We study different solid phases of 4 He, by means of Path Integral Monte Carlo simulations based on a recently developed worm algorithm. Our study includes simulations that start off from a high-T gas phase, which is then "quenched" down to T =0.2 K. The low-T properties of the system crucially depend on the initial state. While an ideal hcp crystal is a clear-cut insulator, the disordered system freezes into a superglass, i.e., a metastable amorphous solid featuring off-diagonal long-range order and superfluidity. He is still controversial, both at the experimental and theoretical levels. Two of us have recently proven that, irrespective of its microscopic structure, any supersolid crystal should contain gapless vacancies and/or interstitials [2]. In other words, any continuous-space supersolid is generically incommensurate (i.e., the number of atoms per unit cell is not an integer) and squeezeable, i.e., by applying pressure it should be possible to squeeze matter from a container with supersolid into a buffer volume containing the same supersolid. However, this very experiment has yielded a negative result for solid 4 He [3].A wealth of numerical studies clearly indicate that 4 He is a commensurate (thus insulating) crystal. The finite activation energy of a vacancy computed numerically is large, ∼ 15 K, and claimed consistent with the experimental observations [4]. The activation energy of an interstitial, ∼ 50 K [5], is significantly larger than that of a vacancy. A simulation study of exchanges in an ideal hcp crystal [5], yielded indirect evidence that the system is not superfluid. In sharp contrast, the variational (T =0) calculation of Ref. 6 claims a finite condensate fraction in the commensurate 4 He crystal. Thus, additional investigation is warranted.The experiment of Kim and Chan itself has revealed a number of facts pointing to a strongly inhomogeneous scenario of superfluidity, chiefly the contaminating effect of a small concentration of 3 He, and non-XY behavior of the superfluid density at the critical temperature. The need of exploring inhomogeneous (metastable) scenarios of supersolidity, dictated both by theory and experiments, has already resulted in some relevant theoretical developments, revealing superfluid interfaces in a lattice solid [7] and a superfluid layer at the boundary between the 4 He crystal and a disordered substrate [8].The numerical observation of a metastable disordered supersolid, (a superglass phase of 4 He) is reported in the present Letter. To be specific in the definition, by glass we mean a spatially disordered (metastable) phase, indistinguishable from a solid [9] on a time scale much shorter than the typical relaxation time, t rel , which in turn should be dramatically longer than the inverse Debye frequency, ω −1 D . Superglass is the term that we use for such a phase, if it also displays superfluidity. Note that our definition of glass does not address the behavior of the system at time scales t > ∼ t rel , whereupon it may undergo structural relaxation into the...

We discuss techniques to generate long-range interactions in a gas of ground state alkali atoms, by weakly admixing excited Rydberg states with laser light. This provides a tool to engineer strongly correlated phases with reduced decoherence from inelastic collisions and spontaneous emission. As an illustration, we discuss the quantum phases of dressed atoms with dipole-dipole interactions confined in a harmonic potential, as relevant to experiments. We show that residual spontaneous emission from the Rydberg state acts as a heating mechanism, leading to a quantum-classical crossover.

The ongoing experimental and theoretical effort aimed at understanding non-classical rotational inertia in solid helium, has sparked renewed interest in the supersolid phase of matter, its microscopic origin and character, and its experimental detection. The purpose of this colloquium is a) to provide a general theoretical framework for the phenomenon of supersolidity and b) to review some of the experimental evidence for solid 4 He, and discuss its possible interpretation in terms of physical effects underlain by extended defects (such as dislocations). We provide quantitative support to our theoretical scenarios by means of first principle numerical simulations. We also discuss alternate avenues for the observation of the supersolid phase, not involving helium but rather assemblies of ultracold atoms.