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Quantum phase transition in vortex lattices and mobile impurity in mixed-dimension mixtures

R. H. Chaviguri

Published Apr 9, 2021• 0 citations
Publisher

Abstract

The most recent advances in the ultracold atoms experimental techniques allowed the production of the ultracold gases mixtures in the laboratory.Motivated by these developments, in this project we study systems involving two ultracold atoms mixtures.In the first part, we consider a Bose-Einstein condensate (BEC) with a vortex lattice weakly interacting with another utracold dilute bosonic gas.We apply the Bose-Hubbard (BH) model to describe the atoms of the minority species trapped in the vortex lattice.As occurs in a static optical lattice, we predict the quantum phase transition between the Mott insulator to superfluid phases, which now can be controlled by changing the intra and inter-species scattering length.Considering the intrinsic lattice dynamics, the Tkachenko modes of the vortex lattice, we derive an extended BH Hamiltonian and analyzed new properties in the phase diagram that arise from a long-range attractive potential and density-dependent hopping.In the second part, we study the properties of a mobile impurity living in two dimensions and interacting with a 2 and 3 BEC cloud.The resulting impurity-bath interaction leads to the formation of a polaron (particle "dressed" by the phonon excitations of the BEC), which is characterized by its spectral function.We determine the energy dispersion, spectral weight, effective mass and lifetime of the polaron.These analysis allowed us to identify a dissipative regime for higher impurity velocities, with an increasing scattering rate of phonons.In addition, we observe a self-localization regime for lower impurity velocities which may be a signature for molecular formation.In spite of qualitatively similar results obtained for the 2 and 3 bath, we had differences related to the self-localization and dissipation limits, that allowed us to conclude that a 2 BEC bath would be a better candidate to observe stable quasi-particle properties.

DOI
10.11606/t.76.2021.tde-03092021-150549

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In this thesis we investigate the properties of mixtures of Bose gases in one dimensions at zero temperature using quantum Monte-Carlo methods. First we investigate the limiting case of an impurity interacting with an atomic bath. We characterize the impurity, by calculating its effective mass, binding energy as well as the contact parameter between the impurity and 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. Then we describe uniform balanced mixtures with repulsive interactions. We investigate the miscibility phase diagram of the two components and find that correlations do not alter the phase diagram predicted by mean-field theories. We investigate the Andreev-Bashkin effect , a non-dissipative drag between the the two components of the gas and find that the drag becomes very large in the strongly interacting regime. In non-homogeneous systems we also investigate the frequency of the spin-dipole mode. Finally we describe mixtures with attractive inter-species interactions, where one can obtain a liquid ground state because of the competition between the inter-species attraction and intra-species repulsion. We characterize the the liquid and we find that the liquid state can be formed if the ratio of coupling strengths between inter-species attractive and intra-species repulsive interactions exceeds a critical value.
We investigate the quantum phases of ultracold atoms trapped in a vortex lattice using a mixture of two bosonic species (AAA and BBB), in the presence of an artificial gauge field. Heavy atoms of species BBB are confined in the array of vortices generated in species AAA, and they are described through a Bose-Hubbard model. In contrast to the optical-lattice setups, the vortex lattice has an intrinsic dynamics, given by its Tkachenko modes. Including these quantum fluctuations in the effective model for BBB atoms yields an extended Bose-Hubbard model, with an additional ``phonon'' -mediated long-range attraction. The ground-state phase diagram of this model is computed through a variational Ansatz and the quantum Monte Carlo technique. When compared with the ordinary Bose-Hubbard case, the long-range interatomic attraction causes a shift and resizing of the Mott-insulator regions. Finally, we discuss the experimental feasibility of the proposed scheme, which relies on the proper choice of the atomic species and on a large control of physical parameters, like the scattering lengths and the vorticity.
We map out the global phase diagram of a single mobile impurity in the two-dimensional Bose-Hubbard model, spanning the bath evolution from a compressible superfluid (SF) to an incompressible Mott insulator (MI) and the full range of impurity-bath coupling. Using sign-problem-free worm-algorithm quantum Monte Carlo, we identify two distinct self-trapping mechanisms that organize the entire diagram. In the compressible SF, increasing impurity-bath coupling ∣Uib∣|U_{\mathrm{ib}}|∣Uib​∣ drives an interaction-driven self-trapping crossover signaled by a collapse of the \emph{impurity} winding number: a light, extended polaron evolves continuously into a heavy polaron and ultimately into a self-trapped state -- a repulsive \emph{saturated bubble} or an attractive \emph{bound cluster} -- even while the bath remains globally superfluid, demonstrating self-trapping without any bath phase transition. By contrast, when the bath is tuned across the SF-MI transition at fixed UibU_{\mathrm{ib}}Uib​, localization is compressibility controlled. The vanishing bath compressibility quenches long-wavelength density redistribution and suppresses polaronic dressing, converting the SF polaron into a weakly dressed, nearly free defect upon entering the MI when ∣Uib∣≤8.0|U_{\mathrm{ib}}| \le 8.0∣Uib​∣≤8.0. Then increasing ∣Uib∣|U_{\mathrm{ib}}|∣Uib​∣ triggers a distinct Mott-specific route: the impurity binds a quantized vacancy or particle excitation, manifested by discrete changes ΔNb=±1ΔN_b=\pm1ΔNb​=±1 in the total bath occupation. Together, our results provide a unified microscopic picture of impurity self-trapping in correlated lattice bosons, governed by winding collapse in the SF and by compressibility loss and defect quantization across the SF-MI boundary.
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Mobile impurity atoms immersed in Bose–Einstein condensates provide a new platform for exploring Bose polarons. Recent experimental advances in the field of ultracold atoms make it possible to realize such systems with highly tunable microscopic parameters and to explore equilibrium and dynamical properties of polarons using a rich toolbox of atomic physics. In this paper we present a detailed theoretical analysis of Bose polarons in one-dimensional systems of ultracold atoms. By combining a non-perturbative renormalization group approach with numerically exact diffusion Monte Carlo calculations we obtain not only detailed numerical results over a broad range of parameters but also qualitative understanding of different regimes of the system. We find that an accurate description of Bose polarons requires the inclusion of two-phonon scattering terms which go beyond the commonly used Fröhlich model. Furthermore we show that when the Bose gas is in the strongly interacting regime, one needs to include interactions between the phonon modes. We use several theoretical approaches to calculate the polaron energy and its effective mass. The former can be measured using radio-frequency spectroscopy and the latter can be studied experimentally using impurity oscillations in a harmonic trapping potential. We compare our theoretical results for the effective mass to the experiments by Catani et al (2012 Phys. Rev. A 85 023623). In the weak-to-intermediate coupling regimes we obtain excellent quantitative agreement between theory and experiment, without any free fitting parameter. We supplement our analysis by full dynamical simulations of polaron oscillations in a shallow trapping potential. We also use our renormalization group approach to analyze the full phase diagram and identify regions that support repulsive and attractive polarons, as well as multi-particle bound states.