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arXiv:0806.2950 · Physical Review A

Ultracold dipolar gas in an optical lattice: The fate of metastable states

C. Trefzger, C. Menotti, Maciej Lewenstein

Published Oct 7, 2008• 57 citations
arXivHTMLPDF

Abstract

We study the physics of ultracold dipolar bosons in optical lattices. We show that dipole-dipole interactions lead to the appearance of many insulating metastable states. We study the stability and lifetime of these states using a generalization of the instanton theory. We also investigate possibilities to prepare, control, and manipulate these states using time-dependent superlattice modifications and modulations. We show that the transfer from one metastable configuration to another necessarily occurs via superfluid states, but can be controlled fully at the quantum level. We show how the metastable states can be created in the presence of a trapping potential. Our findings open the way toward applications of the metastable states as quantum memories.

DOI
10.1103/physreva.78.043604

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•Jan 1, 2008•0 citations
We study the physics of ultracold dipolar bosons in optical lattices. We show that dipole-dipole interactions lead to the appearance of many insulating metastable states. We study the stability and lifetime of these states using a generalization of the instanton theory. We also investigate possibilities to prepare, control, and manipulate these states using time-dependent superlattice modifications and modulations. We show that the transfer from one metastable configuration to another necessarily occurs via superfluid states, but can be controlled fully at the quantum level. We show how the metastable states can be created in the presence of a trapping potential. Our findings open the way toward applications of the metastable states as quantum memories.
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.
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.
The recent advances in creating nearly degenerate quantum dipolar gases in optical lattices are opening the doors for the exploration of equilibrium physics of quantum systems with anisotropic and long-range dipolar interactions. In this paper we study the zero- and finite-temperature phase diagrams of a system of hard-core dipolar bosons at half-filling, trapped in a two-dimensional square optical lattice. The dipoles are aligned parallel to one another and tilted out of the optical lattice plane by means of an external electric field. At zero-temperature, the system is a superfluid (SF) at all tilt angles θ provided that the strength of dipolar interaction is below a critical value . Upon increasing the interaction strength while keeping θ fixed, the SF phase is destabilized in favor of a checkerboard or a stripe solid (SS) depending on the tilt angle. We explore the nature of the phase transition between the two solid phases, identifying a region of metastable emulsion states intervening between the two solid lobes. Additionally, we study the stability of these quantum phases against thermal fluctuations and find that the SS is the most robust, making it the best candidate for experimental observation.
This thesis contains a study of ultracold paramagnetic atoms or polar molecules characterized by a long-range anisotropic dipolar interaction. We particularly focus on two aspects of ultracold dipolar gases. In the first problem the ground state properties of dipolar Bose-Einstein condensates (BEC) are investigated. This problem has gained importance due to recent experimental advances in achieving a condensate of Chromium atoms and ongoing research to produce quantum degenerate polar molecules. In the second problem, we consider possible applications of ultracold polar molecules to rotation sensing and interferometry. First, we concentrate on the interplay between the trapping geometry and dipole-dipole interaction for a polarized dipolar bosonic condensate. As the dipole-dipole interaction is attractive along the polarized direction, the lowest energy state of the BEC is always a collapsed state. However by applying a trapping potential along the polarization direction it is possible to achieve a metastable dipolar BEC. By numerically solving the Gross-Pitaevskii equation, we show that below a critical interaction strength, a metastable state exists depending on the trapping geometry. We also show that a novel feature of dipolar BEC is the appearance of different structural metastable ground states for certain combinations of trapping geometry and particle number. Next, by mixing in single component fermions we show that dipolar BEC can be stabilized against collapse in pancake shaped or cylindrical traps. We also show that the excitation spectrum of the BEC may have a minimum for non-zero momentum, termed a “roton minimum”. This minimum leads to a transition to stable or metastable density-wave states depending on the density of the bosons and boson-fermion interaction strength. In the second problem, we study a proposal for a large-angle coherent beam splitter for polar molecules. By taking into account the effect of a quasi-static external electric field on the rotational levels of the polarized molecules we show that it is possible to coherently split a stationary cloud of molecules into two counter-propagating components. We then investigate the effect of longitudinal acceleration on the transverse motion of the particles, assuming that the longitudinal motion of the molecules can be approximated classically by a wave packet with some mean velocity while the transverse motion is governed by quantum mechanics. We propose a particular time-dependent shape of acceleration to minimize the excitations in the transverse motion. Our theory is also applicable to the general case of particles moving along a circular guide with time-dependent longitudinal velocity. In addition, we include the effects of velocity fluctuations due to noise in the accelerating field.
Optical lattices make it possible to trap and coherently control large ensembles of ultracold atoms. They provide the possibility to create lattice potentials that mimic the structure of solid-state systems, and to control these potentials dynamically. In this thesis, we study how dynamical manipulations of the lattice geometry can be used to perform different tasks, ranging from quantum information processing to the creation of diatomic molecules. We first examine the dynamical properties of ultracold atoms trapped in a lattice whose periodicity is dynamically doubled. We derive a model describing the dynamics of the atoms during this process, and compute the different interaction parameters of this model. We investigate different ways of using this lattice manipulation to optimise the initialisation time of a Mott-insulating state with one atom per site, and provide a scaling law related to the interaction parameters of the system. We go on to show that entangling operations between the spin of adjacent atoms are realisable with optical lattices forming arrays of double-well potentials. We study the creation of a lattice containing a spin-encoded Bell-pair in each double-well, and show that resilient, highly-entangled many-body states are realisable using lattice manipulations. We show that the creation of cluster-like states encoded on Bell-pairs can be achieved using these systems, and we provide measurement networks that allow the execution of quantum algorithms while maintaining intact the resilience of the system. Finally, we investigate the possibility to create a diatomic molecular state and simulate Fermi systems via the excitation to Rydberg levels of ground-state atoms trapped in optical lattices. We develop a method based on symbolical manipulations to compute the interaction parameters between highly-excited electrons, and evaluate them for different electronic configurations. We use these parameters to investigate the existence of diatomic molecular states with equilibrium distances comparable to typical lattice spacings. Considering the possibility to excite atoms trapped in an optical lattice to Rydberg levels such that the electronic cloud of neighbouring atoms overlap, we propose a model describing their interactions and compute its parameters. If such systems were realised, they would allow the simulation of Fermi systems at a temperature much below the Fermi temperature, thus enabling the observation of quantum phenomena hitherto inaccessible with current technology.