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

Acta Physica Polonica A

Optical Conductivity of Ultra-Cold Bosons in Optical Lattices

B. Grygiel, K. Patucha, T. A. Zaleski

Published Aug 1, 2016• 1 citation
Publisher

Abstract

We study ultra-cold bosonic systems in optical lattice using quantum rotor approach to calculate the currentcurrent correlations, which provides the information about conductivity of the system.The method allows us to go beyond mean-field approximation and track the behavior of the real part of the conductivity along the phase transition between the Mott insulator and superfluid state for various geometries of the lattice.In the phaseordered state at zero temperature, a discrete ingredient appears resulting from the long-range coherence in the system.

DOI
10.12693/aphyspola.130.633

Related papers

Momentum-resolved conductivity of strongly interacting bosons in an optical lattice

B. Grygiel, T. A. Zaleski

Motivated by the recent advancements in experimental techniques in the cold atomic systems, we study the dependence of the conductivity on momentum in a system of strongly interacting bosons in an optical lattice. By employing the quantum rotor approach to the Bose-Hubbard model we calculate the current-current correlation function and subsequently obtain the analytic formula for the momentum-dependent longitudinal conductivity. We analyze the behavior of the conductivity for the square and cubic lattices in both, the superfluid and Mott insulator phases. As a consequence of the particle-hole symmetry, the conductivity for a uniformly filled lattice in the superfluid phase exhibits a linear dependence for a surprisingly wide range of momenta around $\mathbf{k}=0$. This allows us to predict the value of the group velocity of the particle excitations. We also consider the impact of finite temperature and discover that it leads to an additional conductivity channel, which is aligned along the direction of the probe field and located within the energy gap.

Physical review. B./Physical review. B•Sep 27, 2021•1 citation

Optical weight transfer in excitation spectra of ultra-cold bosons in two- and three-dimensional optical lattices

T. A. Zaleski

We investigate the excitations of strongly interacting bosons confined in an optical lattice. Using the combined Bogoliubov method and the quantum rotor approach, we map the Hamiltonian of strongly interacting bosons onto U(1) phase action. This allows us to calculate the density of states for various geometries of optical lattices and its dependence on the presence of the superfluid phase. We observe that the superfluidity is manifested by a sharp coherence peak resulting from long-range order, while the excitation spectrum of the Mott insulator contains a gap.

Journal of Physics B Atomic Molecular and Optical Physics•Jul 4, 2012•7 citations

Hall Conductivity of Strongly Interacting Bosons in Optical Lattice

K. Patucha, B. Grygiel, T. A. Zaleski

We study the Hall conductivity of ultra-cold bosonic atoms in optical lattice described by the Bose-Hubbard model.We use the quantum rotor approximation, which allows to describe lattices with non-zero Chern numbers.As examples of such systems we consider square lattice in a synthetic magnetic field as well as the Haldane model.We derive formula for the Hall conductivity, which strongly resembles the famous TKNN formula.We investigate the behavior of conductivity depending on temperature and model parameters.It appears that bosonic systems substantially differ from the fermionic ones, e.g. the presence of non-zero Hall conductivity is not directly related to non-zero value of the Chern number.

Acta Physica Polonica A•Jan 1, 2019•0 citations

Ultra-Cold Bosons in Optical Lattice: Time-of-Flight Imaging of Atom-Atom Correlations

T. A. Zaleski, T. K. Kopeć

In the present paper, we investigate a system of strongly interacting bosons conned in two-dimensional optical lattice.We propose a combination of the Bogoliubov method with the quantum rotor approach and determine the spatial atomatom correlations.This allows us to calculate time-of-ight absorption images, which exhibit all the characteristic features present in experimental results, namely transition from superuid peaks to Mott insulating blob.

Acta Physica Polonica A•Apr 1, 2012•0 citations

Finite-temperature quantum rotor approach for ultracold bosons in optical lattices

M. Rodríguez Martín, T. A. Zaleski

Interacting bosons in optical lattices directly expose quantum phases in a clean, highly controllable environment. This requires engineering systems with very low entropies, but the resulting temperature--interaction ratios $T/U$ of present experiments remain well above the domain where zero-temperature theories are expected to be reliable. The quantum-rotor approach (QRA), while analytically powerful and extremely flexible, inherits ground-state phase correlations and therefore breaks down once thermal winding of the phase field becomes significant. Here we construct a finite-temperature extension of QRA by (i) performing resummation of winding-number contributions for temperatures ${k}_{B}T/U\ensuremath{\lesssim}0.2$ and (ii) developing an auxiliary-variable expansion that remains accurate toward the classical limit. The resulting closed expression for the phase correlator is inserted into the standard spherical-approximation QRA without sacrificing the method's flexibility with respect to lattice geometry and dimensionality. The approach reproduces the shrinkage of Mott lobes from $T=0$ up to ${k}_{B}T/U\ensuremath{\simeq}0.2$ in quantitative agreement with theoretical predictions and with in-situ imaging experiments. This finite-T QRA thus supplies an analytic, computationally light tool for strongly correlated lattice bosons and sets the stage for amplitude-fluctuation upgrades required at higher temperatures.

