Ground-State Properties and Phase Separation of Binary Mixtures in Mesoscopic Ring Lattices.

Vittorio Penna,Andrea Richaud,Alessandra Contestabile

doi:10.3390/e23070821

Abstract

We investigated the spatial phase separation of the two components forming a bosonic mixture distributed in a four-well lattice with a ring geometry. We studied the ground state of this system, described by means of a binary Bose–Hubbard Hamiltonian, by implementing a well-known coherent-state picture which allowed us to find the semi-classical equations determining the distribution of boson components in the ring lattice. Their fully analytic solutions, in the limit of large boson numbers, provide the boson populations at each well as a function of the interspecies interaction and of other significant model parameters, while allowing to reconstruct the non-trivial architecture of the ground-state four-well phase diagram. The comparison with the L-well () phase diagrams highlights how increasing the number of wells considerably modifies the phase diagram structure and the transition mechanism from the full-mixing to the full-demixing phase controlled by the interspecies interaction. Despite the fact that the phase diagrams for share various general properties, we show that, unlike attractive binary mixtures, repulsive mixtures do not feature a transition mechanism which can be extended to an arbitrary lattice of size L.

Highlights

The demixing effect in bosonic binary mixtures trapped in optical lattices has attracted a fair amount of attention in the last two decades due to both the rich phenomenology stemming from the spatial separation of mixture components [1,2] and to the considerable complexity that the demixing mechanism features
Spatial phase separation greatly enriches the phase diagram of mixtures [9,10] characterized by new types of superfluidity and incompressible states [11,12], rules the coexistence of different phases in the presence of trapping potential [13,14], it is involved in the formation of quantum emulsions [15,16] and represents a robust property of mixtures able to survive at non-zero temperature and in spite of the confinement effect [17]
Designed almost fifteen years ago [18], the realization of traps with a ring geometry has been studied in [19,20] to support the development of atomtronics devices, while the technique used for realizing a double well [21,22] supplies a viable scheme to construct linear open arrays of potential wells

Summary

Introduction

The demixing effect in bosonic binary mixtures trapped in optical lattices has attracted a fair amount of attention in the last two decades due to both the rich phenomenology stemming from the spatial separation of mixture components [1,2] and to the considerable complexity that the demixing mechanism features. A parallel study on attractive mixtures, whose production has been recently studied in [32] together with the formation of droplet states, has revealed how the transition from mixed fully delocalized components to mixed components confined in a single well (supermixed state) [33] is controlled by the interspecies interaction and the population imbalance, but it is totally independent from the number of potential wells forming the lattice. This leads to the central problem addressed in this paper.

Coherent-State Picture of BH Model

Phase Separation in the BH Dimer

Phase Diagram of the Four-Well System

Phase Diagram Derivation and Characteristic Ground-State Energies

Discussion

Conclusions