Matteo Ciardi

The superfluid-insulator transition in systems of lattice bosons is usually analyzed in the framework of the Bose-Hubbard model, and has been extensively studied by theory and simulations. Less attention has been paid to the remnants of the transition in truncated lattices, with or without periodic boundary conditions. Here we consider the hard-core limit of the extended Bose-Hubbard model on small square and triangular grids—i.e., sections of the square and triangular lattices containing up to 13 sites. By mapping out the zero-temperature phase diagram through exact diagonalization, we find ground-state characteristics that are markedly different from those emerging in the thermodynamic limit, together with similarities. The dichotomy between superfluidlike and insulatinglike behavior is then investigated in two-dimensional systems of a few interacting bosons in the continuum, subject to confining and optical-lattice potentials mimicking the 3 × 3 square grid. Using path-integral Monte Carlo simulations, we compute kinetic and potential energies, as well as superfluidity and exchange-cycle statistics, finding hints of Bose-Hubbard behavior even in systems of just five particles.

Fundamental theories and models of many-body physics can be probed in experiments on ultracold atoms held in place by electromagnetic fields. In particular, of considerable interest are systems under curved confinement, since they can yield exotic states of matter which would be impossible to obtain in flat space. In this study we focus on relatively small samples, where curvature effects are stronger, and analyze by Monte Carlo simulations the peculiar structure arising in an assembly of soft-core bosons subject to a trapping potential with spherical symmetry. Upon suitable tuning of the parameters, 100 particles or so group together in clusters arranged in a shell with icosahedral symmetry. As the number of particles increases, a second shell gradually develops, concentric to (and partly overlapping with) the original one, where clusters are in perfect registry with the first shell, thus forming a dodecahedral pattern. Cluster arrangements with the symmetry of other polyhedra are seen for different sets of parameters. At low temperature the superfluid density is nonuniform in the radial direction; heating the system progressively, superfluidity eventually vanishes while still clusters are present, a behavior resembling the transition from supersolid to normal solid on a plane. Two shells of clusters are also observed in systems of classical or distinguishable quantum particles, but in those cases the shells are more fragile to thermal fluctuations.

We investigate the physics of ultracold dipolar molecules using path-integral quantum Monte Carlo simulations, and construct the complete phase diagram extending from weak to strong interactions and from small to mesoscopic particle numbers. Our calculations predict the formation of self-bound quantum droplets at interaction strengths lower than previous estimates for molecular condensates. Strikingly, we observe that, for stronger interactions, the oblate quantum droplet transitions to a two-dimensional sheet or superfluid membrane with a thickness of a single molecule. As interactions are increased further the system continually loses superfluidity while correlations develop, and is eventually found to undergo a transition to a crystalline monolayer that remains self-bound without external confinement. The spontaneous formation of such two-dimensional phases from a three-dimensional quantum gas is traced back to the peculiar anisotropic form of the dipole-dipole interaction generated by microwave dressing of rotational molecular states. For sufficiently large particle numbers, crystallization takes place for comparably low interaction strengths that do not promote two-body bound states and should thus be observable in ongoing experiments without limitations from three-body recombination.

He 4 nanodroplets doped with an alkali ion feature a snowball of crystallized layers surrounded by superfluid helium. For large droplets, we predict that a transitional supersolid layer can form, bridging between the solid core and the liquid bulk, where the He 4 density displays modulations of icosahedral group symmetry. To identify the different phases, we combine density functional theory with the semiclassical Gaussian time-dependent Hartree method for localized many-body systems. This hybrid approach can handle large particle numbers and provides insight into the physical origin of the supersolid layer. For small droplets, we verify that the predictions of our approach are in excellent agreement with Path-Integral Monte Carlo calculations. Published by the American Physical Society 2025

