Characterizing the phase transition of anomalous Dicke model via Loschmidt echo and studying different phases in 1D and 2D lattice structures

Hong-Yu Chen, Bo Li, Dong-Yan Lü, Xu-Wu Wang, Qing-Lan Wang, Ya-Wen Li () and Yuan Zhou ()
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Hong-Yu Chen: Hubei University of Automotive Technology, Shiyan Key Laboratory of Electromagnetic Induction and Energy Saving Technology and Shiyan Key Laboratory of Quantum Information and Precision Optics, Hubei Key Laboratory of Energy Storage and Power Battery and Hubei Key Laboratory of Automotive Power Train and Electronic Control
Bo Li: Hubei University of Automotive Technology, Shiyan Key Laboratory of Electromagnetic Induction and Energy Saving Technology and Shiyan Key Laboratory of Quantum Information and Precision Optics, Hubei Key Laboratory of Energy Storage and Power Battery and Hubei Key Laboratory of Automotive Power Train and Electronic Control
Dong-Yan Lü: Hubei University of Automotive Technology, Shiyan Key Laboratory of Electromagnetic Induction and Energy Saving Technology and Shiyan Key Laboratory of Quantum Information and Precision Optics, Hubei Key Laboratory of Energy Storage and Power Battery and Hubei Key Laboratory of Automotive Power Train and Electronic Control
Xu-Wu Wang: Hubei University of Automotive Technology, Shiyan Key Laboratory of Electromagnetic Induction and Energy Saving Technology and Shiyan Key Laboratory of Quantum Information and Precision Optics, Hubei Key Laboratory of Energy Storage and Power Battery and Hubei Key Laboratory of Automotive Power Train and Electronic Control
Qing-Lan Wang: Hubei University of Automotive Technology, Shiyan Key Laboratory of Electromagnetic Induction and Energy Saving Technology and Shiyan Key Laboratory of Quantum Information and Precision Optics, Hubei Key Laboratory of Energy Storage and Power Battery and Hubei Key Laboratory of Automotive Power Train and Electronic Control
Ya-Wen Li: Shangluo University, School of Electronic Information and Electrical Engineering
Yuan Zhou: Hubei University of Automotive Technology, Shiyan Key Laboratory of Electromagnetic Induction and Energy Saving Technology and Shiyan Key Laboratory of Quantum Information and Precision Optics, Hubei Key Laboratory of Energy Storage and Power Battery and Hubei Key Laboratory of Automotive Power Train and Electronic Control

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 12, 1-22

Abstract: Abstract This paper introduces a theoretical method for characterizing the quantum phase transitions (QPTs) of the anomalous Dicke model (ADM) by employing the Loschmidt echo (LE) to access the photon number variance. The ADM features a normal phase (NP) and two superradiant phases: electric (SEP) and magnetic (SMP), respectively. We further extend the ADM to one-dimensional (1D) chain-like and two-dimensional (2D) square-like lattice structures. Analysis of the energy bands in these lattice models reveals the emergence of unstable phases, which are primarily induced by photon–photon hopping interactions between adjacent cavities, namely the dispersion relation. We map the unstable phases onto the phase diagram and analyze the boundaries between different phases, along with the properties of the energy bands within each phase region. This work provides valuable insights into the applications of QPTs and quantum manipulations through the unconventional Dicke-lattice model. Graphical abstract

Date: 2025
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DOI: 10.1140/epjb/s10051-025-01103-0

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