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arXiv:1412.3615 · Journal of Physics B Atomic Molecular and Optical Physics

Localization–delocalization transition of dipolar bosons in a four-well potential

G. Mazzarella, Vittorio Penna

Published Mar 4, 2015• 5 citations
arXivHTMLPDF

Abstract

Abstract We study interacting dipolar atomic bosons in a four-well potential within a ring geometry and outline how a four-site Bose–Hubbard (BH) model including next–nearest–neighbor interaction terms can be derived for the above four-well system. We analyze the ground state of dipolar bosons by varying the strength of the (effective) interaction between particles in next–nearest-neighbor wells. We perform this analysis both numerically and analytically by reformulating the dipolar-boson model within the continuous variable picture applied in Buonsante et al (2011 Phys. Rev. A 84 061601(R)) . By using this approach we show that when the (effective) next-nearest–neighbor interaction crosses a precise value of the on-site interaction, the ground state exhibits a change from the uniform state (pertaining to the delocalization regime) to a macroscopic two-pulse state, with strongly localized bosons (localization regime). These predictions are confirmed by the results obtained by diagonalizing numerically the four-site extended BH Hamiltonian.

DOI
10.1088/0953-4075/48/6/065001

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Abstract We study interacting dipolar atomic bosons in a four-well potential within a ring geometry and outline how a four-site Bose–Hubbard (BH) model including next–nearest–neighbor interaction terms can be derived for the above four-well system. We analyze the ground state of dipolar bosons by varying the strength of the (effective) interaction between particles in next–nearest-neighbor wells. We perform this analysis both numerically and analytically by reformulating the dipolar-boson model within the continuous variable picture applied in Buonsante et al (2011 Phys. Rev. A 84 061601(R)) . By using this approach we show that when the (effective) next-nearest–neighbor interaction crosses a precise value of the on-site interaction, the ground state exhibits a change from the uniform state (pertaining to the delocalization regime) to a macroscopic two-pulse state, with strongly localized bosons (localization regime). These predictions are confirmed by the results obtained by diagonalizing numerically the four-site extended BH Hamiltonian.
We study interacting dipolar atomic bosons in a triple-well potential within a ring geometry. This system is shown to be equivalent to a three-site Bose-Hubbard model. We analyze the ground state of dipolar bosons by varying the effective on-site interaction. This analysis is performed both numerically and analytically by using suitable coherent-state representations of the ground state. The latter exhibits a variety of forms ranging from the SU(3) coherent state in the delocalization regime to a macroscopic catlike state with fully localized populations, passing for a coexistence regime where the ground state displays a mixed character. We characterize the quantum correlations of the ground state from the bipartition perspective. We calculate both numerically and analytically (within the previous coherent-state representation) the single-site entanglement entropy which, among various interesting properties, exhibits a maximum value in correspondence to the transition from the catlike to the coexistence regime. In the latter case, we show that the ground-state mixed form corresponds, semiclassically, to an energy exhibiting two almost-degenerate minima.
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We investigate the ground-state properties of a two-species condensate of interacting bosons in a double-well potential. Each atomic species is described by a two-space-mode Bose-Hubbard model. The coupling of the two species is controlled by the interspecies interaction W. To analyze the ground state when W is varied in both the repulsive ( W > 0 ) and the attractive ( W < 0 ) regime, we apply two different approaches. First we solve the problem numerically (i) to obtain an exact description of the ground-state structure and (ii) to characterize its correlation properties by studying (the appropriate extensions to the present case of) the quantum Fisher information, the coherence visibility and the entanglement entropy as functions of W. Then we approach analytically the description of the low-energy scenario by means of the Bogoliubov scheme. In this framework the ground-state transition from delocalized to localized species (with space separation for W > 0 , and mixing for W < 0 ) is well reproduced. These predictions are qualitatively corroborated by our numerical results. We show that such a transition features a spectral collapse reflecting the dramatic change of the dynamical algebra of the four-mode model Hamiltonian.
An atomic Josephson junction realized with dipolar bosons in a double-well potential can be described by an extended Bose-Hubbard model in which dipolar interactions generate an effective on-site interaction and nearest-neighbor pair tunneling. Using mean-field theory and exact diagonalization, we investigate how this correlated process affects zero-temperature equilibrium and dynamical properties of the system. In equilibrium, we show that pair tunneling induces ground-state parity modulations and significantly reshapes the phase diagram, producing qualitative changes in the quantum phase transitions toward NOON and phase-NOON states, as well as quantitative shifts of the critical points. Out of equilibrium, we demonstrate that it modifies the conditions for macroscopic quantum self-trapping, and assess its impact by comparing mean-field and fully quantum evolution, including the emergence of dynamical quantum phase transitions.
We consider a ring-shaped triple-well potential with few polar bosons with in-plane dipole orientation. By diagonalizing the extended Bose-Hubbard Hamiltonian, we investigate the ground-state properties of the system as we rotate the dipole angle and vary the on-site and dipole-dipole interaction strengths. We find that the anisotropic character of the dipolar interactions, as well as the competition between dipole and on-site interactions, leads to different ground states and that the entanglement between sites also depends on the number of particles. We further characterize the system by studying the condensed fraction and coherence properties for different polarization angles, highlighting the possible effect of the dipolar interaction as a manipulation tool.
This thesis is devoted to the study of dipolar lattice gases, i.e. many-body quantum systems of particles with a strong magnetic or electric dipole moment in optical lattices. Such systems are adequately described by the extended Hubbard model, which accounts for inter-site dipole-dipole interactions (DDI). These interactions, due to their long-range and anisotropic character, result in rich groundstate physics and intriguing dynamics as we illustrate in this thesis for the particular case of bosons in one- and quasi-one-dimensional lattices. We start by focusing on the non-trivial role played by the transversal confinement in one-dimensional dipolar lattice gases. We show that weakening the transversal confinement enhances beyond-nearest-neighbor interactions. Then, we analyze how this affects the ground-state physics of hard-core bosons with repulsive dipolar interactions and reveal quantitative differences to the standard case of the DDI falling off as 1/r^3 where r is the inter-particle distance. With attractive interactions, a new quantum liquid phase of self-bound lattice droplets emerges without the need for super-exchange processes. In the soft-core regime, proper consideration of the transversal confinement not only quantitatively shifts phase boundaries, but introduces novel phases with peculiar correlations in the site occupancies that may be either topological or topologically trivial. Furthermore, we study the effect of the transversal confinement on the dynamical properties of one-dimensional hard-core bosons at half-filling. We show in particular that the localization-to-delocalization transition induced by Hilbert space fragmentation resembles that of a system with an effective power-law decay different from 1/r^3 which can be controlled by the transversal confinement. To conclude this thesis, we analyze ground-state properties of hard-core dipolar bosons in a square ladder at unit rung filling with an energy bias between the two legs. We show that the interplay between the energy bias and the dipolar tail results in a peculiar topological quantum floating phase.