We analyze the finite-temperature phase diagram of a dipolar Bose-Einstein condensate confined in a tubular geometry. The effect of thermal fluctuations is accounted for by means of Bogoliubov theory employing the local density approximation. In the considered geometry, the superfluid-supersolid phase transition can be of first and second order. We discuss how the corresponding transition point is affected by the finite temperature of the system. Published by the American Physical Society 2024
We analyze the finite-temperature phase diagram of a dipolar Bose-Einstein condensate confined in a tubular geometry. The effect of thermal fluctuations is accounted for by means of Bogoliubov theory employing the local density approximation. In the considered geometry, the superfluid-supersolid phase transition can be of first and second order. We discuss how the corresponding transition point is affected by the finite temperature of the system. Published by the American Physical Society 2024
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.
Motivated by a recent experiment [L. Chomaz et al., Nat. Phys. 14, 442 (2018)], we perform numerical simulations of a dipolar Bose-Einstein condensate (BEC) in a tubular, periodic confinement at T=0 within density functional theory, where the beyond-mean-field correction to the ground-state energy is included in the local density approximation. We study the excitation spectrum of the system by solving the corresponding Bogoliubov--de Gennes equations. The calculated spectrum shows a roton minimum, and the roton gap decreases by reducing the effective scattering length. As the roton gap disappears, the system spontaneously develops a periodic linear structure formed by denser clusters of atomic dipoles immersed in a dilute superfluid background. This structure shows the hallmarks of a supersolid system, i.e., (i) a finite nonclassical translational inertia along the tube axis and (ii) the appearance of two gapless modes, i.e., a phonon mode associated with density fluctuations and resulting from the translational discrete symmetry of the system, and a Nambu-Goldstone gapless mode corresponding to phase fluctuations, resulting from the spontaneous breaking of the gauge symmetry. A further decrease in the scattering length eventually leads to the formation of a periodic linear array of self-bound droplets.
We provide a theoretical characterization of the dynamical crossing of the superfluid-supersolid phase transition for a dipolar condensate confined in an elongated trap, as observed in the recent experiment by Biagioni et al. [G. Biagioni, N. Antolini, A. Ala\~na, M. Modugno, A. Fioretti, C. Gabbanini, L. Tanzi, and G. Modugno, Phys. Rev. X 12, 021019 (2022)]. By means of the extended Gross-Pitaevskii theory, which includes the Lee-Huang-Yang quantum fluctuation correction, we first analyze the ground-state configurations of the system as a function of the interparticle scattering length, for both trap configurations employed in the experiment. Then, we discuss the effects of the ramp velocity, by which the scattering length is tuned across the transition, on the collective excitations of the system in both the superfluid and supersolid phases. We find that, when the transverse confinement is sufficiently strong and the transition has a smooth (continuous) character, the system essentially displays a (quasi) one-dimensional behavior, its excitation dynamics being dominated by the axial breathing modes. Instead, for shallower transverse trapping, when the transition becomes discontinuous, the collective excitations of the supersolid display a coupling with the transverse modes, signaling the onset of a dimensional crossover.
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.
Dipolar Bose-Einstein condensates represent a powerful platform for the exploration of quantum many-body phenomena arising from long-range interactions. A series of recent experiments has demonstrated the formation of supersolid states of matter. Subsequent theoretical works have shown that quantum fluctuations can affect the underlying phase transition and may lead to the emergence of supersolids with various lattice structures in dipolar condensates. In this work, we explore the signatures of such different geometries in confined finite condensates. In addition to previously found triangular lattices, our analysis reveals a rich spectrum of states, from honeycomb patterns to striped supersolids. By optimizing relevant parameters, we show that transitions between distinct supersolids should be observable in current experiments.