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.
Limit of spin squeezing in trapped Bose-Einstein condensates
Laboratoire Kastler Brossel, École Normale Supérieure and CNRS, UPMC（卡斯特尔布罗塞尔实验室，巴黎高等师范学院和法国国家科学研究中心，巴黎第六大学）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）
Enhanced squeezing for quantum gravimetry in a Bose-Einstein condensate with focussing
ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland（澳大利亚国立大学量子科学与技术系）；Department of Quantum Science and Technology, Research School of Physics, Australian National University（澳大利亚国立大学物理研究学院量子科学与技术系）
