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Acta Physica Polonica B

Mott Insulator to Superfluid Phase Transition in Bravais Lattices via the Jaynes--Cummings--Hubbard Model

C. B. Gomes, Francisco A. G. Almeida, André M. C. Souza

Published Jan 1, 2015• 1 citation
Publisher

Abstract

The complexity (or simplicity) of a system can be characterized through very many paths.A quite interesting and operational one, which we follow here, consists in making use of entropic concepts.The thermodynamical and statistical-mechanical foundations of this approach, as well as its (analytical, computational, observational, and experimental) applications for natural, artificial and social systems will be briefly reviewed.

DOI
10.5506/aphyspolb.46.1239

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The complexity (or simplicity) of a system can be characterized through very many paths.A quite interesting and operational one, which we follow here, consists in making use of entropic concepts.The thermodynamical and statistical-mechanical foundations of this approach, as well as its (analytical, computational, observational, and experimental) applications for natural, artificial and social systems will be briefly reviewed.
We study the dynamics of phase transitions in the one-dimensional Bose-Hubbard model. To drive the system from a Mott insulator to a superfluid phase, we change the tunneling frequency at a finite rate. We investigate the buildup of correlations during fast and slow transitions using variational wave functions, dynamical Bogoliubov theory, Kibble-Zurek mechanism, and numerical simulations. We show that time-dependent correlations satisfy characteristic scaling relations that can be measured in optical lattices filled with cold atoms.
The Properties of the Mott insulator to superfluid phase transition are obtained through the fermionic approximation in the Jaynes-Cummings-Hubbard model on linear, square, SC, FCC, and BCC Bravais lattices. For varying excitation number and atom-cavity frequency detuning. We find that the Mott lobes and the critical hopping are not scalable only for the FCC lattice. At the large excitation number regime, the critical hopping is scalable for all the lattices and it does not depend on the detuning.