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arXiv:2303.06894 · Photonics

Axial Collective Mode of a Dipolar Quantum Droplet

P. B. Blakie

Published Apr 1, 2023• 4 citations
arXivHTMLPDF

Abstract

In this work, we investigate the ground state properties and collective excitations of a dipolar Bose–Einstein condensate that self-binds into a quantum droplet, stabilized by quantum fluctuations. We demonstrate that a sum rule approach can accurately determine the frequency of the low energy axial excitation, using properties of the droplet obtained from the ground state solutions. This excitation corresponds to an oscillation in the length of the filament-shaped droplet. Additionally, we evaluate the static polarizabilities, which quantify change in the droplet dimensions in response to a change in harmonic confinement.

DOI
10.3390/photonics10040393

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In this work, we investigate the ground state properties and collective excitations of a dipolar Bose–Einstein condensate that self-binds into a quantum droplet, stabilized by quantum fluctuations. We demonstrate that a sum rule approach can accurately determine the frequency of the low energy axial excitation, using properties of the droplet obtained from the ground state solutions. This excitation corresponds to an oscillation in the length of the filament-shaped droplet. Additionally, we evaluate the static polarizabilities, which quantify change in the droplet dimensions in response to a change in harmonic confinement.
We calculate the collective excitations of a dipolar Bose-Einstein condensate in the regime where it self-binds into droplets stabilized by quantum fluctuations. We show that the filament-shaped droplets act as a quasi-one-dimensional waveguide along which low-angular-momentum phonons propagate. The evaporation (unbinding) threshold occurring as the atom number N is reduced to the critical value N_{c} is associated with a monopolelike excitation going soft as ε_{0}∼(N-N_{c})^{1/4}. Considering the system in the presence of a trapping potential, we quantify the crossover from a trap-bound condensate to a self-bound droplet.
We theoretically investigate the ground-state properties and breathing-mode collective excitations of three-dimensional dipolar Bose gases in anisotropic harmonic traps incorporating quantum fluctuations. Combining a Gaussian variational ansatz with a non-perturbative sum-rule analysis, we derive explicit analytical expressions for both axial and radial breathing-mode frequencies, which are validated by numerical solutions of the time-dependent extended Gross-Pitaevskii equation. Our theoretical predictions show excellent agreement with existing experimental data for 166^{166}166Er and 162^{162}162Dy gases. By constructing comprehensive phase diagrams across the parameter space of the sss-wave scattering length, atom number, and trap aspect ratio, we reveal both discontinuous first-order phase transitions and smooth crossovers between the dilute Bose-Einstein condensate and dense quantum droplet phases. We confirm that the enhanced incompressibility induced by quantum fluctuations significantly elevates the breathing-mode frequencies in the droplet phase compared to conventional weakly interacting Bose gases. Furthermore, the system undergoes a phase transition and a crossover over the scattering length under the quasi-two-dimensional and quasi-one-dimensional confinements, characterized by discontinuous jumps and continuous crossovers in peak density and atomic cloud sizes, respectively. Our work offers a rigorous and highly accurate framework to characterize collective excitations in dipolar quantum gases, providing quantitative insights for forthcoming ultracold atom experiments in lanthanide atoms and polar molecules.
We theoretically consider the properties of a dipolar Bose-Einstein condensate with a vortex. Our theory includes the influence of the leading order quantum fluctuation corrections which allows the condensate to stabilize into a droplet state in the regime of dominant dipole interactions. We develop numerical techniques to accurately and efficiently calculate the stationary vortex states and the quasi-particle excitations. These methods are carefully benchmarked where possible. We make a brief study of self-bound vortex droplets, considering their basic properties, and presenting a phase diagram for where they exist. We also compare our calculations to results which appeared from another group during our research. We show that their results suffer from serious numerical issues and are unreliable. We focus on studying the properties of a vortex line in an elongated dipolar Bose-Einstein condensate confined by a prolate trap. Increasing the strength of the dipole-dipole interactions relative to the short ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response, and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.
We consider quantum droplets in dipolar Bose-Einstein condensates embedded in optical lattices within the framework of Gross-Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole-dipole interaction provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the dipole-dipole interaction increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of dipole-dipole interaction. In presence of optical lattices, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
Abstract We consider quantum droplets in dipolar Bose–Einstein condensates embedded in optical lattices (OLs) within the framework of Gross–Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole–dipole interaction (DDI) provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the DDI increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of DDI. In presence of OLs, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.