Abstract
We derive the complete mixing-demixing phase-diagram relevant to a bosonic binary mixture confined in a ring trimer and modeled within the Bose-Hubbard picture. The mixing properties of the two quantum fluids, which are shown to be strongly affected by the fragmented character of the confining potential, are evaluated by means of a specific indicator imported from Statistical Thermodynamics and are shown to depend only on two effective parameters incorporating the asymmetry between the heteronuclear species. To closely match realistic experimental conditions, our study is extended also beyond the pointlike approximation of potential wells by describing the systems in terms of two coupled Gross-Pitaevskii equations. The resulting mean-field analysis confirms the rich scenario of mixing-demixing transitions of the mixture and also constitutes an effective springboard towards a viable experimental realization. We additionally propose an experimental realization based on a realistic optical-tweezers system and on the bosonic mixture 23Na + 39K, thanks to the large tunability of their intra- and inter-species scattering lengths.
Highlights
Ultracold mixtures of different atomic species have a long experimental history both for studies in bulk1 and in optical lattices2–5 and allowed the investigation of a plethora of intriguing phenomena such as entropy exchange6, miscibility in degenerate gases7, beyond-mean-field effects8–10, universality of three-body losses11–13 and ultracold chemistry14
A large amount of recent theoretical studies have revealed a colorful phenomenology ranging from phase separation mechanism15,16, demixing of dipolar mixtures17, and quantum emulsions18,19 to the critical properties of quasiparticles spectrum across the transition20, thermal suppression21 and the role of entanglement22 in phase separation, and cascades of quantum phase transitions of vector bosons23
We present a mean-field (MF) approach based on the solution of two coupled stationary Gross-Pitaevskii equations (GPEs)
Summary
We consider a bosonic binary mixture confined in a three-well potential with periodic boundary conditions (i.e. a ring trimer) This is well described by the Bose-Hubbard Hamiltonian. The CVP, originally introduced to investigate the spatial fragmentation of a condensate in a two-well potential, is a semi-classical approximation scheme based on the replacement of the inherently discrete quantum numbers associated to the Fock-state basis with continuous variables. This technique has proved to be effective in capturing the essential critical behaviour of complex many-body systems. ∑anidyiyi=: =1 m, ei/nNfobrrceipnrgespeanrttincloermnuamlizbeedr conservation in both conboson populations and are regarded as continuous in view of the fact that the total numbers of bosons Na and Nb are assumed to be large
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