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arXiv:1307.3510 · Physical Review A

Sharp crossover from composite fermionization to phase separation in microscopic mixtures of ultracold bosons

Miguel Ángel García-March, Bruno Juliá-Díaz, G. E. Astrakharchik, Thomas Busch, Jordi Boronat, A. Polls

Published Dec 3, 2013• 42 citations
arXivHTMLPDF

Abstract

We show that a two-component mixture of a few repulsively interacting ultracold atoms in a one-dimensional trap possesses very diverse quantum regimes and that the crossover between them can be induced by tuning the interactions in one of the species. Starting from the composite fermionization regime, in which the interactions between both components are large and neither gas is phase coherent, our results show that a phase-separated state can be reached by increasing the interaction in one of the species. In this regime, the weakly interacting component stays at the center of the trap and becomes almost fully phase coherent, while the strongly interacting one is expelled to the edges of the trap. The crossover is sharp, as can be witnessed in the system's energy and in the occupation of the lowest natural orbital of the weakly interacting species. We show that such a transition is a few-atom effect which disappears for a large population imbalance.

DOI
10.1103/physreva.88.063604

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We show that a two-component mixture of a few repulsively interacting ultracold atoms in a one-dimensional trap possesses very diverse quantum regimes and that the crossover between them can be induced by tuning the interactions in one of the species. Starting from the composite fermionization regime, in which the interactions between both components are large and neither gas is phase coherent, our results show that a phase-separated state can be reached by increasing the interaction in one of the species. In this regime, the weakly interacting component stays at the center of the trap and becomes almost fully phase coherent, while the strongly interacting one is expelled to the edges of the trap. The crossover is sharp, as can be witnessed in the system's energy and in the occupation of the lowest natural orbital of the weakly interacting species. We show that such a transition is a few-atom effect which disappears for a large population imbalance.
We show the emergence of a strongly interacting Bose-Fermi mixture from a two-component Fermi mixture with population imbalance. By analyzing in situ density profiles of 6Li atoms in the BCS-BEC crossover regime, we identify a critical interaction strength, beyond which all minority atoms pair up with majority atoms and form a Bose condensate. This is the regime where the system can be effectively described as a boson-fermion mixture. We determine the dimer-fermion and dimer-dimer scattering lengths and beyond-mean-field contributions. Our study realizes a gedanken experiment of bosons immersed in a Fermi sea of one of their constituents, revealing the composite nature of the bosons.
We present a many-body description for two-component ultracold bosonic gases when one of the species is in the weakly interacting regime and the other is either weakly or strongly interacting. In the one-dimensional limit the latter is a hybrid in which a Tonks-Girardeau gas is immersed in a Bose-Einstein condensate, which is an example of a class of quantum system involving a tunable, superfluid environment. We describe the process of phase separation microscopically as well as semiclassically in both situations and show that quantum correlations are maintained even in the separated phase.
We explore a few-fermion mixture consisting of two components that are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where the physics of a single impurity in the Fermi sea is discussed to the partially imbalanced and equal population configurations are investigated. For the numerical calculations the multiconfigurational time-dependent Hartree method is employed, extending its application to few-fermion systems. Apart from numerical calculations we generalize our ansatz for a correlated pair wave function proposed recently [I. Brouzos and P. Schmelcher, Phys. Rev. Lett. 108, 045301 (2012)] for bosons to mixtures of fermions. From weak to strong coupling between the components the energies, the densities and the correlation properties of one-dimensional systems change vastly with an upper limit set by fermionization where for infinite repulsion all fermions can be mapped to identical ones. The numerical and analytical treatments are in good agreement with respect to the description of this crossover. We show that for equal populations each pair of different component atoms splits into two single peaks in the density while for partial imbalance additional peaks and plateaus arise for very strong interaction strengths. The case of a single-impurity atom shows rich behavior of the energy and density as we approach fermionization and is directly connected to recent experiments [G. Z\"urn et al., Phys. Rev. Lett. 108, 075303 (2012)].
Ultracold atom experiments offer the unique opportunity to study mixing of different types of superfluid states. Our interest is in superfluid mixtures comprising of particles with different statistics---Bose and Fermi. Such scenarios occur naturally, for example, in dense quantum chromodynamics (QCD) matter. Interestingly, cold atomic experiments are performed in traps with finite spatial extent, thus critically destabilizing the occurrence of various homogeneous phases. Critical to this analysis is the understanding that the trapped system can undergo phase separation, resulting in a unique situation where phase transition in either species (bosons or fermions) can overlap with the phase separation between possible phases. In the present work, we illustrate how this intriguing interplay manifests in an interacting two-species atomic mixture---one bosonic and another fermionic with two spin components---within a realistic trap configuration. We further show that such interplay of transitions can render the nature of the ground state to be highly sensitive to the experimental parameters and the dimensionality of the system.
We investigate the tunneling dynamics of an ultracold bosonic impurity species which interacts repulsively with a second, larger Bose gas. Both species are held in a finite-sized quasi-one-dimensional box potential. In addition, the impurity bosons experience a periodic potential generated by an optical lattice. We initially prepare our binary mixture in its ground state, such that the impurities and Bose gas are phase separated and the impurities localize pairwise in adjacent sites of the periodic potential, by tuning the interaction strengths and the lattice depth correspondingly. The dynamics is initiated by suddenly lowering the repulsive interspecies interaction strength, thereby entering a different regime in the crossover diagram. For specific postquench interspecies interaction strengths we find that a single impurity tunnels first to the neighboring empty site and depending on the quench strength can further tunnel to the next-neighboring site. Interestingly, this effect is highly sensitive to the presence of the Bose gas and does not occur when the Bose gas does not interact with the impurity species throughout the dynamics. Moreover, we find that the tunneling process is accompanied by strong entanglement between the Bose gas and the impurity species as well as correlations among the impurities.
We investigate the ground state of a few-body Bose-Fermi mixture in a one-dimensional harmonic trap with varying interaction strengths and mass ratio. A bunching-antibunching crossover of the bosonic species for increasing interspecies' repulsion is observed within our fully correlated ab initio studies. Interestingly, this crossover is suppressed if the bosonic repulsion exceeds a critical value which strongly depends on the mass ratio. In order to unveil the physical origin of this crossover, we employ different levels of approximations: while a species mean-field approach can account for the antibunching, only the inclusion of the interspecies correlations can lead to the bunching. We show that these correlations effectively create an induced bosonic interaction, which in turn elucidates the occurrence of the bosonic bunching. Finally, we derive a two-site extended Bose-Hubbard model which reveals the low-energy physics of the bosons for the case of much heavier fermions.