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arXiv:1107.1103 · Physical Review A

Dipolar bosons on an optical lattice ring

Michał Maik, Pierfrancesco Buonsante, A. Vezzani, Jakub Zakrzewski

Published Nov 14, 2011• 20 citations
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Abstract

We consider an ultrasmall system of polarized bosons on an optical lattice with a ring topology, interacting via long-range dipole-dipole interactions. Dipoles polarized perpendicular to the plane of the ring reveal sharp transitions between different density-wave phases. As the strength of the dipolar interactions is varied, the behavior of the transitions is first-order-like. For dipoles polarized in the plane of the ring, the transitions between possible phases show pronounced sensitivity to the lattice depth. The abundance of possible configurations may be useful for quantum-information applications.

DOI
10.1103/physreva.84.053615

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We consider an ultrasmall system of polarized bosons on an optical lattice with a ring topology, interacting via long-range dipole-dipole interactions. Dipoles polarized perpendicular to the plane of the ring reveal sharp transitions between different density-wave phases. As the strength of the dipolar interactions is varied, the behavior of the transitions is first-order-like. For dipoles polarized in the plane of the ring, the transitions between possible phases show pronounced sensitivity to the lattice depth. The abundance of possible configurations may be useful for quantum-information applications.
Strongly interacting finite ensembles of dipolar bosons in commensurately filled one-dimensional optical lattices exhibit diverse quantum phases that are rich in physics. As the strength of the long-range boson–boson interaction increases, the system transitions across different phases: from a superfluid, through a Mott-insulator and a Tonks–Girardeau gas to a crystal state. The signature of these phases and their transitions can be unequivocally identified by an experimentally detectable order parameter, recently described in Phys. Rev. A 98 235301 (2018 [ 33 ]). Herein, we calculate the momentum distributions and the normalized Glauber correlation functions of dipolar bosons in a one-dimensional optical lattice in order to characterize all their phases. To understand the behavior of the correlations across the phase transitions, we first investigate the eigenfunctions and eigenvalues of the one-body reduced density matrix as a function of the dipolar interaction strength. We then analyze the real- and momentum-space Glauber correlation functions, thereby gaining a spatially and momentum-resolved insight into the coherence properties of these quantum phases. We find an intriguing structure of non-local correlations that, independently of other observables, reveal the phase transitions of the system. In particular, spatial localization and momentum delocalization accompany the formation of correlated islands in the density as interactions become stronger. Our study showcases that precise control of intersite correlations is possible through the manipulation of the depth of the lattice, while intrasite correlations can be influenced by changing the dipolar interaction strength.
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The superfluid--Mott-insulator phase transition of dipolar bosons in optical lattice is analyzed. By using the Bogoliubov approach and decoupling approximation, the energy spectrum and zero-temperature phase diagram of dipolar bosonic atoms in an optical lattice are obtained analytically. The results show that in these systems the superfluid--Mott-insulator phase transition can be induced by tuning the dipole-dipole interaction and the position of the phase boundary can be moved when the on-site interaction is varied. Corresponding to a large on-site interaction, the dipole-dipole interaction is attractive near the critical point of the superfluid--Mott-insulator phase transition.
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.
solitons, vortices, and topological excitations. PACS. 03.75.Nt – Other Bose-Einstein condensation phenomena. Abstract. – Motivated by the recent experiment on the Bose-Einstein condensation of 52 Cr atoms with long-range dipolar interactions (Werner J. et al., Phys. Rev. Lett., 94 (2005) 183201), we consider a system of bosons with repulsive nearest and next-nearest neighbor interactions in an optical lattice. The ground state phase diagram, calculated using the Gutzwiller ansatz, shows, apart from the superfluid (SF) and the Mott insulator (MI), two modulated phases, i.e., the charge density wave (CDW) and the supersolid (SS). Excitation spectra are also calculated which show a gap in the insulators, gapless, phonon mode in the superfluid and the supersolid, and a mode softening of superfluid excitations in the vicinity of the modulated phases. We discuss the possibility of observing these phases in cold dipolar atoms and propose experiments to detect them. The recent observation [2] of quantum phase transition of interacting bosons in an optical lattice has given a new impetus to the study of correlated bosons. The possibility of manipulating both the interactions among the constituents as well as disorder in the system