Sebastiano Pilati

Phase separation in a polarized Fermi gas at zero temperature.

We investigate the phase diagram of asymmetric two-component Fermi gases at zero temperature as a function of polarization and interaction strength. The equations of state of the uniform superfluid and normal phase are determined using quantum Monte Carlo simulations. We find three different mixed states, where the superfluid and the normal phase coexist in equilibrium, corresponding to phase separation between (a) the polarized superfluid and the fully polarized normal gas, (b) the polarized superfluid and the partially polarized normal gas, and (c) the unpolarized superfluid and the partially polarized normal gas.

Fermi-Liquid Behavior of the Normal Phase of a Strongly Interacting Gas of Cold Atoms

We measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit and compare it to quantum Monte Carlo calculations. Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids. We show that these measurements shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas.

Critical Temperature of Interacting Bose Gases in Two and Three Dimensions

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.

Dilute Bose gas with correlated disorder: a path integral Monte Carlo study

We investigate the thermodynamic properties of a dilute Bose gas in a correlated random potential using exact path integral Monte Carlo methods. The study is carried out in continuous space and disorder is produced in the simulations by a three-dimensional (3D) speckle pattern with tunable intensity and correlation length. We calculate the shift of the superfluid transition temperature due to disorder and we highlight the role of quantum localization by comparing the critical chemical potential with the classical percolation threshold. The equation of state of the gas is determined in the regime of strong disorder, where superfluidity is suppressed and the normal phase exists down to very low temperatures. We find a T2 dependence of the energy in agreement with the expected behavior in the Bose glass phase. We also discuss the major role played by the disorder correlation length and we make contact with a Hartree–Fock mean-field approach that holds if the correlation length is very large. The density profiles are analyzed as a function of temperature and interaction strength. Effects of localization and the depletion of the order parameter are emphasized in the comparison between local condensate and total density. At very low temperature, we find that the energy and the particle distribution of the gas are very well described by the T=0 Gross–Pitaevskii theory, even in the regime of very strong disorder.

The Beliaev technique for a weakly interacting Bose gas

Aiming at simplicity of explicit equations and, at the same time, controllable accuracy of the theory, we present our results for all the thermodynamic quantities and correlation functions for a weakly interacting Bose gas at short-to-intermediate distances obtained within an improved version of Beliaevs diagrammatic technique. With a controllably small (but essentially finite) Bogoliubovs symmetry-breaking term, Beliaevs diagrammatic technique becomes regular in the infrared limit. Up to higher-order terms (for which we present parametric order-of-magnitude estimates), the partition function and entropy of the system formally correspond to those of a non-interacting bosonic (pseudo-)Hamiltonian with a temperature-dependent Bogoliubov-type dispersion relation. Away from the fluctuation region, this approach provides the most accurate?in fact, the best possible within the Bogoliubov-type pseudo-Hamiltonian framework?description of the system with controlled accuracy. It produces accurate answers for the off-diagonal correlation functions up to distances where the behavior of correlators is controlled by generic hydrodynamic relations and, thus, can be accurately extrapolated to arbitrarily large scales. In the fluctuation region, the non-perturbative contributions are given by universal (for all weakly interacting U(1) systems) constants and scaling functions, which can be obtained separately?by simulating classical U(1) models?and then used to extend the description of the weakly interacting Bose gas to the fluctuation region. The technique works in all spatial dimensions, and we explicitly checked the validity of this technique against first-principle Monte Carlo simulations for various thermodynamic properties and the single-particle density matrix.

Superfluid Transition in a Bose Gas with Correlated Disorder

The superfluid transition of a three-dimensional gas of hard-sphere bosons in a disordered medium is studied using quantum Monte Carlo methods. Simulations are performed in continuous space both in the canonical and in the grand-canonical ensemble. At fixed density we calculate the shift of the transition temperature as a function of the disorder strength, while at fixed temperature we determine both the critical chemical potential and the critical density separating normal and superfluid phases. In the regime of strong disorder the normal phase extends up to large values of the degeneracy parameter, and the critical chemical potential exhibits a linear dependence in the intensity of the random potential. The role of interactions and disorder correlations is also discussed.

Quantum Monte Carlo simulation of a two-dimensional Bose gas

The equation of state of a homogeneous two-dimensional Bose gas is calculated using quantum Monte Carlo methods. The low-density universal behavior is investigated using different interatomic model potentials, both finite ranged and strictly repulsive and zero ranged, supporting a bound state. The condensate fraction and the pair distribution function are calculated as a function of the gas parameter, ranging from the dilute to the strongly correlated regime. In the case of the zero-range pseudopotential we discuss the stability of the gaslike state for large values of the two-dimensional scattering length, and we calculate the critical density where the system becomes unstable against cluster formation.

Equation of state of an interacting bose gas at finite temperature : A path-integral Monte Carlo study

By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same s-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.

Zero-temperature equation of state and phase diagram of repulsive fermionic mixtures

We compute the zero-temperature equation of state of a mixture of two fermionic atomic species with repulsive interspecies interactions using second-order perturbation theory. We vary the interaction strength, the population and the mass imbalance, and we analyze the competition between different states: homogeneous, partially separated and fully separated. The canonical phase diagrams are determined for various mass ratios, including the experimentally relevant case of the 6Li-40K mixture. We find substantial differences with respect to the equal-mass case: phase separation occurs at weaker interaction strength, and the partially-separated state can be stable even in the limit of a large majority of heavy atoms. We highlight the effects due to correlations by making comparison with previous mean-field results.

One-dimensional repulsive Fermi gas in a tunable periodic potential

By using unbiased continuous-space quantum Monte Carlo simulations, we investigate the ground-state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yangs theory for the energy of a homogeneous Fermi gas [C.-N. Yang, Phys. Rev. Lett. 19, 1312 (1967)] is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model [E. H. Lieb and F. Y. Wu, Phys. Rev. Lett. 20, 1445 (1968)], comparing two approaches to map the continuous space to the discrete-lattice model: The first is based on (noninteracting) Wannier functions and the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs and also in very shallow OLs if the interaction strength approaches the Tonks-Girardeau limit. In deep OLs we find quantitative agreement with density-matrix renormalization-group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi-long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.