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arXiv:1211.5515

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

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

Published Nov 23, 2012• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1211.5515

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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.
In this paper, we investigate systematically the quantum phase transition between the Mott-insulator and superfluid states of the Jaynes–Cummings Hubbard model in triangular, square, honeycomb and kagomé lattices. With the help of Green's function method, by treating the hopping term in the Jaynes–Cummings Hubbard model as perturbation, we calculate the phase boundaries of Jaynes–Cummings Hubbard models on different geometrical lattices analytically up to second order for both detuning and . It is shown that the Mott phase becomes more unstable when increasing the polariton number n . Meanwhile, the Mott lobe of n = 0 is enlarged while other Mott lobes shrink as the detuning parameter increases.
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Regular arrays of electromagnetic resonators, in turn coupled coherently to individual quantum two-level systems, exhibit a quantum phase transition of polaritons from a superfluid phase to a Mott-insulating phase. The critical behavior of such a Jaynes-Cummings lattice thus resembles the physics of the Bose-Hubbard model. We explore this analogy by elaborating on the mean-field theory of the phase transition and by presenting several useful mappings which pinpoint both similarities and differences of the two models. We show that a field-theory approach can be applied to prove the existence of multicritical curves analogous to the multicritical points of the Bose-Hubbard model, and we provide analytical expressions for the position of these curves.
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