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

arXiv:1108.3013 · New Journal of Physics

Multi-orbital and density-induced tunneling of bosons in optical lattices

Dirk-Sören Lühmann, Ole Jürgensen, K. Sengstock

Published Mar 13, 2012• 85 citations
arXivHTMLPDF

Abstract

We show that multi-orbital and density-induced tunneling have a significant impact on the phase diagram of bosonic atoms in optical lattices. Off-site interactions lead to density-induced hopping, the so-called bond-charge interactions, which can be identified with an effective tunneling potential and can reach the same order of magnitude as conventional tunneling. In addition, interaction-induced higher-band processes also give rise to strongly modified tunneling, on-site and bond-charge interactions. We derive an extended occupation-dependent Hubbard model with multi-orbitally renormalized processes and compute the corresponding phase diagram. It substantially deviates from the single-band Bose–Hubbard model and predicts strong changes of the superfluid-to-Mott-insulator transition. In general, the presented beyond-Hubbard physics plays an essential role in bosonic lattice systems and has an observable influence on experiments with tunable interactions.

DOI
10.1088/1367-2630/14/3/033021

Related papers

Density-induced processes in quantum gas mixtures in optical lattices

Ole Jürgensen, K. Sengstock, Dirk-Sören Lühmann

We show that off-site processes and multiorbital physics have a crucial impact on the phase diagram of quantum gas mixtures in optical lattices. In particular, we discuss Bose-Fermi mixtures where the intra- and interspecies interactions induce competing density-induced hopping processes, the so-called bond-charge interactions. Furthermore, higher bands strongly influence tunneling and on-site interactions. We apply a multiorbital interaction-induced dressing of the lowest band, which leads to renormalized hopping processes. These corrections give rise to an extended Hubbard model with intrinsically occupation-dependent parameters. The resulting decrease of the tunneling competes with a decrease of the total on-site interaction energy, both affecting the critical lattice depth of the superfluid to Mott-insulator transition. In contrast to the standard Bose-Fermi Hubbard model, we predict a large shift of the transition to shallower lattice depths with increasing Bose-Fermi attraction. The applied theoretical model allows an accurate prediction of the modified tunneling amplitudes and the critical lattice depth, both being recently observed experimentally.

arXiv:1207.3963•Physical Review A•Oct 22, 2012•27 citations

Effective multibody-induced tunneling and interactions in the Bose-Hubbard model of the lowest dressed band of an optical lattice

Ulf Bissbort, F. Deuretzbacher, Walter Hofstetter

We construct the effective lowest-band Bose-Hubbard model incorporating interaction-induced on-site correlations. The model is based on ladder operators for local correlated states, which deviate from the usual Wannier creation and annihilation, allowing for a systematic construction of the most appropriate single-band low-energy description in the form of the extended Bose-Hubbard model. A formulation of this model in terms of ladder operators not only naturally contains the previously found effective multibody interactions, but also contains multibody-induced single-particle tunneling, pair tunneling, and nearest-neighbor interaction processes of higher orders. An alternative description of the same model can be formulated in terms of occupation-dependent Bose-Hubbard parameters. These multiparticle effects can be enhanced using Feshbach resonances, leading to corrections which are well within experimental reach and of significance to the phase diagram of ultracold bosonic atoms in an optical lattice. We analyze the energy-reduction mechanism of interacting atoms on a local lattice site and show that this cannot be explained only by a spatial broadening of Wannier orbitals on a single-particle level, which neglects correlations.

arXiv:1108.6047•Physical Review A•Aug 15, 2012•41 citations

Density-dependent tunneling in the extended Bose–Hubbard model

Michał Maik, Philipp Hauke, Omjyoti Dutta +2 more

Recently, it has become apparent that when the interactions between polar molecules in optical lattices become strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two-dimensional extended Bose–Hubbard model. Using quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V , we show that the ground-state phase diagrams differ significantly from those expected from the standard extended Bose–Hubbard model.

arXiv:1306.5608•New Journal of Physics•Nov 20, 2013•33 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

Three-body on-site interactions in ultracold bosonic atoms in optical lattices and superlattices

Manpreet Singh, Arya Dhar, Tapan Mishra +2 more

The Mott-insulator--superfluid transition for ultracold bosonic atoms in an optical lattice has been extensively studied in the framework of the Bose-Hubbard model with two-body on-site interactions. In this paper, we analyze the additional effect of the three-body on-site interactions on this phase transition in an optical lattice and the transitions between the various phases that arise in an optical superlattice. Using the mean-field theory and the density matrix renormalization group method, we find the phase diagrams depicting the relationships between various physical quantities in an optical lattice and superlattice. We also propose a possible experimental signature to observe the on-site three-body interactions.

