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arXiv:2207.07711 · Physical Review A

Crossing the superfluid-supersolid transition of an elongated dipolar condensate

Aitor Alaña, Nicolò Antolini, Giulio Biagioni, I. L. Egusquiza, Michele Modugno

Published Oct 14, 2022• 9 citations
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Abstract

We provide a theoretical characterization of the dynamical crossing of the superfluid-supersolid phase transition for a dipolar condensate confined in an elongated trap, as observed in the recent experiment by Biagioni et al. [G. Biagioni, N. Antolini, A. Ala\~na, M. Modugno, A. Fioretti, C. Gabbanini, L. Tanzi, and G. Modugno, Phys. Rev. X 12, 021019 (2022)]. By means of the extended Gross-Pitaevskii theory, which includes the Lee-Huang-Yang quantum fluctuation correction, we first analyze the ground-state configurations of the system as a function of the interparticle scattering length, for both trap configurations employed in the experiment. Then, we discuss the effects of the ramp velocity, by which the scattering length is tuned across the transition, on the collective excitations of the system in both the superfluid and supersolid phases. We find that, when the transverse confinement is sufficiently strong and the transition has a smooth (continuous) character, the system essentially displays a (quasi) one-dimensional behavior, its excitation dynamics being dominated by the axial breathing modes. Instead, for shallower transverse trapping, when the transition becomes discontinuous, the collective excitations of the supersolid display a coupling with the transverse modes, signaling the onset of a dimensional crossover.

DOI
10.1103/physreva.106.043313

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We provide a theoretical characterization of the dynamical crossing of the superfluid-supersolid phase transition for a dipolar condensate confined in an elongated trap, as observed in the recent experiment by Biagioni et al. [G. Biagioni, N. Antolini, A. Ala~na, M. Modugno, A. Fioretti, C. Gabbanini, L. Tanzi, and G. Modugno, Phys. Rev. X 12, 021019 (2022)]. By means of the extended Gross-Pitaevskii theory, which includes the Lee-Huang-Yang quantum fluctuation correction, we first analyze the ground-state configurations of the system as a function of the interparticle scattering length, for both trap configurations employed in the experiment. Then, we discuss the effects of the ramp velocity, by which the scattering length is tuned across the transition, on the collective excitations of the system in both the superfluid and supersolid phases. We find that, when the transverse confinement is sufficiently strong and the transition has a smooth (continuous) character, the system essentially displays a (quasi) one-dimensional behavior, its excitation dynamics being dominated by the axial breathing modes. Instead, for shallower transverse trapping, when the transition becomes discontinuous, the collective excitations of the supersolid display a coupling with the transverse modes, signaling the onset of a dimensional crossover.
We characterize the role of roton instability in the formation of a supersolid state of an elongated dipolar condensate, following a quench of the contact interactions across the superfluid-supersolid transition, as observed in recent experiments. We perform dynamical simulations by means of the extended Gross-Pitaevskii equation including quantum corrections, for different final values of the $s\text{\ensuremath{-}}\mathrm{wave}$ scattering length. The corresponding excitation spectrum is computed using an effective one-dimensional description, which provides a reasonably accurate prediction for the growth rate of the most unstable mode observed in the simulations. To analyze the behavior of the system, we employ the inverse participation ratio, which conveniently characterizes the different degree of localization in the superfluid and supersolid phases. By means of a suitable effective ansatz for the density, we derive a simple yet effective expression for the formation time of the supersolid. This expression provides valuable insights regarding its scaling behavior with respect to the sss-wave scattering length.
Supersolids are a fundamental quantum phase of matter where the global phase and translational symmetries are spontaneously broken.The recently discovered supersolidity in quantum gases of strongly magnetic atoms gives the opportunity to explore in depth how superfluidity and crystalline order are mixed in this fascinating phase.The dipolar supersolid is usually created from a Bose-Einstein condensate, i.e., a standard superfluid, crossing a quantum phase transition that is related to the crystallization transitions of ordinary matter.In this work, we assess experimentally and theoretically the character of the superfluidsupersolid quantum phase transition.We find that one-row supersolids can have already two types of phase transitions, discontinuous and continuous, that are reminiscent of the first-and second-order transitions predicted in the thermodynamic limit in 2D and 1D, respectively.The dimensional crossover is peculiar to supersolids, is controlled via the transverse confinement and the atom number, and can be justified on the general ground of the Landau theory of phase transitions.The quasiadiabatic crossing of a continuous phase transition opens new directions of investigation for supersolids.
We theoretically investigate a supersolid structure taking the form of stacked, disk-shaped superfluid droplets connected via a dilute superfluid, in an antidipolar condensate. A phase diagram is determined for varying the particle number and scattering length, identifying the regions of a regular dipolar superfluid, supersolid stacks, and isolated stacked disk-shaped droplets in an experimentally realizable trapping potential. The collective Bogoliubov excitation spectrum across the superfluid-supersolid phase transition is studied, and the transition point is found to be associated with the breaking of the degeneracy of the two lowest-lying modes. The dynamical generation of the supersolid stacks is also investigated by ramping down the scattering length across the phase transition. Moreover, we have studied the impact of vortex-line penetration on the phase transition. We have found that the presence of a vortex line causes the supersolid region to move towards weaker contact interactions. Our detailed numerical simulations highlight that an antidipolar condensate can create such supersolid stacks within an experimentally reachable parameter regime.
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.
Abstract The properties of a supersolid state (SS) in quasi-one-dimensional dipolar Bose–Einstein condensate is studied, considering two possible mechanisms of realization—due to repulsive three-body atomic interactions and quantum fluctuations in the framework of the Lee–Huang–Yang theory. The role of both mechanisms in the formation of SS properties has been emphasized. The proposed theoretical model, based on minimization of the energy functional, allows evaluating the amplitude of the SS for an arbitrary set of parameters in the extended Gross–Pitaevskii equation (eGPE). To explore the dynamics of the SS first we numerically construct its ground state in different settings, including periodic boundary conditions, box-like trap and parabolic potential, then impose a perturbation. In oscillations of the perturbed supersolid we observe the key manifestation of SS, namely the free flow of the superfluid fraction through the crystalline component of the system. Two distinct oscillation frequencies of the supersolid associated with the superfluid fraction and crystalline components of the wave function are identified from numerical simulations of the eGPE.