Lattice Polarons across the Superfluid to Mott Insulator Transition.

We study the physics of a mobile impurity confined in a two-dimensional lattice, moving within a Bose-Hubbard bath at zero temperature. Exploiting the quantum Gutzwiller formalism, we develop a beyond-Fröhlich model of the bath-impurity interaction to describe the properties of the polaronic quasiparticle formed by the dressing of the impurity by quantum fluctuations of the bath. We find a stable and well-defined polaron throughout the entire phase diagram of the bath, except for the very low tunneling limit of the hard-core superfluid. The polaron properties are highly sensitive to the different universality classes of the quantum phase transition between the superfluid and Mott insulating phases, providing an unambiguous probe of correlations and collective modes in a quantum critical many-body environment.

Particle-Hole Character of the Higgs and Goldstone Modes in Strongly Interacting Lattice Bosons.

We study the low-energy excitations of the Bose-Hubbard model in the strongly interacting superfluid phase using a Gutzwiller approach. We extract the single-particle and single-hole excitation amplitudes for each mode and report emergent mode-dependent particle-hole symmetry on specific arc-shaped lines in the phase diagram connecting the well-known Lorentz-invariant limits of the Bose-Hubbard model. By tracking the in-phase particle-hole symmetric oscillations of the order parameter, we provide an answer to the long-standing question about the fate of the pure amplitude Higgs mode away from the integer-density critical point. Furthermore, we point out that out-of-phase symmetric oscillations in the gapless Goldstone mode are responsible for a full suppression of the condensate density oscillations. Possible detection protocols are also discussed.

Pair-supersolid phase in a bilayer system of dipolar lattice bosons.

The competition between tunneling and interactions in bosonic lattice models generates a whole variety of different quantum phases. While, in the presence of a single species interacting via on site interaction, the phase diagram presents only superfluid or Mott insulating phases, for long-range interactions or multiple species, exotic phases such as supersolid or pair-superfluid appear. In this Letter, we show for the first time that the coexistence of effective multiple species and long-range interactions leads to the formation of a novel pair-supersolid phase, namely, a supersolid of composites. We propose a possible implementation with dipolar bosons in a bilayer two-dimensional optical lattice.

Metastable states of a gas of dipolar bosons in a 2D optical lattice.

We investigate the physics of dipolar bosons in a two-dimensional optical lattice. It is known that due to the long-range character of dipole-dipole interaction, the ground state phase diagram of a gas of dipolar bosons in an optical lattice presents novel quantum phases, like checkerboard and supersolid phases. In this Letter, we consider the properties of the system beyond its ground state, finding that it is characterized by a multitude of almost degenerate metastable states, often competing with the ground state. This makes dipolar bosons in a lattice similar to a disordered system and opens possibilities of using them as quantum memories.

Quantum fluctuations and collective oscillations of a Bose-Einstein condensate in a 2D optical lattice.

We use Bogoliubov theory to calculate the beyond mean field correction to the equation of state of a weakly interacting Bose gas in the presence of a tight 2D optical lattice. We show that the lattice induces a characteristic 3D to 1D crossover in the behavior of quantum fluctuations. Using the hydrodynamic theory of superfluids, we calculate the corresponding shift of the collective frequencies of a harmonically trapped gas. We find that this correction can be of the order of a few percent and hence easily measurable in current experiments. The behavior of the quantum depletion of the condensate is also discussed.

Efficient and robust initialization of a qubit register with fermionic atoms.

We show that fermionic atoms have crucial advantages over bosonic atoms in terms of loading in optical lattices for use as a possible quantum computation device. After analyzing the change in the level structure of a nonuniform confining potential as a periodic potential is superimposed to it, we show how this structure combined with the Pauli principle and fermion degeneracy can be exploited to create unit occupancy of the lattice sites with very high efficiency.

Expansion of an interacting fermi gas.

We study the expansion of a dilute ultracold sample of fermions initially trapped in an anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular, the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similar to what happens with Bose-Einstein condensates. Vice versa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.