arXiv:1203.1412•Physical Review A•May 21, 2012•38 citations

Bond order via cavity-mediated interactions

Titas Chanda, Rebecca Kraus, Jakub Zakrzewski +1 more

We numerically study the phase diagram of bosons tightly trapped in the lowest band of an optical lattice and dispersively coupled to a single-mode cavity field. The dynamics is encompassed by an extended Bose-Hubbard model. Here, the cavity-mediated interactions are described by a two-body potential term with a global range and by a correlated tunneling term where the hopping amplitude depends on a global observable. We determine the ground-state properties in one dimension by means of the density matrix renormalization group algorithm, focusing on the effects due to the correlated tunneling. The latter is responsible for the onset of bond orders, manifesting in one insulating and two gapless bond-ordered phases. We discuss the resulting phases for different geometries that correspond to different relative strengths of the correlated tunneling coefficient. We finally analyze the scaling of the entanglement entropy in the gapless bond-ordered phases that appear entirely due to global interactions and determine the corresponding central charges.

arXiv:2201.05466•Physical review. B./Physical review. B•Aug 22, 2022•15 citations
We show that multi-orbital and density-induced tunneling have a significant impact on the phase diagram of bosonic atoms in optical lattices. Off-site interactions lead to density-induced hopping, the so-called bond-charge interactions, which can be identified with an effective tunneling potential and can reach the same order of magnitude as conventional tunneling. In addition, interaction-induced higher-band processes also give rise to strongly modified tunneling, on-site and bond-charge interactions. We derive an extended occupation-dependent Hubbard model with multi-orbitally renormalized processes and compute the corresponding phase diagram. It substantially deviates from the single-band Bose–Hubbard model and predicts strong changes of the superfluid-to-Mott-insulator transition. In general, the presented beyond-Hubbard physics plays an essential role in bosonic lattice systems and has an observable influence on experiments with tunable interactions.
We show that off-site processes and multiorbital physics have a crucial impact on the phase diagram of quantum gas mixtures in optical lattices. In particular, we discuss Bose-Fermi mixtures where the intra- and interspecies interactions induce competing density-induced hopping processes, the so-called bond-charge interactions. Furthermore, higher bands strongly influence tunneling and on-site interactions. We apply a multiorbital interaction-induced dressing of the lowest band, which leads to renormalized hopping processes. These corrections give rise to an extended Hubbard model with intrinsically occupation-dependent parameters. The resulting decrease of the tunneling competes with a decrease of the total on-site interaction energy, both affecting the critical lattice depth of the superfluid to Mott-insulator transition. In contrast to the standard Bose-Fermi Hubbard model, we predict a large shift of the transition to shallower lattice depths with increasing Bose-Fermi attraction. The applied theoretical model allows an accurate prediction of the modified tunneling amplitudes and the critical lattice depth, both being recently observed experimentally.
We construct the effective lowest-band Bose-Hubbard model incorporating interaction-induced on-site correlations. The model is based on ladder operators for local correlated states, which deviate from the usual Wannier creation and annihilation, allowing for a systematic construction of the most appropriate single-band low-energy description in the form of the extended Bose-Hubbard model. A formulation of this model in terms of ladder operators not only naturally contains the previously found effective multibody interactions, but also contains multibody-induced single-particle tunneling, pair tunneling, and nearest-neighbor interaction processes of higher orders. An alternative description of the same model can be formulated in terms of occupation-dependent Bose-Hubbard parameters. These multiparticle effects can be enhanced using Feshbach resonances, leading to corrections which are well within experimental reach and of significance to the phase diagram of ultracold bosonic atoms in an optical lattice. We analyze the energy-reduction mechanism of interacting atoms on a local lattice site and show that this cannot be explained only by a spatial broadening of Wannier orbitals on a single-particle level, which neglects correlations.
Recently, it has become apparent that when the interactions between polar molecules in optical lattices become strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two-dimensional extended Bose–Hubbard model. Using quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V , we show that the ground-state phase diagrams differ significantly from those expected from the standard extended Bose–Hubbard model.
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 Mott-insulator--superfluid transition for ultracold bosonic atoms in an optical lattice has been extensively studied in the framework of the Bose-Hubbard model with two-body on-site interactions. In this paper, we analyze the additional effect of the three-body on-site interactions on this phase transition in an optical lattice and the transitions between the various phases that arise in an optical superlattice. Using the mean-field theory and the density matrix renormalization group method, we find the phase diagrams depicting the relationships between various physical quantities in an optical lattice and superlattice. We also propose a possible experimental signature to observe the on-site three-body interactions.
We numerically study the phase diagram of bosons tightly trapped in the lowest band of an optical lattice and dispersively coupled to a single-mode cavity field. The dynamics is encompassed by an extended Bose-Hubbard model. Here, the cavity-mediated interactions are described by a two-body potential term with a global range and by a correlated tunneling term where the hopping amplitude depends on a global observable. We determine the ground-state properties in one dimension by means of the density matrix renormalization group algorithm, focusing on the effects due to the correlated tunneling. The latter is responsible for the onset of bond orders, manifesting in one insulating and two gapless bond-ordered phases. We discuss the resulting phases for different geometries that correspond to different relative strengths of the correlated tunneling coefficient. We finally analyze the scaling of the entanglement entropy in the gapless bond-ordered phases that appear entirely due to global interactions and determine the corresponding central charges.