One-dimensional mixtures of several ultracold atoms: a review

Abstract

Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two-and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higherspin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification. :1903.12189v3 [cond-mat.quant-gas] CONTENTS arXiv

Unconventional pairing in one-dimensional systems of a few mass-imbalanced ultracold fermions

“…We assume that interactions between particles from different components can be modeled with a zero-range δlike potential of strength g. This approximation is reasonable and relevant to experiments in ultra-cold quantum gases [32]. It should be emphasized that the methods originating in the Feshbach resonance phenomenon and based on varying the external confinement in perpendicular directions allow to tune the effective onedimensional scattering length between atoms, and consequently the strength of contact interactions in these systems [33][34][35].…”

Geometry-induced entanglement in a mass-imbalanced few-fermion system

“…In this way, we want to draw a much closer analogy between critical transitions in systems containing a finite number of particles (but having infinitely many configurations accessible) with standard quantum phase transitions occurring in systems of infinite sizes. Since fewfermion systems of equal mass atoms has been engineered almost for a decade [23][24][25] and there are experimental setups where mass-imbalanced fermionic mix-tures with a large number of particles are realized [26][27][28][29][30], we believe that the path of exploration proposed here may be important when the next generation of experiments of mass-imbalanced few-fermion mixtures will be performed [31,32].…”

Spin–orbit coupling in the presence of strong atomic correlations

“…While solving large many-body systems with approaches beyond mean-field is a very difficult task and only possible in special cases [12][13][14], few-particle systems can actually be amenable to exact treatments across the whole range of interactions and correlation strengths [15][16][17][18][19]. Several treatments of SOC in such systems have already been carried out [20][21][22][23][24][25][26] and, for example, a mapping to an effective spin model was recently suggested by a perturbative approach to account for weak Raman coupling [21].…”