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arXiv:1103.3145 · Journal of Physics B Atomic Molecular and Optical Physics

Ultracold dipolar gases in optical lattices

C. Trefzger, C Menotti, Barbara Capogrosso-Sansone, Maciej Lewenstein

Published Sep 2, 2011• 174 citations
arXivHTMLPDF

Abstract

This tutorial is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules that interact via dipolar forces, and that are cooled below the quantum degeneracy temperature, typically in the nK range. When such a degenerate quantum gas is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur. These systems realize then extended Hubbard-type models, and can be brought to a strongly correlated regime. The physical properties of such gases, dominated by the long-range, anisotropic dipole-dipole interactions, are discussed using the mean-field approximations, and exact Quantum Monte Carlo techniques (the Worm algorithm).

DOI
10.1088/0953-4075/44/19/193001

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•Jan 1, 2009•0 citations
This tutorial is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules that interact via dipolar forces, and that are cooled below the quantum degeneracy temperature, typically in the nK range. When such a degenerate quantum gas is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur. These systems realize then extended Hubbard-type models, and can be brought to a strongly correlated regime. The physical properties of such gases, dominated by the long-range, anisotropic dipole-dipole interactions, are discussed using the mean-field approximations, and exact Quantum Monte Carlo techniques (the Worm algorithm).
This paper reviews the recent theoretical and experimental advances in the study of ultra-cold gases made of bosonic particles interacting via the long-range, anisotropic dipole–dipole interaction, in addition to the short-range and isotropic contact interaction usually at work in ultra-cold gases. The specific properties emerging from the dipolar interaction are emphasized, from the mean-field regime valid for dilute Bose–Einstein condensates, to the strongly correlated regimes reached for dipolar bosons in optical lattices.
In this dissertation I present results for lattice boson systems based on quantum Monte Carlo simulations by the Worm algorithm. Lattice bosons can be realized by ultracold gases in optical lattices and, under certain conditions, they are described by the Bose-Hubbard model. I will discuss the ground state, i.e. the phase diagram and properties of elementary excitations, as well as finite temperature thermodynamic properties of the two- and three-dimensional systems. These results provide bench-marks and guidance for experimentalists. I will also discuss the phase diagram of the one-dimensional hard-core Bose-Hubbard model with three-body interactions. The model is realized by cold polar molecules in optical lattices. The ground state presents a novel solid phase at unconventional filling, characterized by coexisting charge density wave and bond orders. Such phase has not been predicted by the preexisting mean field theory.
This chapter examines ultracold dipolar gases. First, it discusses the general properties of dipole–dipole interaction and explains how ultracold dipolar systems can be realized in experiments. The chapter reviews the properties of ultracold trapped dipolar Bose gases, pointing out the appearance of the roton minimum in the excitation spectrum. It then moves on to dipolar gases in a lattice, and investigates the corresponding extended Hubbard models. Dipolar bosons in a 2D optical lattice are discussed within the Gutzwiller approximation in more detail, with an emphasis on the appearance of multiple metastable states. Next, the chapter considers quantum Monte Carlo studies of dipolar gases, and discusses some further dipolar effects, which can be realized with cold atoms.
Abstract. This article reviews the recent theoretical and experimental advances in the study of ultracold gases made of bosonic particles interacting via the longrange, anisotropic dipole-dipole interaction, in addition to the short-range and isotropic contact interaction usually at work in ultracold gases. The specific properties emerging from the dipolar interaction are emphasized, from the meanfield regime valid for dilute Bose-Einstein condensates, to the strongly correlated regimes reached for dipolar bosons in optical lattices. CONTENTS 2 Contents 1
Disorder is ubiquitous in condensed matter systems, but a thorough understanding of these systems is hindered by poor control over the nature of disorder and competing interactions. Ultracold gases trapped in optical lattices, on the other hand, offer an unprecedented level of control over interactions and disorder, and are ideal candidates to test theoretical predictions and study fascinating phenomena resulting from the interplay between disorder, interaction, and quantum degeneracy. In this dissertation, I present my research on strongly correlated many-body lattice bosons in the presence of disordered potentials. My results are based on quantum Monte Carlo simulations by the Worm algorithm. Experimentally, lattice bosons can be realized by ultracold gases in optical lattices. I studied the ground state phase diagram of the above systems in the presence of diagonal (quasi-periodic disordered potential or random disordered potential) and off-diagonal disorder (in the form of site dilution). First, I will discuss the ground state phase diagram of two-dimensional bosons in quasi-periodic lattices. Then, I will discuss the phase diagram as well as finite temperature thermodynamic properties of two-dimensional dipolar lattice bosons in the presence of random diagonal disordered potentials. Finally, I will discuss the phase diagram of two-dimensional hard-core lattice bosons system in the presence of long-range hopping and long-range two-body interactions both in the absence of disorder and in the presence of site dilution (equivalent to off-diagonal disorder). This system is equivalent to the long-range XXZ model as realized by polar molecules trapped in a deep optical lattice. These results provide theoretical guidance for experimentalists to find quantum phase transitions as well as exotic quantum phases in strongly correlated bosonic lattice systems.
Ultracold dilute atomic gases are highly controllable systems whose properties are fundamentally determined by the interatomic interactions.In typical experiments on ultra cold gases particles interact dominantly via a short-range isotropic potential.However, during the last years a new generation of experiments is starting to explore systems, where an additional interaction, the long-range and anisotropic dipole-dipole interaction plays a significant or possibly dominant role.The effects induced by the anisotropy of the dipole-dipole interaction are crucially enhanced if the dipolar gas is confined in a deep optical lattice.In this thesis we study novel phenomena in such systems of dipolar gases in deep optical lattices.The nonlocal nonlinearity introduced by the dipole-dipole interaction plays a crucial role in the physics of dipolar Bose-Einstein condensates.In particular, it may distort significantly the stability of straight vortex lines.Remarkably, in the presence of a periodic potential along the vortex line, the spectrum of transverse modes shows a roton-like minimum, which eventually destabilizes the straight vortex when the BEC as a whole is still stable, opening the possibility for new scenarios for vortex line configurations in dipolar gases.We have analyzed this instability, and showed that it leads to a second-order-like phase transition from a straight vortex line into novel helical or snake-like configurations, depending on the dipole orientation.Strong 1D lattices usually lead to unconnected two-dimensional gases.The long-range character of the dipole-dipole interactions leads to a novel scenario where non-overlapping gases at different sites may interact significantly.We show that the excitations of non-overlapping condensates in 1D optical lattices acquire a band-like character, being collectively shared by different sites.In particular, the hybridization of the modes significantly enhances the rotonization of the excitations, and may induce roton-instability.We discuss the observability of this effect in on-going experiments.Fermionic polar molecules in deep 1D optical lattices may form selfassembled filaments when the electric dipoles are oriented along the lattice axis.These composites are bosons or fermions depending on the number of molecules per chain, leading to a peculiar and complex Bose-Fermi mixture, vi which we discuss in detail for the simplest case of a three-well potential.We show that the interplay between filament binding energy, transverse filament modes, and trimer Fermi energy leads to a rich variety of possible scenarios ranging from a degenerate Fermi gas of trimers to a binary mixture of two different types of bosonic dimers.We study the intriguing zero temperature and finite temperature physics of these composites for the particular case of an ideal filament gas loaded in 1D sites, and discuss possible methods to probe these chain mixtures.