Double commutator method for a two band Bose-Einstein condensate: superfluid density of a flat band superfluid

• URL: http://arxiv.org/abs/2503.23656v2
• Date: Tue, 01 Apr 2025 22:04:38 GMT
• Title: Double commutator method for a two band Bose-Einstein condensate: superfluid density of a flat band superfluid
• Authors: Yi-Cai Zhang,
• Abstract summary: We prove that the sum of the superfluid and normal densities is equal to the weight of the f-sum rule.<n>We investigate the superfluid density of a flat band Bose-Einstein condensate (BEC)<n>Our findings indicate that the superfluid density is directly proportional to the product of the square of the sound velocity and the compressibility.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: In this work, we propose a double commutator method for a general two-band bosonic superfluid. First and foremost, we prove that the sum of the superfluid and normal densities is equal to the weight of the f-sum rule. This weight can be easily determined by analyzing the ground state wave function. Once we have determined the excitation gap of the upper band, we can calculate the normal density by evaluating the average value of a double commutator between the velocity operator and the Hamiltonian. As an application of this method, we investigate the superfluid density of a flat band Bose-Einstein condensate (BEC). Using the Bogoliubov method, we calculate the sound velocity and excitation gap, which allows us to obtain the normal and superfluid densities explicitly. Our findings indicate that the superfluid density is directly proportional to the product of the square of the sound velocity and the compressibility. Furthermore, the existence of a non-vanishing superfluid density depends on the form of the interaction. For example, in the case of U(2) invariant interactions, the superfluid density is zero. Additionally, we have observed that for small interactions, the superfluid density is directly proportional to the product of the interaction parameter and the quantum metric. The double commutator method indicates that the correction of the excitation gap by interactions is the origin of the non-vanishing superfluid density of a flat band BEC. Up to the linear order of the interaction parameters, all the results for the excitation gap, the normal and superfluid densities in a flat band BEC can also be obtained through a simple perturbation theory. Our work provides another unique perspective on the superfluid behavior of a flat band BEC.

