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Journal of Physics B Atomic Molecular and Optical Physics

Phase diagram of multi-component bosonic mixtures: emergence of mixed superfluid and insulating phases

Apurba Barman, Saurabh Basu

Published Jan 30, 2015• 8 citations
Publisher

Abstract

Abstract A three-component bosonic mixture is capable of demonstrating a significantly rich phase diagram in comparison with a two-component mixture or a single-component fluid. With experimental studies of multi-component mixtures gaining momentum and comparatively few theoretical efforts, we consider an interacting three-component Bose gas on a lattice and, via a strong coupling expansion of the Bose–Hubbard model, look into a variety of situations, such as the intraspecies and intraspecies interactions being the same and different, attractive and repulsive, etc. A scenario of rich phase diagrams emerges where one species of atoms can be in the superfluid phase while the other two may be in insulating phases. Such a mixed-phase diagram with different species coexisting in different phases is an exciting one: a possibility that can be explored in experiments. Numerical solution of the mean field equations has further demonstrated the occurrence of insulating phases with fractional filling of each species of atoms. Such insulating phases with fractional occupancies are counterintuitive in the context of incompressible phases.

DOI
10.1088/0953-4075/48/5/055301

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We obtain the ground-state quantum phase diagram for a two-species Bose mixture in a one-dimensional optical lattice using the finite-size density-matrix renormalization group method. We discuss our results for different combinations of inter- and intraspecies interaction strengths with commensurate and incommensurate fillings of the bosons. The phases we have obtained are a superfluid and a Mott insulator, and a phase separation where the two different species reside in spatially separate regions. The spatially separated phase is further classified into phase-separated superfluid and Mott insulator. The phase separation appears for all the fillings we have considered, whenever the interspecies interaction is slightly larger than the intraspecies interactions.
Superfluid-insulator transitions in a one-dimensional mixture of two-color fermions and scalar bosons are studied within the framework of the Bose-Fermi-Hubbard model. Zero-temperature phase diagrams are constructed for repulsive intraspecies interactions and attractive or repulsive interspecies couplings. In addition to the trivial Mott insulator phases, we report the emergence of nontrivial insulator phases that depend on the sign of the boson-fermion interaction. These nontrivial insulator phases satisfy the conditions ${\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\rho}}_{F}=n$ and ${\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}\frac{1}{2}{\ensuremath{\rho}}_{F}=n$, with the plus (minus) sign for repulsive (attractive) interactions and nnn an integer. Far from fermionic half filling, the boson-fermion interaction drives a gapless-gapped transition in the spin sector. Our findings could be observed experimentally in state-of-the-art cold-atom setups.
We study a behaviour of mixture of two species of ultracold bosons trapped in optical lattice.Using mean-field approximation, we determine the phase diagram of the system for wide range of parameters.We observe that each of the groups of atoms can condense into superfluid state or localize and form the Mott insulator, which yields that the whole system is either superfluid, the Mott insulator, or a mixed state.It appears that introduction of interaction between different kinds of atoms can strongly renormalise the phase diagram.It can alter the critical behaviour modifying multi-criticality of crossing points and order of phase transitions between mixed and superfluid states.
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We study the ground-state properties of mixtures of strongly interacting bosonic atoms in an optical lattice. Applying a mean-field approximation to the Hubbard model for Bose-Bose mixtures, we calculate the densities and superfluid order parameters for both species. Due to the repulsive interaction between the two species, the system exhibits phase separation. First, in the extreme limit of the zero-hopping case, we derive analytical expressions for the phase boundaries. In particular, we derive the conditions for phase separation in the Mott insulator phase. We find that the conditions for the phase separation depend on the on-site interactions as well as the occupation numbers. In particular, we show that the coexisting state appears by varying the on-site inter-species interaction. We also show the phase diagram of the finite hopping case. Second, we calculate the spatial density profile of 87^{87}87Rb-41^{41}41K mixtures in the combined potential of a parabolic trap and an optical lattice using the local density approximation. We fixed the number of 87^{87}87Rb and varied the number of 41^{41}41K, and used the parameters estimated by experiments. We show that the phase separated 87^{87}87Rb-41^{41}41K mixtures distribute like in a parabolic trap case. Furthermore, we find that phase separated mixtures distribute a nesting structure.
We address the possibility of realizing Bose-Einstein condensation as a first-order phase transition by admixture of particles of different species. To this aim we perform a comprehensive analysis of phase diagrams of two-component mixtures of bosons at finite temperatures. As a prototype model, we analyze a binary mixture of Bose particles interacting via an infinite-range (Kac-scaled) two-body potential. We obtain a rich phase diagram, where the transition between the normal and Bose-Einstein-condensed phases may be either continuous or first order. The phase diagram hosts lines of triple points, tricritical points, and quadruple points. We address the structure of the phase diagram depending on the relative magnitudes of the inter- and intraspecies interaction couplings. In addition, even for purely repulsive interactions, we identify a first-order liquid-gas-type transition between noncondensed phases characterized by different particle concentrations. In the obtained phase diagram, a surface of such first-order transitions terminates with a line of critical points.