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arXiv:1009.1465 · Physical Review A

Phase diagram of spin- 12 bosons in a one-dimensional optical lattice

Laurent de Forges de Parny, M. Traynard, F. Hébert, V. G. Rousseau, Richard T. Scalettar, G. G. Batrouni

Published Dec 3, 2010• 12 citations
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Abstract

Systems of two coupled bosonic species are studied using mean field theory and the quantum Monte Carlo method. The phase diagram is characterized on the basis of both the mobility of the particles (Mott insulating or superfluid) and whether or not the system is magnetic (different populations for the two species). The phase diagram is shown to be population balanced for negative spin-dependent interactions, regardless of whether it is insulating or superfluid. For positive spin-dependent interactions, the superfluid phase is always polarized, and the two populations are imbalanced. However, the Mott-insulating phase with even commensurate filling always has balanced populations. In contrast, the Mott phase with odd commensurate filling has balanced populations in a very strong interaction and polarizes as the interaction gets weaker while still in the Mott phase.

DOI
10.1103/physreva.82.063602

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Systems of two coupled bosonic species are studied using mean field theory and the quantum Monte Carlo method. The phase diagram is characterized on the basis of both the mobility of the particles (Mott insulating or superfluid) and whether or not the system is magnetic (different populations for the two species). The phase diagram is shown to be population balanced for negative spin-dependent interactions, regardless of whether it is insulating or superfluid. For positive spin-dependent interactions, the superfluid phase is always polarized, and the two populations are imbalanced. However, the Mott-insulating phase with even commensurate filling always has balanced populations. In contrast, the Mott phase with odd commensurate filling has balanced populations in a very strong interaction and polarizes as the interaction gets weaker while still in the Mott phase.
We study a two-species bosonic Hubbard model on a two-dimensional square lattice by means of quantum Monte Carlo simulations. In addition to the usual contact repulsive interactions between the particles, the Hamiltonian has an interconversion term which allows the transformation of two particles from one species to the other. The phases are characterized by their solid or superfluid properties and by their polarization, i.e., the difference in the populations. When interspecies interactions are smaller than the intraspecies ones, the system is unpolarized, whereas in the opposite case the system is unpolarized in even Mott insulator lobes and polarized in odd Mott lobes and also in the superfluid phase. We show that in the latter case the transition between the Mott insulator of total density 2 and the superfluid can be of either second or first order depending on the relative values of the interactions, whereas the transitions are continuous in all other cases.
We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of spin-1 bosons trapped in a square optical lattice. The phase diagram is characterized by the mobility of the particles (Mott insulating or superfluid phase) and by their magnetic properties. For ferromagnetic on-site interactions, the whole phase diagram is ferromagnetic and the Mott insulators-superfluid phase transitions are second order. For antiferromagnetic on-site interactions, spin nematic order is found in the odd Mott lobes and in the superfluid phase. Furthermore, the superfluid-insulator phase transition is first or second order depending on whether the density in the Mott is even or odd. Inside the even Mott lobes we observe a singlet-to-nematic transition for certain values of the interactions. This transition appears to be first order.
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.
We consider the two-species bosonic Hubbard model with variable interspecies interaction and hopping strength in the grand canonical ensemble with a common chemical potential. We analyze the superfluid-insulator (SI) transition for the relevant parameter regimes and compute the ground state phase diagram in the vicinity of odd filling Mott states. We find that the superfluid-insulator transition occurs with (a) simultaneous onset of superfluidity of both species or (b) coexistence of Mott insulating state of one species and superfluidity of the other or, in the case of unit filling, (c) complete depopulation of one species. The superfluid-insulator transition can be first order in a large region of the phase diagram. We develop a variational mean-field method which takes into account the effect of second order quantum fluctuations on the superfluid-insulator transition and corroborate the mean-field phase diagram using a quantum Monte Carlo study.
We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.
The superfluid--Mott-insulator phase transition of ultracold spin-1 bosons with ferromagnetic and antiferromagnetic interactions in an optical lattice is theoretically investigated. Two counterpropagating linearly polarized laser beams with the angle $\ensuremath{\theta}$ between the polarization vectors ($\mathrm{lin}\text{\ensuremath{-}}\ensuremath{\theta}\text{\ensuremath{-}}\mathrm{lin}$ configuration), driving an Fg=1{F}_{g}=1Fg​=1 to Fe=1{F}_{e}=1Fe​=1 internal atomic transition, create the optical lattice and at the same time couple atomic ground states with magnetic quantum numbers $m=\ifmmode\pm\else\textpm\fi{}1$. Due to the coupling the system can be described as a two-component one. At $\ensuremath{\theta}=0$ the system has a continuous isospin symmetry, which can be spontaneously broken, thereby fixing the number of particles in the atomic components. The phase diagram of the system and the spectrum of collective excitations, which are density waves and isospin waves, are worked out. In the case of ferromagnetic interactions, the superfluid--Mott-insulator phase transition is always second order, but in the case of antiferromagnetic interactions for some values of system parameters it is first order and the superfluid and Mott phases can coexist. Varying the angle $\ensuremath{\theta}$ one can control the populations of atomic components and continuously turn on and tune their asymmetry.