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arXiv:2506.03071 · Physical Review Letters

Creating and Melting a Supersolid by Heating a Quantum Dipolar System

Raúl Bombín, Jordi Boronat, Ferran Mazzanti, Juan Sánchez-Baena

Published Sep 29, 2025• 3 citations
arXivHTMLPDF

Abstract

Recent experiments have shown that raising the temperature of a dipolar gas under certain conditions leads to a transition to a supersolid state. Here, we employ the path integral Monte Carlo method, which exactly accounts for both thermal and correlation effects, to study that phenomenology in a system of ^{162}Dy atoms in the canonical ensemble. Our microscopic description allows the quantitative characterization of the emergence of spatial order and superfluidity, the two ingredients that define a supersolid state. Our calculations prove that temperature on its own can promote the formation of a supersolid in a dipolar system. Furthermore, we bridge this exotic phenomenology with the more usual melting of the supersolid at a higher temperature. Our results offer insight into the interplay between thermal excitations, the dipole-dipole interaction, quantum statistics, and supersolidity.

DOI
10.1103/nkm3-1725

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Recent experiments have shown that raising the temperature of a dipolar gas under certain conditions leads to a transition to a supersolid state. Here, we employ the path integral Monte Carlo method, which exactly accounts for both thermal and correlation effects, to study that phenomenology in a system of ^{162}Dy atoms in the canonical ensemble. Our microscopic description allows the quantitative characterization of the emergence of spatial order and superfluidity, the two ingredients that define a supersolid state. Our calculations prove that temperature on its own can promote the formation of a supersolid in a dipolar system. Furthermore, we bridge this exotic phenomenology with the more usual melting of the supersolid at a higher temperature. Our results offer insight into the interplay between thermal excitations, the dipole-dipole interaction, quantum statistics, and supersolidity.
Temperature plays a non-trivial role in dipolar systems, being able to either induce or destroy spatial density modulations. In order to shed light into the interplay between thermal effects and quantum correlations, we employ the path integral Monte Carlo method (PIMC) to obtain the phase diagram of a system of dipolar bosons in an infinite cylindrical geometry and at finite temperatures. For a fixed total density, we vary the scattering length of the interaction and the temperature, and characterize the structure and superfluidity of the emerging phases. The PIMC method accounts for thermal effects and quantum correlations at all orders, and can be used to quantitatively estimate the superfluid fraction of the system. Remarkably, we find a regime of parameters where, starting from a supersolid, the spatial order vanishes with temperature before the superfluidity does. We also find a region of the phase diagram where the superfluid fraction displays a non-monotonous dependence with temperature. Our results extend previous descriptions, relying on Bogoliubov theory, to larger temperatures in the thermodynamic limit and illustrate how spatial modulations and superfluidity are lost as temperature is increased.
It is intuitive to think that heating any material leads to an increase in random thermal motion and, thereby, usually counteracts any ordering efforts. For example, heating ice leads to the formation of a liquid and ultimately to a gas. However, experiments with dipolar Bose-Einstein condensates suggested that this general phenomenology does not always take place [1]. In order to describe the surprising superfluid-supersolid transition upon an increase in temperature at fixed condensed particle number we employ Bogoliubov theory with local density approximation [2], [3] and, indeed, find that such behaviour can also be expected theoretically [Fig. 1(a)]. With this approach we find [3] that the scaling with respect to density of the shift in energy due to thermal fluctuations is opposite to that of quantum fluctuations and, therefore, promotes the formation of high density regions [Fig. 1(b)]. Consistent with that we find that an increase in temperature promotes roton-softening [Fig. 1(c)]. Furthermore, we find good agreement between the experimentally measured density and the theoretical prediction including thermal fluctuations, whereas not taking thermal corrections into account yields a different result [Fig. 1(d)]. These findings call for further investigation of the surprising thermodynamic behaviour of ultracold quantum ferrofluids.
Raising the temperature of a material enhances the thermal motion of particles. Such an increase in thermal energy commonly leads to the melting of a solid into a fluid and eventually vaporises the liquid into a gaseous phase of matter. Here, we study the finite-temperature physics of dipolar quantum fluids and find surprising deviations from this general phenomenology. In particular, we describe how heating a dipolar superfluid from near-zero temperatures can induce a phase transition to a supersolid state with a broken translational symmetry. We discuss the observation of this effect in experiments on ultracold dysprosium atoms, which opens the door for exploring the unusual thermodynamics of dipolar quantum fluids.
A mesoscopic system of dipolar bosons trapped by a harmonic potential is considered. The system has a number of physical realizations including dipole excitons, atoms with large dipolar moment, polar molecules, and Rydberg atoms in inhomogeneous electric field. We carry out a diffusion Monte Carlo simulation to define the quantum properties of a two-dimensional system of trapped dipoles at zero temperature. In dimensionless units the system is described by two control parameters, namely, the number of particles and the strength of the interparticle interaction. We have shown that when the interparticle interaction is strong enough a mesoscopic crystal is formed. As the strength of interactions is decreased a multistage melting takes place. Off-diagonal order in the system is tested using natural-orbitals analysis. We have found that the system might be Bose condensed even in the case of strong interparticle interactions. There is a set of parameters for which a spatially ordered structure is formed while simultaneously the fraction of Bose-condensed particles is nonzero. This might be considered as a realization of a mesoscopic supersolid.
This thesis discusses the experiments on 2D dipolar Bose gas of ultracold erbium atoms. Long-range and anisotropic dipole-dipole interaction induces complex orders in quantum many-body systems. Highly magnetic lanthanide atoms such as dysprosium and erbium have the largest magnetic moment in the periodic table, which has attracted significant attention in the past decades. Starting from quantum degenerate dysprosium and erbium atoms, exotic phases like quantum droplets, supersolid, dipolar quantum solid in the Hubbard regime have been studied. However, the 2D dipolar superfluid still remains understudied, despite being theoretically discussed for over two decades. Although tremendous theoretical proposals predict different phenomena in 2D dipolar superfluids, our first interest is to know how the superfluidity emerges in the 2D dipolar gases at finite temperatures. Our observations suggest that the superfluid transition can be well described by the Berezinskii-Kosterlitz-Thouless transition with an effective contact interaction as a function of dipolar orientation. With the 2D dipolar superfluid with strong DDI, we characterized the elementary excitation of the matter: the collective breathing mode. Our measurements establish how the competition between local and nonlocal interaction in strongly dipolar 2D superfluid retains quasi-scale invariance or strongly breaks scale invariance. By further searching the interaction parameters, we created stripes with global coherence, which are the first supersolid stripes in 2D. Experiments including measuring density fluctuation, coherence, and collective mode have been performed to understand the 2D supersolid. At last, we also observe unconventional light scattering from round-disk dipolar BECs, which provides new possibilities for atom optics.
The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasicrystal phase. Additionally, a potential intermediate hexatic phase with quasi-long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.