Related papers

• Constrained many-body phases in a $\mathbb{Z}_2$-Higgs lattice gauge theory [39.58317527488534]
  We study a one-dimensional $mathbbZ$ lattice gauge theory coupled to soft-core bosonic matter at unit filling.<n>Through a combination of analytical perturbative approaches, we uncover a rich phase diagram driven by gauge-field-mediated resonant pair hopping.<n>The presence of a bunching state with large number fluctuations motivates experimental realizations in hybrid boson-qubit quantum simulation platforms.
  arXiv  Detail & Related papers  (2025-03-05T19:00:07Z)
• Dipole-dipole interactions mediated by a photonic flat band [44.99833362998488]
  We study the photon-dipole interactions between emitters dispersively coupled to the photonic analogue of a flat band (FB) We show that the strength of such photon-mediated interactions decays exponentially with distance with a characteristic localization length. We find that the localization length grows with the overlap between CLSs according to an analytically-derived universal scaling law valid for a large class of FBs both in 1D and 2D.
  arXiv  Detail & Related papers  (2024-05-30T18:00:05Z)
• Quantum droplets in two-dimensional Bose mixtures at finite temperature [0.0]
  We investigate the formation of quantum droplets at finite temperature in attractive Bose mixtures. By means of exact path-integral Monte Carlo methods we determine the equilibrium density of the gas and the liquid. We find that the superfluid response develops suddenly, following the density jump from the gas to the liquid state.
  arXiv  Detail & Related papers  (2024-05-15T14:20:31Z)
• Nonlocal order parameter of pair superfluids [0.196629787330046]
  We show that pair superfluids can be rigorously defined in terms of a nonlocal order parameter, named odd parity. Our results shed new light on the role of correlated density fluctuations in pair superfluids.
  arXiv  Detail & Related papers  (2024-04-24T16:45:43Z)
• Effect of trap imperfections on the density of a quasi-two-dimensional uniform dipolar quantum Bose gas [0.0]
  We investigate the impact of weak static perturbations of a flat potential on the density of a quasi-two-dimensional dipolar Bose gas. We first study cosinusoidal potential perturbations at a given spatial frequency. We then study potential perturbations characterized by a static white-noise spectrum over a given momentum range.
  arXiv  Detail & Related papers  (2024-03-07T18:15:41Z)
• Probing pair correlations in Fermi gases with Ramsey-Bragg interferometry [41.94295877935867]
  We propose an interferometric method to probe pair correlations in a gas of spin-1/2 fermions. The method consists of a Ramsey sequence where both spin states of the Fermi gas are set in a superposition of a state at rest and a state with a large recoil velocity. The off-diagonal long-range order is directly reflected in the behavior of the interferometric signal for long interrogation times.
  arXiv  Detail & Related papers  (2023-12-21T15:46:29Z)
• Ground-state Properties and Bogoliubov Modes of a Harmonically Trapped One-Dimensional Quantum Droplet [4.864202986612716]
  We study the stationary and excitation properties of a one-dimensional quantum droplet in a Bose mixture trapped in a harmonic potential. We explicitly show how the spectrum of the excitation is split into discrete modes, and finally taken over by the harmonic trap.
  arXiv  Detail & Related papers  (2023-09-11T05:39:53Z)
• The density of a one-dimensional Bose gas far from an impurity [55.2480439325792]
  We consider an impurity in a weakly-interacting Bose gas and calculate the density profile of the Bose gas. The effect of quantum fluctuations drastically changes this behavior, leading to a power law decay of the density deviation from the mean density. The obtained results are exact in the impurity coupling strength and account for the leading order in the interaction between the particles of the Bose gas.
  arXiv  Detail & Related papers  (2023-08-29T08:56:24Z)
• Fragmented superconductivity in the Hubbard model as solitons in Ginzburg-Landau theory [39.58317527488534]
  Superconductivity and charge density waves are observed in close vicinity in strongly correlated materials. We investigate the nature of such an intertwined state of matter stabilized in the phase diagram of the elementary $t$-$tprime$-$U$ Hubbard model. We provide conclusive evidence that the macroscopic wave functions of the superconducting fragments are well-described by soliton solutions of a Ginzburg-Landau equation.
  arXiv  Detail & Related papers  (2023-07-21T18:00:07Z)
• Attractive Solution of Binary Bose Mixtures: Liquid-Vapor Coexistence and Critical Point [0.0]
  We study the thermodynamic behavior of attractive binary Bose mixtures using exact path-integral Monte-Carlo methods. We calculate the isothermal curves in the pressure vs density plane for different values of the attraction strength. We also point out that the density discontinuity at the transition could be observed in experiments of mixtures in traps.
  arXiv  Detail & Related papers  (2023-04-24T18:00:00Z)
• Observation of anisotropic superfluid density in an artificial crystal [0.0]
  We investigate the anisotropic speed of sound of an atomic superfluid in a 1D optical lattice. Because the speed of sound derives from the SF density, this implies that the SF density is itself anisotropic.
  arXiv  Detail & Related papers  (2023-01-03T17:55:32Z)
• In-Gap Band Formation in a Periodically Driven Charge Density Wave Insulator [68.8204255655161]
  Periodically driven quantum many-body systems host unconventional behavior not realized at equilibrium. We investigate such a setup for strongly interacting spinless fermions on a chain, which at zero temperature and strong interactions form a charge density wave insulator.
  arXiv  Detail & Related papers  (2022-05-19T13:28:47Z)
• Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity [62.997667081978825]
  We study the effect of the boundary on a system of weakly interacting bosons in one dimension. The quantum contribution to the boson density gives rise to small corrections of the bound state energy levels.
  arXiv  Detail & Related papers  (2020-07-21T13:12:33Z)
• Density Deconvolution with Normalizing Flows [26.395910367497592]
  We exploit the superior density estimation performance of normalizing flows and allow for arbitrary noise distributions. Experiments on real data demonstrate that flows can already out-perform Gaussian mixtures for density deconvolution.
  arXiv  Detail & Related papers  (2020-06-16T18:00:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.