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Acta Physica Polonica A

Phase Diagram of Mixtures of Ultracold Bosons in Optical Lattice

Sergii Anufriiev, T. A. Zaleski

Published Aug 1, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.12693/aphyspola.130.629

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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.
We study a critical behavior of mixtures of two species of ultracold bosons trapped in an optical lattice. Using mean-field approximation, we determine the ground-state phase diagram of the system for a wide range of parameters. The introduction of interactions between different species of atoms strongly renormalizes the phase diagram. It can alter the critical behavior modifying multicriticality of crossing points and order of phase transitions in their vicinity between mixed and superfluid states. For selected values of model parameters, the behavior of the system falls out of the XYXYXY model universality class, which usually is a hallmark of superfluid phase transition. We supplement our analysis with analytical calculations to explain the observed scenario.
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 investigate the ground state phase diagram for a two species Bose mixture in a one dimensional optical lattice using the finite size density matrix renormalization group (FSDMRG) method. We present our result for different combinations of inter and intra-species repulsion strengths with a commensurate filling factor. We obtain a superfluid (SF) to Mott insulator (MI) transition when the inter species interaction term is less than the intra-species interaction term. However, when the former is slightly greater than the latter we find that the two different species reside in spatially separate regions.
We study the quantum phase transition of ultracold atoms in the honeycomb optical lattice. The Hamiltonian of ultracold bosonic atoms in the honeycomb optical lattice is derived. We take the mean-field approximation and further solve the Hamiltonian with the numerical diagonalization method. We obtain the phase diagram and find that the Mott-insulator (MI), density wave (DW) and modulated superfluid (MS) phases appear. Furthermore, the phase diagram is analyzed according to the order parameter and the average number of particles.
A mixture of ultracold bosons and fermions placed in an optical lattice constitutes a novel kind of quantum gas, and leads to phenomena, which so far has been discussed neither in atomic physics, nor in condensed matter physics. We discuss the phase diagram at low temperatures, and in the limit of strong atom-atom interactions, and predict the existence of quantum phases that involve pairing of fermions with one or more bosons, or, respectively, bosonic holes. The resulting composite fermions may form, depending on the system parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an insulator with fermionic domains. We discuss the feasibility for observing such phases in current experiments.