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Register a new userQuantum Monte Carlo study of the dynamic structure factor in the gas and crystal phase of hard-sphere bosons
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We investigate the dynamic structure factor of a system of Bose particles at zero temperature using quantum Monte Carlo methods. Interactions are modeled using a hard-sphere potential of size $a$ and simulations are performed for values of the gas parameter $na^3$ ranging from the dilute regime up to densities $n$ where the thermodynamically stable phase is a solid. With increasing density we observe a crossover of the dispersion of elementary excitations from a Bogoliubov-like spectrum to a phonon--maxon--roton curve and the emergence of a broad multiphonon contribution accompanying the single-quasiparticle peak. In particular, for $na^3=0.2138$, which corresponds to superfluid $^4$He at equilibrium density, the extracted spectrum turns out to be in good agreement with the experimental energy--momentum dispersion relation in the roton region and for higher momenta. The behavior of the spectral function at the same density in the stable solid and metastable gas phase above the freezing point is also discussed.
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The dynamic structure factor is a central quantity describing the physics of quantum many-body systems, capturing structure and collective excitations of a material. In condensed matter, it can be measured via inelastic neutron scattering, which is an energy-resolving probe for the density fluctuations. In ultracold atoms, a similar approach could so far not be applied due to the diluteness of the system. Here, we report on a direct, real-time and non-destructive measurement of the dynamic structure factor of a quantum gas exhibiting cavity-mediated long-range interactions. The technique relies on inelastic scattering of photons, stimulated by the enhanced vacuum field inside a high finesse optical cavity. We extract the density fluctuations, their energy and lifetime while the system undergoes a structural phase transition. We observe an occupation of the relevant quasi-particle mode on the level of a few excitations, and provide a theoretical description of this dissipative quantum many-body system.
We studied the superfluid-to-Mott insulator transition for bosonic hard spheres loaded in asymmetric three-dimensional optical lattices by means of diffusion Monte Carlo calculations. The onset of the transition was monitored through the change in the chemical potential around the density corresponding to one particle per potential well. With this method, we were able to reproduce the results given in the literature for three-dimensional symmetric lattices and for systems whose asymmetry makes them equivalent to a set of quasi-one dimensional tubes. The location of the same transition for asymmetric systems akin to a stack of quasi-two dimensional lattices will be also given. Our results were checked against those given by a Bose-Hubbard model for similar arrangements.
We present a theoretical study based upon quantum Monte Carlo methods of the Bose polaron in one-dimensional systems with contact interactions. In this instance of the problem of a single impurity immersed in a quantum bath, the medium is a Lieb-Liniger gas of bosons ranging from the weakly interacting to the Tonks-Girardeau regime, whereas the impurity is coupled to the bath via a different contact potential producing both repulsive and attractive interactions. Both the case of a mobile impurity, having the same mass as the particles in the medium, and of a static impurity with infinite mass are considered. We make use of exact numerical techniques that allow us to calculate the ground-state energy of the impurity, its effective mass as well as the contact parameter between the impurity and the bath. These quantities are investigated as a function of the strength of interactions between the impurity and the bath and within the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. This heavy impurity hardly moves within the medium, thereby realizing the self-localization regime of the Landau-Pekar polaron. Furthermore, we compare our results with predictions of perturbation theory valid for weak interactions and with exact solutions available when the bosons in the medium behave as impenetrable particles.
The ground state properties of spin-polarized deuterium (D$downarrow$) at zero temperature are obtained by means of the diffusion Monte Carlo calculations within the fixed-node approximation. Three D$downarrow$ species have been investigated (D$downarrow_1$, D$downarrow_2$, D$downarrow_3$), corresponding respectively to one, two and three equally occupied nuclear spin states. Influence of the backflow correlations on the ground state energy of the systems is explored. The equilibrium densities for D$downarrow_2$ and D$downarrow_3$ liquids are obtained and compared with ones obtained in previous approximate prediction. The density and the pressure at which the gas-liquid phase transition occurs at $T$=0 is obtained for D$downarrow_1$.
This Dissertation presents results of a thorough study of ultracold bosonic and fermionic gases in three-dimensional and quasi-one-dimensional systems. Although the analyses are carried out within various theoretical frameworks (Gross-Pitaevskii, Bethe ansatz, local density approximation, etc.) the main tool of the study is the Quantum Monte Carlo method in different modifications (variational Monte Carlo, diffusion Monte Carlo, fixed-node Monte Carlo methods). We benchmark our Monte Carlo calculations by recovering known analytical results (perturbative theories in dilute limits, exactly solvable models, etc.) and extend calculations to regimes, where the results are so far unknown. In particular we calculate the equation of state and correlation functions for gases in various geometries and with various interatomic interactions.
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