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.

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

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• Unraveling the Excitation Spectrum of Many-Body Systems from Quantum Quenches
• Interaction-driven dynamical quantum phase transitions in a strongly correlated bosonic system
• Self-consistent Keldysh approach to quenches in weakly interacting Bose-Hubbard model
• Geometry effect of the dynamical quantum phase transitions at finite temperatures
• Orthogonalization speed-up from quantum coherence after a sudden quench
• Finite-rate quench in disordered Chern and $Z_2$ topological insulators
• Machine Learning out of equilibrium correlations in the Bose-Hubbard model