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arXiv:0804.2769 · New Journal of Physics

Probing correlated phases of bosons in optical lattices via trap squeezing

Tommaso Roscilde

Published Feb 11, 2009• 21 citations
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Abstract

We theoretically analyze the response properties of ultracold bosons in optical lattices to the static variation of the trapping potential. We show that, upon an increase of such a potential (trap squeezing), the density variations in a central region, with linear size of ≲10 wavelengths, reflect that of the bulk system upon changing the chemical potential: hence measuring the density variations gives direct access to the bulk compressibility . When combined with standard time-of-flight measurements, this approach has the potential of unambiguously detecting the appearance of the most fundamental phases realized by bosons in optical lattices, with or without further external potentials: superfluid, Mott insulator, band insulator and Bose glass.

DOI
10.1088/1367-2630/11/2/023019

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We theoretically analyze the response properties of ultracold bosons in optical lattices to the static variation of the trapping potential. We show that, upon an increase of such a potential (trap squeezing), the density variations in a central region, with linear size of ≲10 wavelengths, reflect that of the bulk system upon changing the chemical potential: hence measuring the density variations gives direct access to the bulk compressibility . When combined with standard time-of-flight measurements, this approach has the potential of unambiguously detecting the appearance of the most fundamental phases realized by bosons in optical lattices, with or without further external potentials: superfluid, Mott insulator, band insulator and Bose glass.
In this article, we theoretically discuss how quantum simulators based on trapped cold bosons in optical lattices can explore the grand-canonical phase diagram of homogeneous lattice boson models, via control of the trapping potential independent of all other experimental parameters (trap squeezing). Based on quantum Monte Carlo, we establish the general scaling relation linking the global chemical potential to the Hamiltonian parameters for the Bose-Hubbard model in a parabolic trap, describing cold bosons in optical lattices; we find that this scaling relation is well captured by a modified Thomas-Fermi scaling behavior---corrected for quantum fluctuations---in the case of sufficiently high density and/or sufficiently weak interactions, and by a mean-field Gutzwiller ansatz over a much larger parameter range. This scaling relation allows us to control experimentally the chemical potential, independent of all other Hamiltonian parameters, via trap squeezing; given that the global chemical potential coincides with the local chemical potential in the trap center, measurements of the central density as a function of the chemical potential give access to the information on the bulk compressibility of the Bose-Hubbard model. Supplemented with time-of-flight measurements of the coherence properties, the measurement of compressibility enables one to discern among the various possible phases realized by bosons in an optical lattice with or without external (periodic or random) potentials---for example, superfluid, Mott insulator, band insulator, and Bose glass. We theoretically demonstrate the trap-squeezing investigation of these phases in the case of bosons in a one-dimensional optical lattice and in a one-dimensional incommensurate superlattice.
We discuss a technique to probe the properties of an interacting cold atomic gas that can be viewed as a dynamical compressibility measurement. We apply this technique to the study of the superfluid-to-Mott-insulator quantum phase transition in one and three dimensions for a bosonic gas trapped in an optical lattice. Excitations of the system are detected by time-of-flight measurements. The experimental data for the one-dimensional case are in good agreement with the results of a time-dependent density-matrix-renormalization-group calculation.
Finite systems of bosons and/or fermions described by the Hubbard model can be realized using ultracold atoms confined in optical lattices. The ground states of these systems often exhibit a coexistence of compressible superfluid and incompressible Mott insulating domains. We analyze such systems by studying the out-of-equilibrium dynamics following a weak sudden quench of the trapping potential. In particular, we show how the temporal variance of the site occupations reveals the location of spatial boundaries between compressible and incompressible regions. The feasibility of this approach is demonstrated for several models using numerical simulations. We first consider integrable systems, hard-core bosons (spinless fermions) confined by a harmonic potential, where space-separated Mott and superfluid phases coexist. Then, we analyze a nonintegrable system, a $J\text{\ensuremath{-}}V\text{\ensuremath{-}}{V}^{\ensuremath{'}}$ model, with coexisting charge density wave and superfluid phases. We find that the temporal variance of the site occupations is a more effective measure than other standard indicators of phase boundaries such as a local compressibility. Finally, to make contact with experiments, we propose a consistent estimator for such temporal variance. Our numerical experiments show that the phase boundary is correctly spotted using as little as 30 measurements. Based on these results, we argue that analyzing temporal fluctuations is a valuable experimental tool for exploring phase boundaries in trapped atom systems.
We study properties of ultracold bosonic atoms in one-, two-, and three-dimensional optical lattices by large scale quantum Monte Carlo simulations of the Bose-Hubbard model in parabolic confining potentials. Our results indicate that local properties of the atoms can be accessed by probing the system's response to local potential perturbations. Furthermore, we show how the formation of Mott insulating regions is reflected in the momentum distribution of the atoms, amenable to experimental detection. We disprove previous claims concerning the relevance of fine structure in the momentum distribution function. Furthermore, we discuss limitations of local density approximations for confined systems, and demonstrate the absence of quantum criticality due to the inhomogenous potential. Instead, we show that quantum critical behavior can be observed in flat confining potentials. Our results indicate that the experimental detection of the Mott transition in moderately sized optical lattices would be significantly eased in flat confinement potentials.
We investigate the effect of the trapping potential on the quantum phases of strongly correlated ultracold bosons in one-dimensional periodic and quasiperiodic optical lattices. By means of a decoupling meanfield approach, we characterize the ground state of the system and its behavior under variation of the harmonic trapping, as a function of the total number of atoms. For a small atom number the system shows an incompressible Mott-insulating phase, as the size of the cloud remains unaffected when the trapping potential is varied. When the quasiperiodic potential is added the system develops a metastable-disordered phase which is neither compressible nor Mott insulating. This state is characteristic of quasidisorder in the presence of a strong trapping potential.