinger Liquid of Trimers in Fermi Gases with Unequal Masses

Giuliano Orso, Evgeni Burovski, Th. Jolicœur

Published Feb 12, 2010• 49 citations

Abstract

We investigate one dimensional attractive Fermi gases in spin-dependent optical lattices. We show that three-body bound states--"trimers"--exist as soon as the two tunneling rates are different. We calculate the binding energy and the effective mass of a single trimer. We then show numerically that for finite and commensurate densities n(up) = n(down)/2 an energy gap appears, implying that the gas is a one-component Luttinger liquid of trimers with suppressed superfluid correlations. The boundaries of this novel phase are given. We discuss experimental situations to test our predictions.

DOI: 10.1103/physrevlett.104.065301

Related papers

Fermionic trimers in spin-dependent optical lattices

Giuliano Orso, Evgeni Burovski, Th. Jolicœur

We investigate the formation of three-body bound states (trimers) in two-component Fermi gases confined in a one-dimensional optical lattice with spin-dependent tunneling rates. The binding energy and the effective mass of the trimer are obtained from the solution of the Mattis integral equation generalized to the case of unequal Bloch masses. We show that this equation admits multiple solutions corresponding to excited bound states, which are only stable for large mass asymmetry.

arXiv:1010.3105Comptes Rendus PhysiqueJan 1, 20116 citations

Multimer formation in one-dimensional two-component gases and trimer phase in the asymmetric attractive Hubbard model

Guillaume Roux, Evgeni Burovski, Th. Jolicœur

We consider two-component one-dimensional quantum gases at special imbalanced commensurabilities which lead to the formation of multimer (multiparticle bound-states) as the dominant order parameter. Luttinger liquid theory supports a mode-locking mechanism in which mass (or velocity) asymmetry is identified as the key ingredient to stabilize such states. While the scenario is valid both in the continuum and on a lattice, the effects of umklapp terms relevant for densities commensurate with the lattice spacing are also mentioned. These ideas are illustrated and confronted with the physics of the asymmetric (mass-imbalanced) fermionic Hubbard model with attractive interactions and densities such that a trimer phase can be stabilized. Phase diagrams are computed using density-matrix renormalization group techniques, showing the important role of the total density in achieving the latter phase. The effective physics of the trimer gas is studied as well. Last, the effect of a parabolic confinement and the emergence of a crystal phase of trimers are briefly addressed. This model has connections with the physics of imbalanced two-component fermionic gases and Bose-Fermi mixtures as the latter gives a good phenomenological description of the numerics in the strong-coupling regime.

arXiv:1103.2941Physical Review AMay 17, 201126 citations

Multimer formation in 1D two-component gases and trimer phase in the asymmetric attractive Hubbard model

Guillaume Roux, Evgeni Burovski, Th. Jolicœur

We consider two-component one-dimensional quantum gases at special imbalanced commensurabilities which lead to the formation of multimer (multi-particle bound-states) as the dominant order parameter. Luttinger liquid theory supports a mode-locking mechanism in which mass (or velocity) asymmetry is identified as the key ingredient to stabilize such states. While the scenario is valid both in the continuum and on a lattice, the effects of umklapp terms relevant for densities commensurate with the lattice spacing are also mentioned. These ideas are illustrated and confronted with the physics of the asymmetric (mass-imbalanced) fermionic Hubbard model with attractive interactions and densities such that a trimer phase can be stabilized. Phase diagrams are computed using density-matrix renormalization group techniques, showing the important role of the total density in achieving the novel phase. The effective physics of the trimer gas is as well studied. Lastly, the effect of a parabolic confinement and the emergence of a crystal phase of trimers are briefly addressed. This model has connections with the physics of imbalanced two-component fermionic gases and Bose-Fermi mixtures as the latter gives a good phenomenological description of the numerics in the strong-coupling regime.

Jan 1, 20110 citations

Bound states of Fermions in one dimension

Binbin Tian

The formation of bound states of fermions in one dimension has always been one of the key topics in condensed matter physics. Motivated by recent experimental progresses in Prof. Jeremy Levy's group, we study the interplay of both species (spin and transverse band index) and mass imbalance in a mixture of two or more species of fermions with attractive interactions in one dimension. Previous theoretical and experimental efforts have shown the existence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase for the case of two species with equal mass, in addition to the fully paired and fully polarized phases. For the unequal mass case, there are signatures of trion phases as well. We use DMRG to explore the rich possibilities of quantum phases and their transport signatures for the cases of two and more species of Fermions as we vary the interaction strengths and mass imbalances. With this we can gain insights into ongoing experiments with sketched nanowires in LAO/STO and ultracold atoms confined to one-dimensional tubes. We also study the formation of bound states in a single component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a 2-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one emergent neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the 2-component TLL theory. We speculate on the nature of the phase transitions amongst these phases.

Sep 27, 20190 citations

Fermi one-dimensional quantum gas: Luttinger liquid approach and spin charge separation

Alessio Recati, Peter O. Fedichev, W. Zwerger +1 more

We discuss the properties of quasi-one-dimensional quantum gases of fermionic atoms using the Luttinger liquid theory, including the presence of an optical lattice and of a longitudinal trapping potential. We analyse in particular the nature and manifestations of spin–charge separation, where in the case of atoms ‘spin’ and ‘charge’ refers to two internal atomic states and the atomic mass density, respectively.

arXiv:cond-mat/0212195Journal of Optics B Quantum and Semiclassical OpticsApr 1, 200348 citations

Emergent mode and bound states in single-component one-dimensional lattice fermionic systems

Yuchi He, Binbin Tian, David Pekker +1 more

We study the formation of bound states in a one-dimensional, single-component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of three-fermion bound states (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a two-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the two-component TLL theory. We speculate on the nature of the phase transitions amongst these phases.

arXiv:1811.06066Physical review. B./Physical review. BNov 7, 201915 citations