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arXiv:2403.13727 · Physical Review Research

Elastic properties and thermodynamic anomalies of supersolids

Milan Rakic, A. F. Ho, Derek K. K. Lee

Published Oct 16, 2024• 9 citations
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Abstract

We study a supersolid in the context of a Gross-Pitaevskii theory with a nonlocal effective potential. We employ a homogenization technique which allows us to calculate the elastic moduli, supersolid fraction, and other state variables of the system. Our methodology is verified against numerical simulations of elastic deformations. We can also verify that the long-wavelength Goldstone modes that emerge from this technique agree with Bogoliubov theory. We find a thermodynamic anomaly that the supersolid does not obey the thermodynamic relation ∂ P / ∂ V | N = − n ( ∂ P / ∂ N | V ) , which we claim is a feature unique to supersolids. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.043040

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We study a supersolid in the context of a Gross-Pitaevskii theory with a nonlocal effective potential. We employ a homogenization technique which allows us to calculate the elastic moduli, supersolid fraction, and other state variables of the system. Our methodology is verified against numerical simulations of elastic deformations. We can also verify that the long-wavelength Goldstone modes that emerge from this technique agree with Bogoliubov theory. We find a thermodynamic anomaly that the supersolid does not obey the thermodynamic relation ∂ P / ∂ V | N = − n ( ∂ P / ∂ N | V ) , which we claim is a feature unique to supersolids. Published by the American Physical Society 2024
Supersolids are a fascinating quantum phase of matter that have both superfluid and solid properties, and are in some ways an extension of a superfluid, in that it possesses an additional rich and dynamic set of phenomenological features. Supersolids are an example of strongly correlated intertwined order, which is the notion that systems can form phases of matter that are more than the sum of its parts. Put simply, a supersolid is not a superfluid + solid. This intertwined order generates new and exciting physics which looks a little like its constituent components, but also not at all. In this thesis we develop a homogenisation technique, which begins with a microscopic theory of a supersolid and ends with a phenomenological Lagrangian. By doing this we marry two opposite ends of supersolid theory, providing the phenomenological toolset to study supersolids, but rooted in the foundation of microscopic theory. We derive the mathematical framework necessary to employ homogenisation, apply it to the Gross-Pitaevskii Lagrangian, elucidate crucial contributions from the thermodynamic ensemble of a supersolid, and obtain an effective theory of the Goldstone modes. We conduct numerics on a soft-core bosonic system, applying homogenisation to our simulated supersolids, and verify our results with Bogoliubov theory. We find an unexpected result that the supersolid has two distinct values for bulk compressibility, which takes it outside of the class of materials for which this thermodynamic relation holds. To the best of our knowledge, this is the first such example of this particular physical feature in any material. We then extend homogenisation to include beyond-meanfield effects, in order to apply it to a dipolar BEC. The dipolar BEC has a considerably richer phase diagram, in which we find several exciting results.
Due to its peculiar superfluid-crystal duality feature, the supersolid has received great research interest. Recently, researchers have paid much attention to its elastic response properties; however, the inelastic deformation has barely been explored. In this work, we study the transition from elastic to inelastic deformation of a dipolar supersolid Bose-Einstein condensate trapped in a box potential (i.e., a dipolar supersolid with finite size). We obtain the stationary supersolid states (both ground and excited) of the system and examine the relation between the supersolid size and the number of unit cells it can accommodate, which can essentially help us to understand the dynamical responses of the supersolid during a dilation or compression process. We found that within a certain dilation or compression extent, the supersolid can retain its original crystal structure, that is, it endures an elastic deformation; however, when the extent exceeds a critical threshold, the original crystal structure of the supersolid will be disrupted, which signifies an inelastic deformation. Furthermore, we both analytically and numerically determine the critical point of the transition from elastic to inelastic deformation and map out a phase diagram. These results open up new territory in the research of supersolid mechanical properties and may find applications in quantum material science and quantum-based technologies.
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.
Abstract The properties of a supersolid state (SS) in quasi-one-dimensional dipolar Bose–Einstein condensate is studied, considering two possible mechanisms of realization—due to repulsive three-body atomic interactions and quantum fluctuations in the framework of the Lee–Huang–Yang theory. The role of both mechanisms in the formation of SS properties has been emphasized. The proposed theoretical model, based on minimization of the energy functional, allows evaluating the amplitude of the SS for an arbitrary set of parameters in the extended Gross–Pitaevskii equation (eGPE). To explore the dynamics of the SS first we numerically construct its ground state in different settings, including periodic boundary conditions, box-like trap and parabolic potential, then impose a perturbation. In oscillations of the perturbed supersolid we observe the key manifestation of SS, namely the free flow of the superfluid fraction through the crystalline component of the system. Two distinct oscillation frequencies of the supersolid associated with the superfluid fraction and crystalline components of the wave function are identified from numerical simulations of the eGPE.
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.