Exploring the grand-canonical phase diagram of interacting bosons in optical lattices by trap squeezing

Abstract

In this paper 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 independently 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 of 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 high enough density and/or weak enough interactions, and by a mean-field Gutzwiller Ansatz over a much larger parameter range. The above scaling relation allows to control experimentally the chemical potential, independently 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 gives 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 -- e.g. superfluid, Mott insulator, band insulator, and Bose glass. We theoretically demonstrate the trap-squeezing investigation of the above phases in the case of bosons in a one-dimensional optical lattice, and in a one-dimensional incommensurate superlattice.

27 pages, 26 figures. v2: added references and further discussion of the local-density approximation.

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Cited by in corpus (9)

• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Edge states and topological phases in one-dimensional optical superlattices
• Finite temperature study of bosons in a two dimensional optical lattice
• Dynamical Anderson transition in one-dimensional periodically kicked incommensurate lattices
• Topological Properties of Ultracold Bosons in One-Dimensional Quasiperiodic Optical Lattice
• Strongly interacting bosons in multi-chromatic potentials supporting mobility edges: localization, quasi-condensation and expansion dynamics
• Analytical and numerical study of trapped strongly correlated bosons in two- and three-dimensional lattices
• Measuring the Edwards-Anderson order parameter of the Bose glass: a quantum gas microscope approach
• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review