Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Dynamical properties of bosons in an optical lattice with a synthetic magnetic field

Kenichi Kasamatsu, Akira Kato, Yuki Nakano, Tetsuo Matsui

Published Dec 17, 2012• 0 citations
Publisher

Abstract

We study the dynamical properties of bosons in an optical lattice subject to a synthetic magnetic field at zero temperature. First, we consider a superfluid regime where the nearest-neighbor hopping is much larger than the on-site repulsion and a large number of bosons are occupied in each site. Then, the dynamics is well described by the discrete nonlinear Schrödinger equation. Second, we study the dynamics of hard-core bosons as a limit of the strong interparticle interaction by solving the truncated Green's functions for the boson and density operators. We discuss the evolution of the density and the vorticity, which are clearly distinct between two regimes.

DOI
10.1088/1742-6596/400/1/012026

Related papers

Nonequilibrium Gross-Pitaevskii dynamics of boson lattice models

Anatoli Polkovnikov, Subir Sachdev A, S. M. Girvin

Motivated by recent experiments on trapped ultracold bosonic atoms in an optical lattice potential, we consider the nonequilibrium dynamic properties of such bosonic systems for a number of experimentally relevant situations. When the number of bosons per lattice site is large, there is a wide parameter regime where the effective boson interactions are strong, but the ground state remains a superfluid (and not a Mott insulator): we describe the conditions under which the dynamics in this regime can be described by a discrete Gross-Pitaevskii equation. We describe the evolution of the phase coherence after the system is initially prepared in a Mott insulating state, and then allowed to evolve after a sudden change in parameters places it in a regime with a superfluid ground state. We also consider initial conditions with a ``\ensuremath{\pi} phase'' imprint on a superfluid ground state (i.e., the initial phases of neighboring wells differ by \ensuremath{\pi}), and discuss the subsequent appearance of the density wave order and ``Schr\"odinger cat,'' i.e., macroscopic quantum interference, states.

arXiv:cond-mat/0206490•Physical Review A•Nov 12, 2002•138 citations

Finite-temperature phase structures of hard-core bosons in an optical lattice with an effective magnetic field

Yuki Nakano, Kenichi Kasamatsu, Tetsuo Matsui

We study finite-temperature phase structures of hard-core bosons in a two-dimensional optical lattice subject to an effective magnetic field by employing the gauged CP${}^{1}$ model. Based on the extensive Monte Carlo simulations, we study their phase structures at finite temperatures for several values of the magnetic flux per plaquette of the lattice and mean particle density. Despite the presence of the particle number fluctuation, the thermodynamic properties are qualitatively similar to those of the frustrated $XY$ model, with only the phase as a dynamical variable. This suggests that cold-atom simulators of the frustrated $XY$ model are available irrespective of the particle filling at each site.

arXiv:1112.0145•Physical Review A•Feb 16, 2012•6 citations

Extended Bose Hubbard model of interacting bosonic atoms in optical lattices: From superfluidity to density waves

G. Mazzarella, S. M. Giampaolo, Fabrizio Illuminati

For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.

arXiv:cond-mat/0509161•Physical Review A•Jan 26, 2006•76 citations

Strongly Correlated Bosons on a Lattice: A Slave-Boson Approach

K. Ziegler

The grand canonical system of hard-core bosons, subject to thermal fluctuations, is studied on a lattice. Starting from the slave-boson representation we derive an effective Ginzburg-Landau functional for the superfluid order parameter. The order parameter field is a collective field constructed from the slave-boson fields for empty and singly occupied sites. We find two phase transitions; one from a normal fluid at high density to a superfluid and another one from the superfluid to a normal fluid at low density.

Europhysics Letters (EPL)•Sep 1, 1993•16 citations

Detecting the superfluid critical momentum of Bose gases in optical lattices through dipole oscillations

Takuya Saito, Ippei Danshita, Takeshi Ozaki +1 more

We study the stability of superflow of Bose gases in optical lattices by analyzing the Bose-Hubbard model within the Gutzwiller mean-field approximation. We calculate the excitation spectra of the homogeneous Bose-Hubbard model at unit filling to determine the critical momenta for the Landau and dynamical instabilities. These two critical momenta are shown to approach each other when the on-site interaction increases towards the Mott transition point. In order to make a direct connection with realistic experiments, we next take into account a parabolic trapping potential and compute the real-time dynamics of dipole oscillations induced by suddenly displacing the trap center. We consider the following two cases: standard soft-core bosons, whose interparticle interactions include the on-site one only; and hard-core bosons with long-range dipole-dipole interactions. For both cases, we show that the dipole oscillation is significantly damped when the maximum local momentum exceeds a certain threshold, which quantitatively agrees with the critical momentum for the dynamical instability in the homogeneous system. In the case of dipolar hard-core bosons, the dynamical instability of dipole oscillations leads to the formation of checkerboard density waves in the superfluid phase near the boundary to the supersolid phase.

