Phase Transitions in Lattice Boson Models

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.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.

arXiv:1202.0955Physical Review AJan 10, 20122 citations

Quantum phase transitions in the interacting boson model

Pavel Cejnar, Jan Jolie

arXiv:0807.3467Progress in Particle and Nuclear PhysicsAug 16, 2008216 citations

Field-Induced Phase Transitions of Repulsive Spin-1 Bosons in Optical Lattices

Karen Rodríguez, Arturo Argüelles, Alexei K. Kolezhuk +2 more

We study the phase diagram of repulsively interacting spin-1 bosons in optical lattices at unit filling, showing that an externally induced quadratic Zeeman effect may lead to a rich physics characterized by various phases and phase transitions. We find that the main properties of the system may be described by an effective field model, which provides the precise location of the phase boundaries for any dimension, in excellent agreement with our numerical calculations for one-dimensional (1D) systems. Thus, our work provides a quantitative guide for the experimental analysis of various types of field-induced quantum phase transitions in spin-1 lattice bosons. These transitions, which are precluded in spin-1/2 systems, may be realized by using an externally modified quadratic Zeeman coupling, similar to recent experiments with spinor condensates in the continuum.We study the phase diagram of repulsively interacting spin-1 bosons in optical lattices at unit filling, showing that an externally induced quadratic Zeeman effect may lead to a rich physics characterized by various phases and phase transitions. We find that the main properties of the system may be described by an effective field model, which provides the precise location of the phase boundaries for any dimension, in excellent agreement with our numerical calculations for one-dimensional (1D) systems. Thus, our work provides a quantitative guide for the experimental analysis of various types of field-induced quantum phase transitions in spin-1 lattice bosons. These transitions, which are precluded in spin-1/2 systems, may be realized by using an externally modified quadratic Zeeman coupling, similar to recent experiments with spinor condensates in the continuum.

arXiv:1009.3875Physical Review LettersMar 9, 201145 citations

PHASE TRANSITIONS AND CRITICAL POINTS IN THE INTERACTING BOSON MODEL

J. E. García-Ramos, J. M. Arias, José Barea +1 more

Symmetries in Nuclear StructureApr 1, 20040 citations

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.