arXiv:1907.01986 · Physical Review Letters

Excitation Spectrum of a Trapped Dipolar Supersolid and Its Experimental Evidence

G. Natale, Rick van Bijnen, A. Patscheider, Daniel Petter, Manfred J. Mark, Lauriane Chomaz, Francesca Ferlaino

Published Aug 1, 2019• 237 citations

Abstract

We study the spectrum of elementary excitations of a dipolar Bose gas in a three-dimensional anisotropic trap across the superfluid-supersolid phase transition. Theoretically, we show that, when entering the supersolid phase, two distinct excitation branches appear, respectively associated with dominantly crystal and superfluid excitations. These results confirm infinite-system predictions, showing that finite-size effects play only a small qualitative role, and connect the two branches to the simultaneous occurrence of crystal and superfluid orders. Experimentally, we probe compressional excitations in an Er quantum gas across the phase diagram. While in the Bose-Einstein condensate regime the system exhibits an ordinary quadrupole oscillation, in the supersolid regime we observe a striking two-frequency response of the system, related to the two spontaneously broken symmetries.

DOI: 10.1103/physrevlett.123.050402

Related papers

Excitation spectrum of a double supersolid in a trapped dipolar Bose mixture

Daniel Scheiermann, Albert Gallemí, Luis Santos

Dipolar Bose-Einstein condensates are excellent platforms for studying supersolidity, characterized by coexisting density modulation and superfluidity. The realization of dipolar mixtures opens intriguing new scenarios, most remarkably the possibility of realizing a double supersolid, composed of two interacting superfluids. We analyze the complex excitation spectrum of a miscible trapped dipolar Bose mixture, showing that it provides key insights about the double-supersolid regime. We show that this regime may be readily probed experimentally by monitoring the appearance of a doublet of superfluid compressional modes, linked to the different superfluid character of each component. Additionally, the dipolar supersolid mixture exhibits a nontrivial spin nature of the dipolar rotons, the Higgs excitation, and the low-lying Goldstone modes. Interestingly, the analysis of the lowest-lying modes allows for monitoring the transition of just one of the components into the incoherent-droplet regime, whereas the other remains coherent, highlighting their disparate superfluid properties.

arXiv:2412.05215Physical Review AMar 13, 20253 citations

Compressibility and speeds of sound across the superfluid-to-supersolid phase transition of an elongated dipolar gas

P. B. Blakie, Lauriane Chomaz, D. Baillie +1 more

We investigate the excitation spectrum and compressibility of a dipolar Bose-Einstein condensate in an infinite tube potential in the parameter regime where the transition between superfluid and supersolid phases occurs. Our study focuses on the density range in which crystalline order develops continuously across the transition. Above the transition the superfluid shows a single gapless excitation band, phononic at small momenta and with a roton at a finite momentum. Below the transition, two gapless excitations branches (three at the transition point) emerge in the supersolid. We examine the two gapless excitation bands and their associated speeds of sound in the supersolid phase. Our results show that the speeds of sound and the compressibility are discontinuous at the transition, indicating a second-order phase transition. These results provide valuable insights into the identification of supersolid phenomena in dipolar quantum gases and the relationship to supersolidity in spin-orbit coupled gases.

arXiv:2306.04794Physical Review ResearchSep 6, 202320 citations

Excitations of a two-dimensional supersolid

Elena Poli, D. Baillie, Francesca Ferlaino +1 more

We present a theoretical study of the excitations of the two-dimensional supersolid state of a Bose-Einstein condensate with either dipole-dipole interactions or soft-core interactions. This supersolid state has three gapless excitation branches arising from the spontaneously broken continuous symmetries. Two of these branches are related to longitudinal sound waves, similar to those in one-dimensional supersolids. The third branch is a transverse wave arising from the nonzero shear modulus of the two-dimensional crystal. We present the results of numerical calculations for the excitations and dynamic structure factor characterizing the density fluctuations and study their behavior across the discontinuous superfluid to supersolid transition. We show that the speeds of sound are described by a hydrodynamic theory that incorporates generalized elastic parameters, including the shear modulus. Furthermore, we establish that dipolar and soft-core supersolids manifest distinct characteristics, falling into the bulk-incompressible and rigid-lattice limits, respectively.

arXiv:2407.01072Physical Review ANov 4, 202421 citations

Supersolidity in Two-Dimensional Trapped Dipolar Droplet Arrays

Jens Hertkorn, Jan-Niklas Schmidt, Mingyang Guo +8 more

We theoretically investigate the ground states and the spectrum of elementary excitations across the superfluid to droplet crystallization transition of an oblate dipolar Bose-Einstein condensate. We systematically identify regimes where spontaneous rotational symmetry breaking leads to the emergence of a supersolid phase with characteristic collective excitations, such as the Higgs amplitude mode. Furthermore, we study the dynamics across the transition and show how these supersolids can be realized with standard protocols in state-of-the-art experiments.

arXiv:2103.09752Physical Review LettersOct 8, 202163 citations

The Excitation Spectra of a Supersolid

Lily Platt

This thesis explores the excitation spectra of supersolids - materials that remarkably manifest both lattice structure and superfluidity. We focus on an ultracold dilute gas exhibiting one-dimensional crystal structure with two gapless excitation branches. Two distinct supersolid systems are examined: a one dimensional Bose-Einstein condensate with softcore interactions, and a three dimensional dipolar Bose Einstein condensate confined within an infinitely long tube-shape potential. We investigate the crystal-like excitations of the supersolid through the use of the linear chain model and by introducing an elastic constant derived from ground-state calculations. Subsequently, we adopt a hydrodynamic approach based on an effective Lagrangian, which depends upon three fields, corresponding to lattice deformations, defect density current, the global phase fluctuations and four elastic parameters. This description of the supersolid allows for the determination of low-energy excitations, as well as the behaviour of the associated density and phase fluctuations of the two gapless branches. We validate our predictions for the low energy excitations by comparison to results from directly solving the Bogoliubov-de-Gennes equations, finding excellent agreement. This thesis provides a deeper understanding of the different types of supersolid systems, and how their low-energy behaviour depends upon their characteristic elastic energy scales.

Sep 20, 20240 citations

Fate of the Amplitude Mode in a Trapped Dipolar Supersolid

Jens Hertkorn, Fabian Böttcher, Mingyang Guo +4 more

We theoretically investigate the spectrum of elementary excitations of a trapped dipolar quantum gas across the BEC-supersolid phase transition. Our calculations reveal the existence of distinct Higgs amplitude and Nambu-Goldstone modes that emerge from the softening roton modes of the dipolar BEC at the phase transition point. On the supersolid side of the transition, the energy of the Higgs amplitude mode increases rapidly, leading to a strong coupling to higher-lying modes. Our Letter highlights how the symmetry-breaking nature of the supersolid state translates to finite-size systems.

arXiv:1907.09315Physical Review LettersNov 6, 201967 citations