By combining first-principles path integral Monte Carlo methods and mean-field techniques, we explore the properties of cylindrically trapped doubly dipolar Bose gases. We first verify the emergence of a pancake quantum droplet at low temperatures, validating previous mean-field calculations. In a regime of small doubly dipolar interactions, first-principles calculations agree with the generalized Gross-Pitaevskii equation. Such an accordance disappears in a large interaction limit. Here the path integral Monte Carlo method estimates the strong doubly dipolar regime with accuracy. In contrast, the Gross-Pitaevskii equation does not seize quantum fluctuations in full. We also provide a complete description of the system's quantum behavior in a wide range of parameters. When the system forms a droplet, the superfluid fraction exhibits an anisotropic behavior if compared to the usual Bose gas regime. Interestingly, we observe that the transition temperature from thermal gas to droplet is higher than that of the thermal gas to a Bose-Einstein condensate, indicating the robustness of the droplet against thermal fluctuations. Further, we investigate the anisotropic behavior of the superfluid fraction during the structural transition from a pancake to a cigar-shaped droplet by varying the ratio between electric and magnetic dipole interaction strengths. Our findings furnish evidence that the stability of doubly dipolar Bose-Einstein condensates can be detected in experiments by means of dysprosium atoms.

By combining first-principles path integral Monte Carlo methods and mean-field techniques, we explore the properties of cylindrically trapped doubly-dipolar Bose gases. We first verify the emergence of a pancake quantum droplet at low temperatures, validating previously mean-field calculations. In a regime of small doubly-dipolar interactions, first-principles calculations agree with the generalized Gross-Pitaevskii equation. Such an accordance disappears in a large interaction limit. Here the path integral Monte Carlo estimates the strong doubly-dipolar regime with accuracy. On the contrary, the Gross-Pitaevskii equation does not seize quantum fluctuations in full. We also provide a complete description of the system's quantum behavior in a wide range of parameters. When the system forms a droplet, the superfluid fraction exhibits an anisotropic behavior if compared to the usual Bose gas regime. Interestingly, we observe that the transition temperature from thermal gas to droplet results higher than that of the thermal gas to a Bose-Einstein condensate, indicating the robustness of the droplet against thermal fluctuations. Further, we investigate the anisotropic behavior of the superfluid fraction during the structural transition from a pancake to a cigar-shaped droplet by varying the ratio between electric and magnetic dipole interaction strengths. Our findings furnish evidence that the stability of doubly-dipolar Bose-Einstein condensates can be detected in experiments by means of dysprosium atoms.

Confinement can have a considerable effect on the behavior of particle systems, and is therefore an effective way to discover new phenomena. A notable example is a system of identical bosons at low temperature under an external field mimicking an isotropic bubble trap, which constrains the particles to a portion of space close to a spherical surface. Using Path Integral Monte Carlo simulations, we examine the spatial structure and superfluid fraction in two emblematic cases. First, we look at soft-core bosons, finding the existence of supersolid cluster arrangements with polyhedral symmetry; we show how different numbers of clusters are stabilized depending on the trap radius and the particle mass, and we characterize the temperature behavior of the cluster phases. A detailed comparison with the behavior of classical soft-core particles is provided too. Then, we examine the case, of more immediate experimental interest, of a dipolar condensate on the sphere, demonstrating how a quasi-one-dimensional supersolid of clusters is formed on a great circle for realistic values of density and interaction parameters. Crucially, this supersolid phase is only slightly disturbed by gravity. We argue that the predicted phases can be revealed in magnetic traps with spherical-shell geometry, possibly even in a lab on Earth. Our results pave the way for future simulation studies of correlated quantum systems in curved geometries.

Confinement can have a considerable effect on the behavior of particle systems and is therefore an effective way to discover new phenomena. A notable example is a system of identical bosons at low temperature under an external field mimicking an isotropic bubble trap, which constrains the particles to a portion of space close to a spherical surface. Using path integral Monte Carlo simulations, we examine the spatial structure and superfluid fraction in two emblematic cases. First, we look at soft-core bosons, finding the existence of supersolid cluster arrangements with polyhedral symmetry; we show how different numbers of clusters are stabilized depending on the trap radius and the particle mass, and we characterize the temperature behavior of the cluster phases. A detailed comparison with the behavior of classical soft-core particles is provided too. Then, we examine the case, of more immediate experimental interest, of a dipolar condensate on the sphere, demonstrating how a quasi-one-dimensional supersolid of clusters is formed on a great circle for realistic values of density and interaction parameters. Crucially, this supersolid phase is only slightly disturbed by gravity. We argue that the predicted phases can be revealed in magnetic traps with spherical-shell geometry, possibly even in a lab on Earth. Our results pave the way for future simulation studies of correlated quantum systems in curved geometries.