Bogoliubov theory of quantum correlations in the time-dependent Bose-Hubbard model

Abstract

By means of an adapted mean-field expansion for large fillings $n\gg 1$, we study the evolution of quantum fluctuations in the time-dependent Bose-Hubbard model, starting in the superfluid state and approaching the Mott phase by decreasing the tunneling rate or increasing the interaction strength in time. For experimentally relevant cases, we derive analytical results for the temporal behavior of the number and phase fluctuations, respectively. This allows us to calculate the growth of the quantum depletion and the decay of off-diagonal long-range order. We estimate the conditions for the observability of the time dependence in the correlation functions in the experimental setups with external trapping present. Finally, we discuss the analogy to quantum effects in the early universe during the inflationary epoch.

arXiv comment11 pages of RevTex4, 2 figures; significantly extended, with several analytically solvable cases added, to appear in Physical Review A

References in corpus (26)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Cold bosonic atoms in optical lattices
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
• Acoustic black holes: horizons, ergospheres, and Hawking radiation
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Evolution of a Bose-condensed gas under variations of the confining potential
• Quench dynamics across quantum critical points
• A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
• Formation of spatial shell structures in the superfluid to Mott insulator transition
• Quantum simulation of cosmic inflation in two-component Bose-Einstein condensates
• Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models
• Sweeping from the superfluid to Mott phase in the Bose-Hubbard model
• Dynamics of the Bose-Hubbard model: transition from Mott insulator to superfluid
• Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition
• Dynamics of the superfluid to Mott insulator transition in one dimension
• Extended Coherence Time with Atom-Number Squeezed Sources
• The Amplitude Mode in the Quantum Phase Model
• Dynamical zero-temperature phase transitions and cosmic inflation/deflation
• Nonadiabatic dynamics of a Bose-Einstein condensate in an optical lattice
• Non-equilibrium coherence dynamics of a soft boson lattice
• Propagation of sound in a Bose Einstein condensate in an optical lattice
• Variational ansatz for the superfluid Mott-insulator transition in optical lattices
• Bogoliubov speed of sound for a dilute Bose-Einstein condensate in a 3d optical lattice
• An Investigation of Mean-field Effects for a Bose Condensate in an Optical Lattice

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