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International Conference on Low Temperature Physics (LT)

Long Lifetime Supersolid of Two Component Dipolar BEC: Dynamics of Supersolid Formation

Shaoxiong Li, Hiroki Saito

Published May 22, 2023• 0 citations
Publisher

Abstract

Recently, experimental and theoretical studies have been actively conducted on the supersolid state of a Bose-Einstein condensate (BEC) with magnetic dipole-dipole interaction (DDI).However, most of these studies have employed a single-component BEC, whose stabilization relies on the beyondmean-field effect with high density, and thus its lifetime is restricted.In this work, we propose a supersolid state of a two-component dipolar BEC, in which a weaker DDI can form the supersolid structure, stabilizing the system without the beyond-mean-field effect.As a result, such a supersolid has a longer lifetime, which enables the observation of long-time dynamics.Here we numerically demonstrate the dynamics of periodic droplet-structure formation triggered by sudden or gradual change of a parameter.We find that the generated droplets have the phase coherence, confirming dynamical formation of supersolid.

DOI
10.7566/jpscp.38.011008

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Recently, experimental and theoretical studies have been actively conducted on the supersolid state of a Bose-Einstein condensate (BEC) with magnetic dipole-dipole interaction (DDI).However, most of these studies have employed a single-component BEC, whose stabilization relies on the beyondmean-field effect with high density, and thus its lifetime is restricted.In this work, we propose a supersolid state of a two-component dipolar BEC, in which a weaker DDI can form the supersolid structure, stabilizing the system without the beyond-mean-field effect.As a result, such a supersolid has a longer lifetime, which enables the observation of long-time dynamics.Here we numerically demonstrate the dynamics of periodic droplet-structure formation triggered by sudden or gradual change of a parameter.We find that the generated droplets have the phase coherence, confirming dynamical formation of supersolid.
Recent studies on supersolidity in a single-component Bose-Einstein condensate (BEC) have relied on the Lee-Huang-Yang (LHY) correction for stabilization of self-bound droplets, which, however, involves a high density inside the droplets, limiting the lifetime of the supersolid. Here we propose a two-component mixture of dipolar and nondipolar BECs, such as an $^{166}\mathrm{Er}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ mixture, to create and stabilize a supersolid without the LHY correction, which can suppress the atomic loss and may allow observation of the long-time dynamics of the supersolid. In such a system, supersolidity can be controlled by the difference in the trap centers between the two components.
We investigate the quench dynamics of quasi-one- and two-dimensional dipolar Bose-Einstein condensates of 164Dy^{164}\mathrm{Dy}164Dy atoms under the influence of a fast rotating magnetic field. The magnetic field thus controls both the magnitude and sign of the dipolar potential. We account for quantum fluctuations, critical to formation of exotic quantum droplet and supersolid phases in the extended Gross-Pitaevskii formalism, which includes the so-called Lee-Huang-Yang correction. An analytical variational ansatz allows us to obtain the phase diagrams of the superfluid and droplet phases. The crossover from the superfluid to the supersolid phase and to single and droplet arrays is probed with particle number and dipolar interaction. The dipolar strength is tuned by rotating the magnetic field with subsequent effects on phase boundaries. Following interaction quenches across the aforementioned phases, we monitor the dynamical formation of supersolid clusters or droplet lattices. We include losses due to three-body recombination over the crossover regime, where the three-body recombination rate coefficient scales with the fourth power of the scattering length (as)({a}_{s})(as​) or the dipole length (add)({a}_{dd})(add​). For fixed values of the dimensionless parameter, ${\ensuremath{\epsilon}}_{dd}={a}_{dd}/{a}_{s}$, tuning the dipolar anisotropy leads to an enhancement of the droplet lifetimes.
We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate.The theory reveals a ground state phase diagram with three distinct regimes-a regular Bose-Einstein condensate and incoherent and coherent arrays of quantum droplets.The coherent droplets are connected by a background condensate, which leads-in addition to the periodic density modulation-to a robust phase coherence throughout the whole system.We further theoretically demonstrate that we are able to dynamically approach the ground state in our experiment and that its lifetime is limited only by three-body losses.Experimentally we probe and confirm the signatures of the phase diagram by observing the in situ density modulation as well as the phase coherence using matter wave interference.
This habilitation thesis pertains to the theoretical and computational investigation of dilute dipolar Bose-Einstein condensates in the bulk, where atoms interact through both short-range and dipole-dipole interactions. Twelve papers are summarized that were published over the period from 2015 to 2024, with four based on theory-experiment collaborations, and the remaining eight papers being purely theoretical. The papers are grouped thematically into three chapters: the first focuses on quantum droplets, which are dilute liquids resulting from a balance between attractive mean-field interactions and beyond-mean-field quantum fluctuations; the second pertains to the exploration and realization of the long-sought supersolid phase of matter, which simultaneously exhibits properties of both a solid and a superuid; and the third addresses binary supersolids in two-component dipolar Bose-Einstein condensates, whose additional degrees of freedom offer the potential for novel physics and provide a pathway to realizing bulk supersolids.
We numerically study the many-body physics of molecular Bose-Einstein condensates with strong dipole-dipole interactions. We observe the formation of self-bound droplets, and explore phase diagrams that feature a variety of exotic supersolid states. In all of these cases, the large and tunable molecular dipole moments enable the study of unexplored regimes and phenomena, including liquidlike density saturation and universal stability scaling laws for droplets, as well as pattern formation and the limits of droplet supersolidity. We discuss a realistic experimental approach to realize both the required collisional stability of the molecular gases and the independent tunability of their contact and dipolar interaction strengths. Our work provides both a blueprint and a benchmark for near-future experiments with bulk molecular Bose-Einstein condensates.
Motivated by a recent experiment [L. Chomaz et al., Nat. Phys. 14, 442 (2018)], we perform numerical simulations of a dipolar Bose-Einstein condensate (BEC) in a tubular, periodic confinement at T=0T=0T=0 within density functional theory, where the beyond-mean-field correction to the ground-state energy is included in the local density approximation. We study the excitation spectrum of the system by solving the corresponding Bogoliubov--de Gennes equations. The calculated spectrum shows a roton minimum, and the roton gap decreases by reducing the effective scattering length. As the roton gap disappears, the system spontaneously develops a periodic linear structure formed by denser clusters of atomic dipoles immersed in a dilute superfluid background. This structure shows the hallmarks of a supersolid system, i.e., (i) a finite nonclassical translational inertia along the tube axis and (ii) the appearance of two gapless modes, i.e., a phonon mode associated with density fluctuations and resulting from the translational discrete symmetry of the system, and a Nambu-Goldstone gapless mode corresponding to phase fluctuations, resulting from the spontaneous breaking of the gauge symmetry. A further decrease in the scattering length eventually leads to the formation of a periodic linear array of self-bound droplets.