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arXiv:2601.05846 · Physical Review Letters

Vorticity-Crystalline Order Coupling in Supersolids: Excitations and Reentrant Phases

Meinolf Schubert, K. Mukherjee, Philipp Stürmer, S. M. Reimann

Published Mar 23, 2026• 1 citation
arXivHTMLPDF

Abstract

Rotation is a natural tool in ultracold gases to break time-reversal symmetry, yet its impact on the collective excitations of supersolids remains largely unexplored. We show theoretically that tuning the rotation frequency, rather than the interparticle interactions, can trigger the superfluid-to-supersolid transition in Bose-Einstein condensates. Computing excitation spectra in the presence of vortices and persistent currents, we uncover a vortex-driven desoftening mechanism whereby quantized vorticity elevates the gapless Goldstone mode to a finite-energy roton, restoring superfluidity. This effect results in reentrant supersolid phases as a function of rotation frequency, revealing a fundamental coupling between topological defects and crystalline order.

DOI
10.1103/gqlr-bgj8

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Rotation is a natural tool in ultracold gases to break time-reversal symmetry, yet its impact on the collective excitations of supersolids remains largely unexplored. We show theoretically that tuning the rotation frequency, rather than the interparticle interactions, can trigger the superfluid-to-supersolid transition in Bose-Einstein condensates. Computing excitation spectra in the presence of vortices and persistent currents, we uncover a vortex-driven desoftening mechanism whereby quantized vorticity elevates the gapless Goldstone mode to a finite-energy roton, restoring superfluidity. This effect results in reentrant supersolid phases as a function of rotation frequency, revealing a fundamental coupling between topological defects and crystalline order.
Supersolids are states of matter that spontaneously break two continuous symmetries: translational invariance due to the appearance of a crystal structure and phase invariance due to phase locking of single-particle wave functions, responsible for superfluid phenomena. While originally predicted to be present in solid helium, ultracold quantum gases provided a first platform to observe supersolids, with particular success coming from dipolar atoms. Phase locking in dipolar supersolids has been probed through e.g. measurements of the phase coherence and gapless Goldstone modes, but quantized vortices, a hydrodynamic fingerprint of superfluidity, have not yet been observed. Here, with the prerequisite pieces at our disposal, namely a method to generate vortices in dipolar gases and supersolids with two-dimensional crystalline order, we report on the theoretical investigation and experimental observation of vortices in the supersolid phase. Our work reveals a fundamental difference in vortex seeding dynamics between unmodulated and modulated quantum fluids. This opens the door to study the hydrodynamic properties of exotic quantum systems with multiple spontaneously broken symmetries, in disparate domains such as quantum crystals and neutron stars.
We investigate the properties of quantized vortices in a dipolar Bose-Einstein condensed gas by means of a generalized Gross-Pitaevskii equation. The size of the vortex core hugely increases by increasing the weight of the dipolar interaction, approaching the transition to the supersolid phase. The critical angular velocity for the existence of an energetically stable vortex decreases in the supersolid, due to the reduced value of the density in the interdroplet region. The angular momentum per particle associated with the vortex line is shown to be smaller than $\ensuremath{\hbar}$, reflecting the reduction of the global superfluidity. The real-time vortex nucleation in a rotating trap is shown to be triggered, as for a standard condensate, by the softening of the quadrupole mode. For large angular velocities, when the distance between vortices becomes comparable to the interdroplet distance, the vortices are arranged into a honeycomb structure, which coexists with the triangular geometry of the supersolid lattice and persists during the free expansion of the atomic cloud.
Abstract Synchronization is a widespread phenomenon in natural and engineered systems, governing the emergence of collective dynamics in different domains including biology and classical and quantum physics. In quantum many-body systems, synchronization has emerged as a tool to probe out-of-equilibrium behaviour and internal correlations. Supersolids—quantum phases that combine crystalline order and superfluidity—offer a platform to explore synchronization in systems with coexisting broken symmetries. Here we investigate the dynamics of a dipolar supersolid subjected to external rotation. We show that, above a critical driving frequency, the crystal revolution undergoes a sudden synchronization with the rotating field seeded by the nucleation of quantized vortices, hallmark of superfluidity. This transition reflects the interplay between the solid-like and superfluid responses of the system. By comparing simulations of the extended Gross–Pitaevskii equation with experimental observations, we demonstrate that synchronization can serve as a dynamical indicator for vortex nucleation. This approach provides a complementary method to determine the critical rotation frequency for vortex formation in supersolids.
