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arXiv:2408.16489 · Physical Review Letters

Anomalous Doppler Effect in Superfluid and Supersolid Atomic Gases

Tomasz Zawiślak, Marija Šindik, S. Stringari, Alessio Recati

Published Jun 3, 2025• 4 citations
arXivHTMLPDF

Abstract

By employing the formalism of hydrodynamics, we derive novel analytic predictions for the Doppler effect in superfluids with broken Galilean invariance and hosting persistent currents at zero temperature. We consider two scenarios: when Galilean invariance is broken explicitly (by external potentials) and spontaneously, as it happens in a supersolid. In the former case, the presence of a stationary current affects the propagation of sound via an anomalous Doppler term proportional to the density derivative of the superfluid fraction. In supersolids, where, according to Goldstone theorem, distinct sounds of hybrid superfluid and crystal nature can propagate, the Doppler effect can be very different for each sound. Quantitative estimates of the Doppler shifts are obtained for Bose-Einstein condensed atomic gases, described by Gross-Pitaevskii theory. The estimates are obtained both calculating the thermodynamic parameters entering the hydrodynamic results and from full time-dependent simulations.

DOI
10.1103/physrevlett.134.226001

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By employing the formalism of hydrodynamics, we derive novel analytic predictions for the Doppler effect in superfluids with broken Galilean invariance and hosting persistent currents at zero temperature. We consider two scenarios: when Galilean invariance is broken explicitly (by external potentials) and spontaneously, as it happens in a supersolid. In the former case, the presence of a stationary current affects the propagation of sound via an anomalous Doppler term proportional to the density derivative of the superfluid fraction. In supersolids, where, according to Goldstone theorem, distinct sounds of hybrid superfluid and crystal nature can propagate, the Doppler effect can be very different for each sound. Quantitative estimates of the Doppler shifts are obtained for Bose-Einstein condensed atomic gases, described by Gross-Pitaevskii theory. The estimates are obtained both calculating the thermodynamic parameters entering the hydrodynamic results and from full time-dependent simulations.
We show that two-component Bose-Einstein condensed mixtures, in presence of a persistent current, exhibit a nontrivial Doppler shift of the sound velocities. The peculiarity is due to the interspecies interaction and the possibility of generating a counterflow persistent current. Analytical predictions are derived using superfluid hydrodynamics. While the existence of anomalous Doppler shifts at finite temperature has been discussed a long time ago in the case of superfluid 4He^{4}\mathrm{He}4He, an experimental verification of the effect is still missing. For this reason, we also propose a protocol for the measurement of the Doppler shifts, based on the density-density response function. The dynamical protocol is simulated by means of coupled Gross-Pitaevskii equations.
Abstract We determine the hydrodynamic modes of the superfluid analog of a smectic-A liquid crystal phase, i.e., a state in which both gauge invariance and translational invariance along a single direction are spontaneously broken. Such a superfluid smectic provides an idealized description of the incommensurate supersolid state realized in Bose–Einstein condensates with strong dipolar interactions as well as of the stripe phase in Bose gases with spin–orbit coupling. We show that the presence of a finite normal fluid density in the ground state of these systems gives rise to a well-defined second-sound type mode even at zero temperature. It replaces the diffusive permeation mode of a normal smectic phase and is directly connected with the classic description of supersolids by Andreev and Lifshitz in terms of a propagating defect mode. An analytic expression is derived for the two sound velocities that appear in the longitudinal excitation spectrum. It only depends on the low-energy parameters associated with the two independent broken symmetries, which are the effective layer compression modulus and the superfluid fraction.
Superfluidity describes the ability of quantum matter to flow without friction. Due to its fundamental role in many transport phenomena, it is crucial to understand the robustness of superfluid properties to external perturbations. Here, we theoretically study the effects of speckle disorder on the propagation of sound waves in a two-dimensional Bose-Einstein condensate at zero temperature. We numerically solve the Gross-Pitaevskii equation in the presence of disorder and employ a superfluid hydrodynamic approach to elucidate the role of the compressibility and superfluid fraction in the propagation of sound. A key result is that disorder reduces the superfluid fraction and hence the speed of sound; it also introduces damping and mode coupling. In the limit of weak disorder, the predictions for the speed of sound and its damping rate are well reproduced by a quadratic perturbation theory. The hydrodynamic description is valid over a wide range of parameters, while discrepancies become evident if the disorder becomes too strong, the effect being more significant for disorder applied in only one spatial direction. Our predictions are well within the reach of state-of-the-art cold-atom experiments and carry over to more general disorder potentials.
We propose a protocol to excite the Goldstone modes of a supersolid dipolar Bose-Einstein condensed gas confined in a ring geometry. By abruptly removing an applied periodic modulation proportional to cos(φ), where φ is the azimuthal angle, we explore the resulting oscillations of the gas by solving the extended Gross-Pitaevskii equation. The value of the two longitudinal sound velocities exhibited in the supersolid phase are analyzed using the hydrodynamic theory of supersolids at zero temperature, which explicitly takes into account both the superfluid and the crystal nature of the system. This approach allows for the determination of the layer compressibility modulus as well as of the superfluid fraction, f_{S}, in agreement with the Leggett estimate of the nonclassical moment of inertia.
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.
We present a unified hydrodynamic approach for the sound propagation in the stripe phases realized in ultracold dipolar gas and spin-orbit-coupled BEC platforms at zero temperature. Despite the deep difference of the two platforms at a microscopic level, a similar hydrodynamic description can be formulated at a macroscopic level. The main difference between the two platforms is the lack of Galilean invariance in the spin-orbit case, resulting in a different identification of the normal (nonsuperfluid) component of the density, which leads to new terms in the equation for the current. In both cases the spectrum comprises two sounds, reflecting the spontaneous breaking of the U(1) and translational symmetries. Both sounds exhibit an anisotropic behavior. A comparison with the first and second sounds of the smectic-A liquid crystal is also presented.