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arXiv:2306.13519 · Science China Physics Mechanics and Astronomy

Quantum phase transition of the Jaynes-Cummings model

Cheng Liu, Jin‐Feng Huang

Published Nov 23, 2023• 25 citations
arXivHTMLPDF
DOI
10.1007/s11433-023-2243-7

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We introduce a modified Jaynes-Cummings model with single-photon cavity radiation field but with the atomic system instead of exchanging a single photon as in the Jaynes-Cummings model, it exchanges instead a squeezed photon with squeezing parameter r. This allows us to interpolate between the Rabi model (r = ∞) and the Jaynes-Cummings model (r = 0) by varying r. The model exhibits a quantum phase transition. Accordingly, the quantum phase transition realized in the Rabi model, giving rise to superradiance, also occurs in the Jaynes-Cummings model.
We explore quantum phase transitions in the multiphoton Jaynes-Cummings-Hubbard model (JCHM). Using the mean-field approximation, we demonstrate that the multiphoton JCHM exhibits quantum phase transitions between the Mott insulator (MI) phase, the superfluid phase, and an additional phase we refer to as the forbidden phase. The multiphoton JCHM MI phases are classified according to a conserved quantity associated with the total number of excited atoms and photons. When this conserved quantity diverges toward positive infinity, this system enters the forbidden phase. By analyzing the system, we observe MI, superfluid, and forbidden phases in both the single- and two-photon JCHMs, although the MI phases in the two-photon case are confined to subspaces with small values of the conserved quantity. In contrast, only the superfluid and forbidden phases appear in the three- and four-photon JCHMs, with no MI phase observed.