Analytical approximations for generalized quantum Rabi models
- URL: http://arxiv.org/abs/2401.05615v1
- Date: Thu, 11 Jan 2024 01:42:17 GMT
- Title: Analytical approximations for generalized quantum Rabi models
- Authors: Chon-Fai Kam and Yang Chen
- Abstract summary: The quantum Rabi model serves as the simplest non-integrable yet solvable model describing the interaction between a two-level system and a single mode of a bosonic field.
We show that the energy spectrum of the generalized quantum Rabi model can be analytically determined by a bi-confluent Fuchsian equation.
- Score: 7.708919339137053
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The quantum Rabi model is essential for understanding interacting quantum
systems. It serves as the simplest non-integrable yet solvable model describing
the interaction between a two-level system and a single mode of a bosonic
field. In this study, we delve into the exploration of the generalized quantum
Rabi model, wherein the bosonic mode of the field undergoes squeezing.
Utilizing the Segal-Bargmann representation of the infinite-dimensional Hilbert
space, we demonstrate that the energy spectrum of the generalized quantum Rabi
model, when both the Rabi coupling strength and the squeezing strength are not
significantly large compared to the field mode frequency, can be analytically
determined by a bi-confluent Fuchsian equation with two regular singularities
at 0 and 1 and an irregular singularity of rank two at infinity.
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