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arXiv:0811.2798 · Physical Review A

Probing condensate order in deep optical lattices

Kuei Sun, Courtney Lannert, Smitha Vishveshwara

Published Apr 27, 2009• 18 citations
arXivHTMLPDF

Abstract

We study interacting bosons in optical lattices in the weak-tunneling regime in systems that exhibit the coexistence of Mott-insulating and condensed phases. We discuss the nature of the condensed ground state in this regime and the validity of the mean-field treatment thereof. We suggest two experimental signatures of condensate order in the system. (1) We analyze the hyperfine configuration of the system and propose a set of experimental parameters for observing radio-frequency spectra that would demonstrate the existence of the condensed phase between Mott-insulating phases. We derive the structure of the signal from the condensate in a typical trapped system, taking into account Goldstone excitations, and discuss its evolution as a function of temperature. (2) We study matter-wave interference patterns displayed by the system upon release from all confining potentials. We show that as the density profiles evolve very differently for the Mott-insulating phase and the condensed phase, they can be distinguished from one another when the two phases coexist.

DOI
10.1103/physreva.79.043422

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We study interacting bosons in optical lattices in the weak-tunneling regime in systems that exhibit the coexistence of Mott-insulating and condensed phases. We discuss the nature of the condensed ground state in this regime and the validity of the mean-field treatment thereof. We suggest two experimental signatures of condensate order in the system. (1) We analyze the hyperfine configuration of the system and propose a set of experimental parameters for observing radio-frequency spectra that would demonstrate the existence of the condensed phase between Mott-insulating phases. We derive the structure of the signal from the condensate in a typical trapped system, taking into account Goldstone excitations, and discuss its evolution as a function of temperature. (2) We study matter-wave interference patterns displayed by the system upon release from all confining potentials. We show that as the density profiles evolve very differently for the Mott-insulating phase and the condensed phase, they can be distinguished from one another when the two phases coexist.
Recent experiments on strongly interacting bosons in optical lattices have revealed the coexistence of spatially separated Mott-insulating and number-fluctuating phases. We explore the condensate properties of the number fluctuating phase trapped between the Mott-insulating regions and derive the associated collective-mode structure. We discuss the crossover of the interlayer properties between two- and three-dimensional behavior as a function of the lattice parameters and estimate the critical temperatures for the transition from the normal to superfluid state.
We propose a method to probe states in the Mott insulator regime produced from a condensate in an optical lattice. We consider a system in which we create time-dependent number fluctuations in a given site by turning off the atomic interactions and lowering the potential barriers on a nearly pure Mott state to allow the atoms to tunnel between sites. We calculate the expected interference pattern and number fluctuations from such a system and show that one can potentially observe a deviation from a pure Mott state. We also discuss a method in which to detect these number fluctuations using time-of-flight imaging.
We investigate the zero-temperature phase diagram of a gas of bosonic atoms in one- and two-color standing-wave lattices in the framework of the Bose-Hubbard model. We first introduce some relevant physical quantities; superfluid fraction, condensate fraction, quasimomentum distribution, and matter-wave interference pattern. We then discuss the relationships between them on the formal level and show that the superfluid fraction, which is the relevant order parameter for the superfluid to Mott-insulator transition, cannot be probed directly via the matter-wave interference patterns. The formal considerations are supported by exact numerical solutions of the Bose-Hubbard model for uniform one-dimensional systems. We then map out the phase diagram of bosons in nonuniform lattices. The emphasis is on optical two-color superlattices which exhibit a sinusoidal modulation of the well depth and can be easily realized experimentally. From the study of the superfluid fraction, the energy gap, and other quantities, we identify additional zero-temperature phases, including a localized and a quasi-Bose-glass phase, and discuss prospects for their experimental observation.
We study the superfluid-Mott-insulator transition of ultracold bosonic atoms in a one-dimensional optical lattice with a double-well confining trap using the density-matrix renormalization group method. At low density, the system behaves similarly as two separated ones inside each well. At high density, however, interesting features appear resulting from the quantum tunnelling between the two wells and the competition between the ``superfluid'' and Mott regions. These interesting features are characterized by a rich step-plateau structure in the visibility and the satellite peaks in the momentum distribution function, with an oscillating pattern as a function of the on-site repulsion. These properties shed light on the understanding of the quantum phase coherence between two coupled condensates.
We experimentally probe the properties of the disordered Bose-Hubbard model using an atomic Bose-Einstein condensate trapped in a 3D disordered optical lattice. Controllable disorder is introduced using a fine-grained optical speckle field with features comparable in size to the lattice spacing along every lattice direction. A precision measurement of the disordering potential is used to compute the single-particle parameters of the system. To constrain theories of the disordered Bose Hubbard model, we have measured the change in condensate fraction as a function of disorder strength for several different ratios of tunneling to interaction energy. We observe disorder-induced, reversible suppression of condensate fraction for superfluid and coexisting superfluid-Mott-insulator phases.
Motivated by recent experiments on trapped ultracold bosonic atoms in an optical lattice potential, we consider the nonequilibrium dynamic properties of such bosonic systems for a number of experimentally relevant situations. When the number of bosons per lattice site is large, there is a wide parameter regime where the effective boson interactions are strong, but the ground state remains a superfluid (and not a Mott insulator): we describe the conditions under which the dynamics in this regime can be described by a discrete Gross-Pitaevskii equation. We describe the evolution of the phase coherence after the system is initially prepared in a Mott insulating state, and then allowed to evolve after a sudden change in parameters places it in a regime with a superfluid ground state. We also consider initial conditions with a ``\ensuremath{\pi} phase'' imprint on a superfluid ground state (i.e., the initial phases of neighboring wells differ by \ensuremath{\pi}), and discuss the subsequent appearance of the density wave order and ``Schr\"odinger cat,'' i.e., macroscopic quantum interference, states.