Solving and Completing the Rabi-Stark Model in the Ultrastrong Coupling Regime

• URL: http://arxiv.org/abs/2308.08115v1
• Date: Wed, 16 Aug 2023 03:01:19 GMT
• Title: Solving and Completing the Rabi-Stark Model in the Ultrastrong Coupling Regime
• Authors: Gen Li, Hao Zhu, and Guo-Feng Zhang
• Abstract summary: We derive the analytical energy spectra in the ultrastrong coupling regime. We observe a regular "staircase" pattern in the mean photon number of the ground state. We analytically determine the phase boundary, which slightly differs from that in the original Rabi-Stark model.
• Score: 10.645443650115086
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: In this work,we employ a unitary transformation with a suitable parameter to convert the quantum Rabi-Stark model into a Jaynes-Cummings-like model. Subsequently, we derive the analytical energy spectra in the ultrastrong coupling regime. The energy spectra exhibit a phenomenon known as spectral collapse, indicating the instability of the model due to the unboundedness of its energy from below at higher coupling parameters. To stabilize the Rabi-Stark model, we introduce a nonlinear photon-photon interaction term. We then compare the modified model with the original model in the classical oscillator (CO) limit. Interestingly, we observe a regular "staircase" pattern in the mean photon number of the ground state. This pattern exhibits a fixed slope and equal step width, which we determine analytically. Moreover, we analytically determine the phase boundary, which slightly differs from that in the original Rabi-Stark model. These findings offer insights into the investigation of those superradiant phase transitions that are unbounded from below due to the phenomenon of spectral collapse.

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