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arXiv:2512.24108 · Physical Review A

Dynamical signatures of superfluidity and shear rigidity in different phases of a dipolar Bose-Einstein condensate

Soumyadeep Halder, H. Ghosh, Axel Pelster, B. Prasanna Venkatesh

Published Jul 1, 2026• 0 citations
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Abstract

We show that a sudden change in the polarization direction of the magnetic dipole moments of the atoms in a dipolar Bose-Einstein condensate (BEC) can serve as a useful dynamical probe to sense its superfluid and solid-like properties. We find that for small angular deviation of the polarization direction, actuated for instance by modifying an external magnetic field, the superfluid state undergoes an undamped scissors mode oscillation, a characteristic signature of superfluidity. In contrast, both the droplet and supersolid states exhibit a scissors-mode oscillation, which is effectively damped due to multiple closely spaced frequency components. Notably, we find that this damping rate provides a qualitative measure for the rigidity of different phases of a dipolar BEC. Furthermore, there exists a maximum angular deviation of the polarization direction, beyond which the droplet and the supersolid states undergo a permanent deformation i.e., we find an analog of the usual elastic to plastic phase transition of solids. We characterize this transition numerically using the fidelity of the condensate wavefunction with the ground state as well as the droplet width and periodicity of the supersolid density of the condensate which are experimentally accessible. Thus, the dynamical protocol introduced here can be an important experimental benchmark to identify and characterize the superfluid and solid properties of different phases of dipolar BECs.

DOI
10.1103/b8n6-kvb1

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We show that a sudden change in the polarization direction of the magnetic dipole moments of the atoms in a dipolar Bose-Einstein condensate (BEC) can serve as a useful dynamical probe to sense its superfluid and solid-like properties. We find that for small angular deviation of the polarization direction, actuated for instance by modifying an external magnetic field, the superfluid state undergoes an undamped scissors mode oscillation, a characteristic signature of superfluidity. In contrast, both the droplet and supersolid states exhibit a scissors-mode oscillation, which is effectively damped due to multiple closely spaced frequency components. Notably, we find that this damping rate provides a qualitative measure for the rigidity of different phases of a dipolar BEC. Furthermore, there exists a maximum angular deviation of the polarization direction, beyond which the droplet and the supersolid states undergo a permanent deformation i.e., we find an analog of the usual elastic to plastic phase transition of solids. We characterize this transition numerically using the fidelity of the condensate wavefunction with the ground state as well as the droplet width and periodicity of the supersolid density of the condensate which are experimentally accessible. Thus, the dynamical protocol introduced here can be an important experimental benchmark to identify and characterize the superfluid and solid properties of different phases of dipolar BECs.
The formation of quantized vortices above a certain critical trap rotation frequency serves as a hallmark signature of superfluidity. Based on the beyond mean-field framework, crucial for the formation of exotic supersolid and droplet states, we investigate dynamical protocols for vortex nucleation in the superfluid and supersolid states of a dipolar Bose-Einstein condensate (BEC) at a trap rotation frequency lower than the conventional critical rotation frequency. We find that the critical rotation frequency depends not only on the dipole-dipole interaction strength, but also on the polarization direction of the external magnetic field. Interestingly, in the superfluid state, the critical rotation frequency increases with the tilt angle of the magnetic field, whereas in the supersolid state, increasing the tilt angle lowers the critical threshold. Leveraging these characteristics of dipolar BECs, along with the robustness of vortices with respect to changes in the polarization direction and sss-wave scattering length, we demonstrate three dynamical protocols for vortex nucleation, even when rotating below the critical rotation frequency, viz., (i) varying the sss-wave scattering length, (ii) changing the polarizing angle, and (iii) successive modulation of both the scattering length and polarizing angle. These dynamical vortex seeding protocols could serve as important benchmarks for future experimental studies.
Distinctive features of supersolids show up in their rotational properties. We calculate the moment of inertia of a harmonically trapped dipolar Bose-Einstein condensed gas as a function of the tunable scattering length parameter, providing the transition from the (fully) superfluid to the supersolid phase and eventually to an incoherent crystal of self-bound droplets. The transition from the superfluid to the supersolid phase is characterized by a jump in the moment of inertia, revealing its first order nature. In the case of elongated trapping in the plane of rotation, we show that the moment of inertia determines the value of the frequency of the scissors mode, which is significantly affected by the reduction of superfluidity in the supersolid phase. The case of an in-plane isotropic trapping is instead well suited to study the formation of quantized vortices, which are shown to be characterized, in the supersolid phase, by a sizeable deformed core, caused by the presence of the surrounding density peaks.
We study dipole-mode and scissors-mode oscillations of a harmonically trapped dipolar supersolid, composed of dipolar droplets arranged on a one-dimensional (1D) or a 2D lattice, to establish the robustness of its crystalline structure under translation and rotation, using a beyond-mean-field model including a Lee-Huang-Yang interaction. The dipolar atoms are polarized in the zzz direction with the supersolid crystalline structure lying in the $x\text{\ensuremath{-}}y$ plane. A stable dipole-mode oscillation is possible in the case of both quasi-1D and quasi-2D dipolar supersolids, whereas a sustained angular scissors-mode oscillation is possible only in the case of a quasi-1D dipolar supersolid between a maximum and a minimum of trap anisotropy in the $x\text{\ensuremath{-}}y$ plane. In both cases there is no visible deformation of the crystalline structure of the dipolar supersolid during the oscillation. The theoretical estimate of the scissors-mode-oscillation frequency is in good agreement with the present results and the agreement improves with an increase in the number of droplets in the supersolid and also with an increase in the confining trap frequencies. The results of this study can be tested experimentally with present knowhow.
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.
We report the observation of the scissors mode of a Bose-Einstein condensed gas of 87Rb atoms in a magnetic trap, which gives direct evidence of superfluidity in this system. The scissors mode of oscillation is excited by a sudden rotation of the anisotropic trapping potential. For a gas above T(c) (normal fluid) we detect the occurrence of oscillations at two frequencies, with the lower frequency corresponding to the rigid body value of the moment of inertia. Well below T(c) the condensate oscillates at a single frequency, without damping, as expected for a superfluid.
The task of experimentally investigating the inherently dual properties of a supersolid, a simultaneous superfluid and solid, has become more critical following the recent experimental exploration of supersolid regimes in dipolar Bose-Einstein condensates (BECs) of ^{164}Dy. We introduce a supersolid order parameter that uses vortex-vortex trajectory correlations to simultaneously reveal the periodic density of the underlying solid and superfluidity in a single measure. We propose experiments using existing technology to optically create and image trajectories of vortex dipoles in dipolar BECs that is applicable to large system sizes. We numerically test our observable and find that vortex-vortex correlations reveal the supersolid lattice structure while distinguishing it from superfluidity even in the presence of dissipation. Our method sets the stage for experiments to use vortex trajectory correlations to investigate fundamental properties of supersolids arising from their dynamics and phase transitions as experimental system sizes are increased.