arXiv:1203.4890•Physical Review A•Aug 21, 2012•13 citations

Superfluid-insulator transition of ultracold bosons in an optical lattice in the presence of a synthetic magnetic field

Subhasis Sinha, K. Sengupta

We study the Mott-insulator–superfluid transition of ultracold bosonic atoms in a two-dimensional square optical lattice in the presence of a synthetic magnetic field with p / q ( p and q being co-prime integers) flux quanta passing through each lattice plaquette. We show that on approach to the transition from the Mott side, the momentum distribution of the bosons exhibits q precursor peaks within the first magnetic Brillouin zone. We also provide an effective theory for the transition and show that it involves q interacting boson fields. We construct, from a mean-field analysis of this effective theory, the superfluid ground states near the transition and compute, for q =2, 3, both the gapped and the gapless collective modes of these states. We suggest experiments to test our theory.

arXiv:1003.0258•Europhysics Letters (EPL)•Feb 1, 2011•19 citations
We study the dynamical properties of bosons in an optical lattice subject to a synthetic magnetic field at zero temperature. First, we consider a superfluid regime where the nearest-neighbor hopping is much larger than the on-site repulsion and a large number of bosons are occupied in each site. Then, the dynamics is well described by the discrete nonlinear Schrödinger equation. Second, we study the dynamics of hard-core bosons as a limit of the strong interparticle interaction by solving the truncated Green's functions for the boson and density operators. We discuss the evolution of the density and the vorticity, which are clearly distinct between two regimes.
Motivated by recent experiments on trapped ultracold bosonic atoms in an optical lattice potential, we consider the nonequilibrium dynamic properties of such bosonic systems for a number of experimentally relevant situations. When the number of bosons per lattice site is large, there is a wide parameter regime where the effective boson interactions are strong, but the ground state remains a superfluid (and not a Mott insulator): we describe the conditions under which the dynamics in this regime can be described by a discrete Gross-Pitaevskii equation. We describe the evolution of the phase coherence after the system is initially prepared in a Mott insulating state, and then allowed to evolve after a sudden change in parameters places it in a regime with a superfluid ground state. We also consider initial conditions with a ``\ensuremath{\pi} phase'' imprint on a superfluid ground state (i.e., the initial phases of neighboring wells differ by \ensuremath{\pi}), and discuss the subsequent appearance of the density wave order and ``Schr\"odinger cat,'' i.e., macroscopic quantum interference, states.
We study finite-temperature phase structures of hard-core bosons in a two-dimensional optical lattice subject to an effective magnetic field by employing the gauged CP1{}^{1}1 model. Based on the extensive Monte Carlo simulations, we study their phase structures at finite temperatures for several values of the magnetic flux per plaquette of the lattice and mean particle density. Despite the presence of the particle number fluctuation, the thermodynamic properties are qualitatively similar to those of the frustrated XYXYXY model, with only the phase as a dynamical variable. This suggests that cold-atom simulators of the frustrated XYXYXY model are available irrespective of the particle filling at each site.
For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.
The grand canonical system of hard-core bosons, subject to thermal fluctuations, is studied on a lattice. Starting from the slave-boson representation we derive an effective Ginzburg-Landau functional for the superfluid order parameter. The order parameter field is a collective field constructed from the slave-boson fields for empty and singly occupied sites. We find two phase transitions; one from a normal fluid at high density to a superfluid and another one from the superfluid to a normal fluid at low density.
We study the stability of superflow of Bose gases in optical lattices by analyzing the Bose-Hubbard model within the Gutzwiller mean-field approximation. We calculate the excitation spectra of the homogeneous Bose-Hubbard model at unit filling to determine the critical momenta for the Landau and dynamical instabilities. These two critical momenta are shown to approach each other when the on-site interaction increases towards the Mott transition point. In order to make a direct connection with realistic experiments, we next take into account a parabolic trapping potential and compute the real-time dynamics of dipole oscillations induced by suddenly displacing the trap center. We consider the following two cases: standard soft-core bosons, whose interparticle interactions include the on-site one only; and hard-core bosons with long-range dipole-dipole interactions. For both cases, we show that the dipole oscillation is significantly damped when the maximum local momentum exceeds a certain threshold, which quantitatively agrees with the critical momentum for the dynamical instability in the homogeneous system. In the case of dipolar hard-core bosons, the dynamical instability of dipole oscillations leads to the formation of checkerboard density waves in the superfluid phase near the boundary to the supersolid phase.
We study the Mott-insulator–superfluid transition of ultracold bosonic atoms in a two-dimensional square optical lattice in the presence of a synthetic magnetic field with p / q ( p and q being co-prime integers) flux quanta passing through each lattice plaquette. We show that on approach to the transition from the Mott side, the momentum distribution of the bosons exhibits q precursor peaks within the first magnetic Brillouin zone. We also provide an effective theory for the transition and show that it involves q interacting boson fields. We construct, from a mean-field analysis of this effective theory, the superfluid ground states near the transition and compute, for q =2, 3, both the gapped and the gapless collective modes of these states. We suggest experiments to test our theory.