arXiv:2512.16364•Physical review. B./Physical review. B•Nov 18, 2025•0 citations

Quantum theory of cold bosonic atoms in optical lattices

Dagim Tilahun, R. A. Duine, Allan H. MacDonald

Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a Mott insulator as the lattice potential depth is increased. We describe an approximate theory of interacting bosons in optical lattices which provides a qualitative description of both superfluid and insulator states. The theory is based on a change of variables in which the boson coherent state amplitude is replaced by an effective potential which promotes phase coherence between different number states on each lattice site. It is illustrated here by applying it to uniform and fully frustrated lattice cases but is simple enough that it can be applied to spatially inhomogeneous lattice systems.

arXiv:1105.2084•Physical Review A•Sep 16, 2011•3 citations
We study ultra-cold bosonic systems in optical lattice using quantum rotor approach to calculate the currentcurrent correlations, which provides the information about conductivity of the system.The method allows us to go beyond mean-field approximation and track the behavior of the real part of the conductivity along the phase transition between the Mott insulator and superfluid state for various geometries of the lattice.In the phaseordered state at zero temperature, a discrete ingredient appears resulting from the long-range coherence in the system.
Motivated by the recent advancements in experimental techniques in the cold atomic systems, we study the dependence of the conductivity on momentum in a system of strongly interacting bosons in an optical lattice. By employing the quantum rotor approach to the Bose-Hubbard model we calculate the current-current correlation function and subsequently obtain the analytic formula for the momentum-dependent longitudinal conductivity. We analyze the behavior of the conductivity for the square and cubic lattices in both, the superfluid and Mott insulator phases. As a consequence of the particle-hole symmetry, the conductivity for a uniformly filled lattice in the superfluid phase exhibits a linear dependence for a surprisingly wide range of momenta around k=0\mathbf{k}=0k=0. This allows us to predict the value of the group velocity of the particle excitations. We also consider the impact of finite temperature and discover that it leads to an additional conductivity channel, which is aligned along the direction of the probe field and located within the energy gap.
We investigate the excitations of strongly interacting bosons confined in an optical lattice. Using the combined Bogoliubov method and the quantum rotor approach, we map the Hamiltonian of strongly interacting bosons onto U(1) phase action. This allows us to calculate the density of states for various geometries of optical lattices and its dependence on the presence of the superfluid phase. We observe that the superfluidity is manifested by a sharp coherence peak resulting from long-range order, while the excitation spectrum of the Mott insulator contains a gap.
We study the Hall conductivity of ultra-cold bosonic atoms in optical lattice described by the Bose-Hubbard model.We use the quantum rotor approximation, which allows to describe lattices with non-zero Chern numbers.As examples of such systems we consider square lattice in a synthetic magnetic field as well as the Haldane model.We derive formula for the Hall conductivity, which strongly resembles the famous TKNN formula.We investigate the behavior of conductivity depending on temperature and model parameters.It appears that bosonic systems substantially differ from the fermionic ones, e.g. the presence of non-zero Hall conductivity is not directly related to non-zero value of the Chern number.
Interacting bosons in optical lattices directly expose quantum phases in a clean, highly controllable environment. This requires engineering systems with very low entropies, but the resulting temperature--interaction ratios T/UT/UT/U of present experiments remain well above the domain where zero-temperature theories are expected to be reliable. The quantum-rotor approach (QRA), while analytically powerful and extremely flexible, inherits ground-state phase correlations and therefore breaks down once thermal winding of the phase field becomes significant. Here we construct a finite-temperature extension of QRA by (i) performing resummation of winding-number contributions for temperatures ${k}_{B}T/U\ensuremath{\lesssim}0.2$ and (ii) developing an auxiliary-variable expansion that remains accurate toward the classical limit. The resulting closed expression for the phase correlator is inserted into the standard spherical-approximation QRA without sacrificing the method's flexibility with respect to lattice geometry and dimensionality. The approach reproduces the shrinkage of Mott lobes from T=0T=0T=0 up to ${k}_{B}T/U\ensuremath{\simeq}0.2$ in quantitative agreement with theoretical predictions and with in-situ imaging experiments. This finite-T QRA thus supplies an analytic, computationally light tool for strongly correlated lattice bosons and sets the stage for amplitude-fluctuation upgrades required at higher temperatures.
Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a Mott insulator as the lattice potential depth is increased. We describe an approximate theory of interacting bosons in optical lattices which provides a qualitative description of both superfluid and insulator states. The theory is based on a change of variables in which the boson coherent state amplitude is replaced by an effective potential which promotes phase coherence between different number states on each lattice site. It is illustrated here by applying it to uniform and fully frustrated lattice cases but is simple enough that it can be applied to spatially inhomogeneous lattice systems.