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arXiv:2309.17098 · Physical Review A

Supersolid-formation-time shortcut and excitation reduction by manipulating the dynamical instability

Aitor Alaña

Published Feb 6, 2024• 4 citations
arXivHTMLPDF

Abstract

Supersolids are a phase of matter exhibiting both superfluidity and a periodic density modulation typical of crystals. When formed via quantum phase transition from a superfluid, they require a formation time before their density pattern develops. In this paper protocols and schemes are proposed for experimental applications, building on earlier descriptions of the role roton instability plays in the supersolid formation process and the associated formation time. In particular, two protocols are put forward to shorten the formation time and lessen the excitation produced when crossing the phase transition. As a case study of the impact that mechanical fluctuations (noise) can have on the phase transition when conducting an experiment, the impact of a mechanical kick before the transition is also investigated. The proposed schemes achieve a shortening of the formation process for comparable levels of excitation, in the framework of extended Gross-Pitaevskii theory.

DOI
10.1103/physreva.109.023308

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Supersolids are a phase of matter exhibiting both superfluidity and a periodic density modulation typical of crystals. When formed via quantum phase transition from a superfluid, they require a formation time before their density pattern develops. In this paper protocols and schemes are proposed for experimental applications, building on earlier descriptions of the role roton instability plays in the supersolid formation process and the associated formation time. In particular, two protocols are put forward to shorten the formation time and lessen the excitation produced when crossing the phase transition. As a case study of the impact that mechanical fluctuations (noise) can have on the phase transition when conducting an experiment, the impact of a mechanical kick before the transition is also investigated. The proposed schemes achieve a shortening of the formation process for comparable levels of excitation, in the framework of extended Gross-Pitaevskii theory.
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.
Dipolar condensates have recently been coaxed to form the long-sought supersolid phase. While one-dimensional supersolids may be prepared by triggering a roton instability, we find that such a procedure in two dimensions (2D) leads to a loss of both global phase coherence and crystalline order. Unlike in 1D, the 2D roton modes have little in common with the supersolid configuration. We develop a finite-temperature stochastic Gross-Pitaevskii theory that includes beyond-mean-field effects to explore the formation process in 2D and find that evaporative cooling directly into the supersolid phase-hence bypassing the first-order roton instability-can produce a robust supersolid in a circular trap. Importantly, the resulting supersolid is stable at the final nonzero temperature. We then experimentally produce a 2D supersolid in a near-circular trap through such an evaporative procedure. Our work provides insight into the process of supersolid formation in 2D and defines a realistic path to the formation of large two-dimensional supersolid arrays.
Dipolar condensates have recently been coaxed into supersolid phases supporting both superfluid and crystal excitations. While one-dimensional (1D) supersolids may be prepared via a roton instability, we find that such a procedure in two dimensions (2D) leads to greater heating. We go on to show that 2D roton modes have little in common with the supersolid configuration: instead, unstable centralized rotons trigger a process of nonlinear crystal growth. By evaporatively cooling directly into the supersolid phase--hence bypassing the first-order roton instability--we experimentally produce a 2D supersolid in a near-circular trap. We develop a stochastic Gross-Pitaevskii theory that includes beyond-meanfield effects to further explore the formation process. We calculate the static structure factor for a 2D supersolid, and compare to a 1D array. These results provide insight into the process of supersolid formation in 2D, and define a realistic path to the formation of large two-dimensional supersolid arrays.
Phase transitions share the universal feature of enhanced fluctuations near the transition point.Here, we show that density fluctuations reveal how a Bose-Einstein condensate of dipolar atoms spontaneously breaks its translation symmetry and enters the supersolid state of matter-a phase that combines superfluidity with crystalline order.We report on the first direct in situ measurement of density fluctuations across the superfluid-supersolid phase transition.This measurement allows us to introduce a general and straightforward way to extract the static structure factor, estimate the spectrum of elementary excitations, and image the dominant fluctuation patterns.We observe a strong response in the static structure factor and infer a distinct roton minimum in the dispersion relation.Furthermore, we show that the characteristic fluctuations correspond to elementary excitations such as the roton modes, which are theoretically predicted to be dominant at the quantum critical point, and that the supersolid state supports both superfluid as well as crystal phonons.
We consider protocols for control of dipolar Bose-Einstein condensates where the critical role is played by the long-range anisotropic interatomic magnetic dipole-dipole interaction. The phase diagram of such a condensate has been explored theoretically and experimentally with certain values of the interatomic scattering length corresponding to superfluid and supersolid phases, where supersolidity appears as a modulation in the ground state density. Preparation of this modulated ground state is challenging, since excitations appear as a result of a finite-time evolution required to produce qualitative changes in the wavefunction density. To solve this problem we consider the time-dependent control of a dipolar Bose-Einstein condensate using shortcuts to adiabaticity techniques, concentrating on design of the time-dependent scattering length, a parameter of the system easily tunable by contemporary experiments. The first technique is the variational approach based on the Euler-Lagrange equations for a separable ansatz describing the evolution of the superfluid state. Secondly, we study the transition from superfluid to supersolid using a direct optimization protocol. We discuss the fidelity of the developed protocols in terms of the evolution time.
In one dimension, quantum fluctuations prevent the appearance of long-range order in a supersolid, and only quasi-long-range order can survive. We derive this quantum critical behavior and study its influence on the superfluid response and properties of the solid. The analysis is based on an effective low-energy description accounting for the two coupled Goldstone modes. We find that the quantum phase transition from the superfluid to the supersolid is shifted by quantum fluctuations from the position where the local formation of a solid structure takes place. For current experimental parameters with dipolar atomic gases, this shift is extremely small and cannot be resolved yet, i.e., current observations in experiments are expected to be in agreement with predictions from mean-field theory based on the extended Gross-Pitaevskii formalism.