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Physical review. B./Physical review. B

Pair superfluidity in generalized Bose-Hubbard models

T. A. Zaleski, T. K. Kopeć

Published Apr 15, 2025• 0 citations
Publisher

Abstract

We investigate pair superfluidity in a generalized Bose-Hubbard model, extending the framework to include pair hopping and direct on-site pair interactions. Our study reveals unique features of the pair superfluid phase, such as reentrant behavior and pockets of the normal state within the superfluid region---phenomena absent in single-particle superfluid models. Through compressibility analysis, we identify Mott insulating features at zero temperature and a complex interplay between temperature, chemical potential, and pair hopping. We highlight the importance of the occupation basis size in accurately modeling pair-superfluid dynamics, demonstrating that excessive truncation leads to unphysical artifacts. Additionally, we present phase diagrams contrasting pair and single-particle superfluidity, showing the distinct nature of their respective transitions and phase boundaries. Our findings provide theoretical insights relevant to experimental platforms, such as ultracold atomic gases and Josephson junction systems, and utilize Floquet engineering as a justification for achieving and controlling pair-hopping dynamics. This paper enhances our understanding of pair superfluidity and paves the way for further exploration of complex quantum many-body systems.

DOI
10.1103/physrevb.111.134510

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We investigate pair superfluidity in a generalized Bose-Hubbard model, extending the framework to include pair hopping and direct on-site pair interactions. Our study reveals unique features of the pair superfluid phase, such as reentrant behavior and pockets of the normal state within the superfluid region---phenomena absent in single-particle superfluid models. Through compressibility analysis, we identify Mott insulating features at zero temperature and a complex interplay between temperature, chemical potential, and pair hopping. We highlight the importance of the occupation basis size in accurately modeling pair-superfluid dynamics, demonstrating that excessive truncation leads to unphysical artifacts. Additionally, we present phase diagrams contrasting pair and single-particle superfluidity, showing the distinct nature of their respective transitions and phase boundaries. Our findings provide theoretical insights relevant to experimental platforms, such as ultracold atomic gases and Josephson junction systems, and utilize Floquet engineering as a justification for achieving and controlling pair-hopping dynamics. This paper enhances our understanding of pair superfluidity and paves the way for further exploration of complex quantum many-body systems.
We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.
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.
We investigate the ground-state and finite-temperature phase diagrams of the Bose-Hubbard model on a honeycomb superlattice. The interplay between the superlattice potential depth $\mathrm{\ensuremath{\Delta}}/t$ and the on-site interaction U/tU/tU/t gives rise to three distinct quantum phases at zero temperature: a superfluid phase, a Mott insulator I phase with unit filling on each site, and a Mott insulator II phase characterized by density imbalance---double occupancy on one sublattice and vacancy on the other at unit filling. The SF-MI transitions are found to be continuous, consistent with second-order quantum phase transitions. We further extend our analysis to finite temperatures within the superfluid regime. Our work highlights how a honeycomb superlattice geometry enables access to interaction- and lattice-modulation-driven quantum phases, including a density-imbalanced Mott insulator and a robust superfluid regime, offering concrete theoretical predictions for cold-atom experiments.
To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into ddd-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase transition from paired superfluid (superfluidity of composite bosons, i.e., Bose-Bose pairs) to Mott insulator and again to a paired superfluid in all one, two, and three dimensions, when the interspecies interaction is sufficiently large and attractive. We hope that some of our results could be tested with ultracold atomic systems.
We investigate the properties of the superfluid phase in the three-dimensional disordered Bose-Hubbard model using quantum Monte Carlo simulations. The phase diagram is generated using Gaussian disorder on the on-site potential. Comparisons with box and speckle disorder show qualitative similarities leading to the reentrant behavior of the superfluid. Quantitative differences that arise are controlled by the specific shape of the disorder. Statistics pertaining to disorder distributions are studied for a range of interaction strengths and system sizes, where strong finite-size effects are observed. Despite this, both the superfluid fraction and compressibility remain self-averaging throughout the superfluid phase. Close to the superfluid--Bose-glass phase boundary, finite-size effects dominate but still suggest that self-averaging holds. Our results are pertinent to experiments with ultracold atomic gases where a systematic disorder averaging procedure is typically not possible.
We study the effects of quantum fluctuations in the two-component Bose-Hubbard model generalizing to mixtures the quantum Gutzwiller approach introduced recently in [Phys. Rev. Research 2, 033276 (2020)]. As a basis for our study, we analyze the mean-field ground-state phase diagram and spectrum of elementary excitations, with particular emphasis on the quantum phase transitions of the model. Within the quantum critical regimes, we address both the superfluid transport properties and the linear response dynamics to density and spin probes of direct experimental relevance. Crucially, we find that quantum fluctuations have a dramatic effect on the drag between the superfluid species of the system, particularly in the vicinity of the paired and antipaired phases absent in the usual one-component Bose-Hubbard model. Additionally, we analyse the contributions of quantum corrections to the one-body coherence and density/spin fluctuations from the perspective of the collective modes of the system, providing results for the few-body correlations in all the regimes of the phase diagram.