Role of Bose statistics in crystallization and quantum jamming.

The indistinguishability of particles is a crucial factor destabilizing crystalline order in Bose systems. We describe this effect in terms of damped quasiparticle modes and in the dual language of Feynman paths, and illustrate it by first-principles simulations of dipolar bosons and bulk condensed 4He. The first major implication is that, contrary to conventional wisdom, zero-point motion alone cannot prevent 4He crystallization at near zero pressure. Second, Bose statistics leads to quantum jamming at finite temperature, dramatically enhancing the metastability of superfluid glasses. Only studies of indistinguishable particles can reliably address these issues.

Excitation spectrum of a supersolid.

Conclusive experimental evidence of a supersolid phase in any known condensed matter system is presently lacking. On the other hand, a supersolid phase has been recently predicted for a system of spinless bosons in continuous space, interacting via a broad class of soft-core, repulsive potentials. Such an interaction can be engineered in assemblies of ultracold atoms, providing a well-defined pathway to the unambiguous observation of this fascinating phase of matter. In this Letter, we study by first principles computer simulations the elementary excitation spectrum of the supersolid, and show that it features two distinct modes, namely, a solidlike phonon and a softer collective excitation, related to broken translation and gauge symmetry, respectively.

Strongly correlated gases of Rydberg-dressed atoms: quantum and classical dynamics.

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.

Supersolid droplet crystal in a dipole-blockaded gas.

A novel supersolid phase is predicted for an ensemble of Rydberg atoms in the dipole-blockade regime, interacting via a repulsive dipolar potential softened at short distances. Using exact numerical techniques, we study the low-temperature phase diagram of this system, and observe an intriguing phase consisting of a crystal of mesoscopic superfluid droplets. At low temperature, phase coherence throughout the whole system, and the ensuing bulk superfluidity, are established through tunnelling of identical particles between neighboring droplets.

Local stress and superfluid properties of solid 4He.

We provide a semiquantitative tool, derived from first-principles simulations, for answering the question of whether certain types of defects in solid 4He support mass superflow. Although ideal crystals of 4He are not supersolid, the gap for vacancy creation closes when applying a moderate stress. While a homogeneous system becomes unstable at this point, the stressed core of crystalline defects (dislocations and grain boundaries) can turn superfluid.

Luttinger liquid in the core of a screw dislocation in helium-4.

On the basis of first-principles Monte Carlo simulations we find that the screw dislocation along the hexagonal axis of an hcp 4He crystal features a superfluid (at T-->0) core. This is the first example of a regular quasi-one-dimensional supersolid--the phase featuring both translational and superfluid orders, and one of the cleanest cases of a Luttinger-liquid system. In contrast, the same type of screw dislocation in solid H2 is insulating.

Superfluidity of grain boundaries in solid 4He.

By large-scale quantum Monte Carlo simulations we show that grain boundaries in 4He crystals are generically superfluid at low temperature, with a transition temperature of the order of approximately 0.5 K at the melting pressure; nonsuperfluid grain boundaries are found only for special orientations of the grains. We also find that close vicinity to the melting line is not a necessary condition for superfluid grain boundaries, and a grain boundary in direct contact with the superfluid liquid at the melting curve is found to be mechanically stable and the grain-boundary superfluidity observed by Sasaki et al. [Science 313, 1098 (2006)10.1126/science.1130879] is not just a crack filled with superfluid.

Worm algorithm and diagrammatic Monte Carlo: a new approach to continuous-space path integral Monte Carlo simulations.

A detailed description is provided of a new worm algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general path integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid 4He in two and three dimensions, as well as the calculation of the chemical potential of hcp 4He.

Fate of vacancy-induced supersolidity in 4He.

The supersolid state of matter, exhibiting nondissipative flow in solids, has been elusive for 35 years. The recent discovery of a nonclassical moment of inertia in solid 4He by Kim and Chan provided the first experimental evidence, although the interpretation in terms of supersolidity of the ideal crystal phase remains a subject to debate. Using quantum Monte Carlo methods we investigate the long-standing question of vacancy-induced superflow and find that vacancies in a 4He crystal phase separate instead of forming a supersolid. On the other hand, nonequilibrium vacancies relaxing on defects of polycrystalline samples could provide an explanation for the experimental observations.

Phase separation in mixtures of hard core bosons.

A theoretical investigation of boson versions of the t-J and t-J(z) models on the square lattice is carried out. In the t-J(z) model, phase separation between a hole-rich and a hole-free phase occurs, at sufficiently low hole doping, for arbitrarily small values of J(z). The boson t-J model, instead, features a uniform ground state at any doping for J/t< or =1.5. No evidence of a striped ground state is found. Relevance of this study to the corresponding fermion models is discussed. Fermi statistics is found to enhance the tendency toward phase separation; in particular, phase separation is predicted, at low doping, in the fermion t-J(z) model, at all values of J(z).

Helium in one-dimensional nanopores: free dispersion, localization, and commensurate/incommensurate transitions with nonrigid orbitals.

The single-particle states of helium within a bundle of carbon nanotubes can range from nearly free-particle dispersion to localization, even within a single bundle. At intermediate effective masses, the corrugation in the external potential can be comparable to the intrasite He-He hard-core interaction. This results in a commensurate/incommensurate transition, where the mobility of the doubly occupied domain-wall solitons at high density greatly exceeds the corresponding hole mobility below the transition.

Condensation of helium in nanotube bundles

Helium atoms are strongly attracted to the interstitial channels within a bundle of carbon nanotubes. The strong corrugation of the axial potential within a channel can produce a lattice gas system wherein the weak mutual attraction between atoms in neighboring channels induces a transition to an anisotropic condensed phase. At low temperatures, the specific heat of the adsorbate phase (with fewer than 2% of the atoms) greatly exceeds that of the host.

Equation of state of solid 3He

We present results of diffusion Monte Carlo calculations for the bcc and hcp phases of solid 3He, using a recent ab initio interatomic potential, including two- and three-body terms. This potential is found to yield an equation of state for condensed 4He in excellent agreement with experiment, in a wide density range. For 3He, we find a systematic discrepancy, worth 0.7 K, between our computed equation of state and a commonly accepted experimental one. We attribute such a discrepancy to an improper choice of reference energy in the determination of the experimental equation of state.