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arXiv:1202.0955 · Physical Review A

State diagram and the phase transition of p bosons in a square bipartite optical lattice

V. S. Shchesnovich

Published Jan 10, 2012• 2 citations
arXivHTMLPDF

Abstract

It is shown that, in a reasonable approximation, the quantum state of $p$ bosons in a bipartite square two-dimensional optical lattice is governed by the nonlinear boson model describing tunneling of boson pairs between two orthogonal degenerate quasimomenta on the edge of the first Brillouin zone. The interplay between the lattice anisotropy and the atomic interactions leads to the second-order phase transition between the number-squeezed and coherent phase states of the $p$ bosons. In the isotropic case of the recent experiment [G. Wirth, M. \"Olschl\"ager, and A. Hemmerich, Nat. Phys. 7, 147 (2011)], the $p$ bosons are in the coherent phase state, where the relative global phase between the two quasimomenta is defined only up to mod($\ensuremath{\pi}$): $\ensuremath{\varphi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. The quantum phase diagram of the nonlinear boson model is given.

DOI
10.1103/physreva.85.013614

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It is shown that, in a reasonable approximation, the quantum state of ppp bosons in a bipartite square two-dimensional optical lattice is governed by the nonlinear boson model describing tunneling of boson pairs between two orthogonal degenerate quasimomenta on the edge of the first Brillouin zone. The interplay between the lattice anisotropy and the atomic interactions leads to the second-order phase transition between the number-squeezed and coherent phase states of the ppp bosons. In the isotropic case of the recent experiment [G. Wirth, M. "Olschl"ager, and A. Hemmerich, Nat. Phys. 7, 147 (2011)], the ppp bosons are in the coherent phase state, where the relative global phase between the two quasimomenta is defined only up to mod(\ensuremathπ\ensuremath{\pi}\ensuremathπ): \ensuremathφ=\ifmmode±\else\textpm\fi\ensuremathπ/2\ensuremath{\varphi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2\ensuremathφ=\ifmmode±\else\textpm\fi\ensuremathπ/2. The quantum phase diagram of the nonlinear boson model is given.
Two sorts of bosons in an optical lattice at commensurate filling factors can form five stable super-fluid and insulating ground states with rich and nontrivial phase diagram. The structure of the ground state diagram is established by mapping a d-dimensional quantum system onto a (d+1)-dimensional classical loop-current model and Monte Carlo (MC) simulations of the latter. Surprisingly, the quantum phase diagram features, besides second-order lines, first-order transitions and two multicritical points. We explain why first-order transitions are generic for models with pairing interactions using microscopic and mean-field (MF) arguments. In some cases, the MC results strongly deviate from the MF predictions.
We study interacting bosons in a two-dimensional square bipartite optical lattice. By focusing on the regime where the first three excited bands are nearly degenerate (i.e., the first-excited ppp bands in one sublattice are nearly degenerate with the sss band of the other sublattice), we derive a multi-orbital tight-binding model which captures the most relevant features of the band structure. In addition, we also derive a corresponding generalized Bose-Hubbard model and solve it numerically under different situations, both with and without a confining trap. It is especially found that the hybridization between sublattices can strongly influence the phase diagrams and, in a trap, enable even appearances of condensed phases intersecting the same Mott insulating plateaus.
The superfluid to Mott insulator transition and the superradiant transition are textbook examples of quantum phase transition and coherent quantum optics, respectively. Recent experiments in ETH and Hamburg have succeeded in loading degenerate bosonic atomic gases in optical lattices inside a cavity, which enables the first experimental study of the interplay between these two transitions. In this Rapid Communication we present the theoretical phase diagram for the ETH Zurich experimental setup, and determine the phase boundaries and the orders of the phase transitions between the normal superfluid phase, the superfluid with superradiant light, the normal Mott insulator, and the Mott insulator with superradiant light. We find that in contrast to the second-order superradiant transition in a weakly interacting Bose condensate, strong correlations in the superfluid nearby a Mott transition can render the superradiant transition to a first-order one. Our results will stimulate further experimental studies of interactions between cavity light and strongly interacting quantum matter.
We study the formation of a chiral mode in a one-dimensional bipartite optical potential with a double-well dispersion. The geometry of the first excited state is tuned such that two degenerate energy minima are formed at the quasimomentum $q=\ifmmode\pm\else\textpm\fi{}\ensuremath{\hbar}{k}_{0}/2$ of the first Brillouin zone. Based on the coupled-mode theory, an unconventional superfluid order ${p}_{q}\ifmmode\pm\else\textpm\fi{}i{p}_{\ensuremath{-}q}$ is formed between the interacting condensate components within the double-well dispersion band under well-defined phase-locked steady states.
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.
The Bose–Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. We propose a mean-field theory based on a constraint SU(3) pseudo-boson representation on the effective model to study the properties of the superfluid-Mott-insulator phase transition. By calculating the elementary excitation spectra and the average particle number fluctuation in the Brillouin zone center, we find that the energy gaps vanish continuously around ( J XY / J z ) c ≈0.175 and ( J XY / J z ) c ≈0.094 for 2D and 3D cubic lattices respectively, where the superfluid order parameters come up from zero and the Mott insulator state changes into a superfluid state.