Stability and Pairing in Quasi-One-Dimensional Bose-Fermi Mixtures

Abstract

We consider a mixture of single-component bosonic and fermionic atoms in an array of coupled one-dimensional "tubes". For an attractive Bose-Fermi interaction, we show that the system exhibits phase separation instead of the usual collapse. Moreover, above a critical inter-tube hopping, all firstorder instabilities disappear in both attractive and repulsive mixtures. The possibility of suppressing instabilities in this system suggests a route towards the realization of paired phases, including a superfluid of p-wave pairs unique to the coupled-tube system, and quantum critical phenomena.PACS numbers: 67.85. Pq, 03.75.Hh, 64.70.Tg Recently, heteronuclear resonances in mixtures of bosonic and fermionic ultracold atoms have attracted noticeable theoretical and experimental interest, due to the possibility of generating and exploring novel quantum phenomena in a controllable manner. For example, by varying the interaction in a Bose-Fermi (BF) mixture, one can, in principle, observe a quantum phase transition from a Bose-Einstein condensate (BEC) to a normal Fermi gas phase by binding bosons and fermions into fermionic molecules [1,2]. Indeed, this feature has already been exploited to create deeply-bound, polar fermionic molecules [3]. However, the single biggest impediment to realizing such novel phenomena in BF mixtures is substantial inelastic collisions. The situation is particularly severe on the attractive side of the heteronuclear resonance, where a collapse of the cloud has been observed [4,5], resulting in a sudden loss of atoms from three-body recombination. On the repulsive side of the resonance, an interaction-induced spatial separation of bosons and fermions [6,7] ensures that the atomic system is relatively stable [8,9]. However, if one sweeps through the resonance, the system once again suffers significant inelastic losses when molecules collide with atoms [10].In this Letter, we argue that many of these obstacles may be circumvented by embedding the mixture in a two-dimensional (2D) array of 1D tubes generated via an anisotropic optical lattice. Such a lattice is experimentally realizable and has already been used to explore the 1D-3D crossover in a Bose gas [11]. While strictly 1D BF mixtures have been investigated extensively in several theoretical works [12,13,14,15,16,17,18,19,20], the novelty of our approach is to allow a finite hopping between tubes, thus preserving the true long-range order of condensed phases as found in 3D, while still maintaining the advantages of a 1D system. In particular, 3-body recombination should be greatly reduced, perhaps even more than in a BF mixture confined to a 3D optical lattice (see, e.g., [21]), since its rate vanishes for shortranged interactions in the 1D limit [22]. Furthermore, we demonstrate using mean-field theory that, similarly to 1D [16] and contrary to expectation [14,20], there is no collapse in a quasi-1D attractive mixture. Crucially, we find that the hopping can be used to suppress firstorder instabilities in BF mixtures and, as such, it may...

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

“…This picture has been, for instance, proposed at large interaction and low-density limit [50]. Bose-Fermi mixtures of 1D models have extensively studied in recent years [17,20,21,23,24,26,27,[51][52][53][54] and a similar picture emerges in certain regimes of three-component Fermi-gases [55]. When |U | is large, ↑ and ↓ fermions naturally form onsite pairs which are effectively hard-core bosons which we label b.…”

Phase equilibrium of binary mixtures in mixed dimensions

“…In the regime where the interaction between bosons and fermions is attractive, a significant reduction of the interatomic distance can lead to a collapse of the mixture, because of three-body recombination processes [38]. As discussed later, the stability of the mixture towards a collapsed phase can be enhanced in one-dimensional geometries [25].…”

“…As already mentioned, one motivation to study this geometry is that, by confining bosons in 1D, the mixture stability is enhanced [25]. Note that, even for purely bosonic gases, the spatial overlap between bosons has been experimentally shown to be strongly suppressed by the strong correlations emerging in 1D [41].…”

“…The equilibrium phase diagram of 1D Bose-Fermi mixtures has been considered by many authors [31][32][33][34][35], while the case of a Bose-Fermi system in an anisotropic optical lattices was studied by one of us in Ref. [25].…”

“…In recent years, these systems have attracted an increasing amount of theoretical attention [21,22], and very recently they have been also experimentally realized [23,24]. Besides its intrinsic interest as a new category of quantum many-body systems, they may also offer advantages for reducing few-body losses and enhancing stability in strongly interacting regimes [25].…”