Abstract Supersolid is an exotic state of matter characterized by both superfluid properties and periodic particle density modulation, due to spontaneous breaking of U(1) gauge symmetry and spatial translation symmetry, respectively. For conventional supersolids, continuous translation symmetry breaking is accompanied by one gapless Goldstone mode in the excitation spectra. An interesting question naturally arises: what is the consequence of breaking discrete translation symmetry for supersolids? In this work, we study the consequence of discrete symmetry breaking in a Z n supersolid resulting from spontaneous breaking of a discrete Z n symmetry, or equivalently, a discrete translation symmetry. This Z n supersolid is realized in the stripe phase of spin–orbit-coupled Bose–Einstein condensate under an external periodic potential with period 1 / n of intrinsic stripe period. For n ⩾ 2 , there are n degenerate ground states with spontaneously broken lattice translation symmetry. The low-energy excitations of Z n supersolid include a pseudo-Goldstone mode, whose excitation gap at long wavelength limit is found to decrease rapidly with n. We further numerically show that, when confined in a harmonic trap, a spin-dependent perturbation can result in the transition between degenerate ground states of Z n supersolid. With the integer n tunable using the experimental technique of generating subwavelength optical lattice, the Z n supersolid proposed here offers a cold atom platform to simulate physics related with generic Z n symmetry breaking in a highly controllable setting.
Abstract Within the mean field Gross–Pitaevskii framework, ultracold atomic condensates with long-range interaction are predicted to have a supersolid-like ground state beyond a critical interaction strength. Such a mean field supersolid-like ground state has periodically modulated superfluid density which implies the coexistence of superfluid and crystalline order. An ultracold atomic system in such a mean field ground state can be subjected to an artificial gauge field created either through rotation or by introducing space dependent coupling among hyperfine states of the atoms using Raman lasers. Starting from this Gross–Pitaevskii energy functional that describes such systems at zero temperature, we construct a hydrodynamic theory to describe the low-energy long-wavelength excitations of a rotating supersolid of weakly interacting ultracold atoms in two spatial dimensions for a generic type of long-range interaction. We treat the supersolidity in such a system within the framework of the well known two-fluid approximation. Considering such a system in the fast rotation limit where a vortex lattice in superfluid coexists with the supersolid lattice, we analytically obtain the dispersion relations of collective excitations around this equilibrium state. The dispersion relation gives the modes of the rotating supersolid which can be experimentally measured within the current technology. We point out that this can clearly identify an ultracold atomic supersolid phase in an unambiguous way.
Vortices are expected to exist in a supersolid but experimentally their detection can be difficult because the vortex cores are localized at positions where the local density is very low. We address here this problem by performing numerical simulations of a dipolar Bose-Einstein Condensate (BEC) in a pancake confinement at T=0T=0T=0 K and study the effect of quantized vorticity on the phases that can be realized depending upon the ratio between dipolar and short-range interaction. By increasing this ratio the system undergoes a spontaneous density modulation in the form of an ordered arrangement of multi-atom "droplets". This modulated phase can be either a "supersolid" (SS) or a "normal solid" (NS). In the SS state droplets are immersed in a background of low-density superfluid and the system has a finite global superfluid fraction resulting in non-classical rotational inertia. In the NS state no such superfluid background is present and the global superfluid fraction vanishes. We propose here a protocol to create vortices in modulated phases of dipolar BEC by "freezing" into such phases a vortex-hosting superfluid (SF) state. The resulting system, depending upon the interactions strengths, can be either a SS or a NS To discriminate between these two possible outcome of a "freezing" experiment, we show that upon releasing of the radial harmonic confinement, the expanding vortex-hosting SS shows tell-tale quantum interference effects which display the symmetry of the vortex lattice of the originating SF, as opposed to the behavior of the NS which shows instead a ballistic radial expansion of the individual droplets. Such markedly different behavior might be used to prove the supersolid character of rotating dipolar condensates.