Finite-Frequency Boson-Number Bounds Across the Quantum Rabi Transition
Abstract
We consider the quantum Rabi model, a fundamental model of quantum optics describing a two-level system coupled to a bosonic mode, including counter-rotating terms. In the limit of large separation between the two-level transition frequency and the bosonic mode frequency, the model exhibits a quantum phase transition at a critical coupling strength. Although the model is exactly solvable, simple analytic expressions for important physical quantities are generally unavailable. We derive rigorous upper and lower bounds for the ground-state energy and boson occupation number across the quantum phase transition at finite frequency ratios. Our results characterize the subcritical, critical, and supercritical regimes and establish the scaling behavior of the boson occupation near the critical point. Exact numerical diagonalization demonstrates the tightness of the derived bounds, while the resulting finite-frequency inequalities provide experimentally testable predictions for trapped-ion quantum simulators.
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BibTeX
@misc{unanyan2026finitefrequency,
title = {{Finite-Frequency Boson-Number Bounds Across the Quantum Rabi Transition}},
author = {Razmik G. Unanyan and Michael Fleischhauer and Nikolay V. Vitanov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21556},
eprint = {2610.21556},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21556},
}
RIS
TY - UNPB
TI - Finite-Frequency Boson-Number Bounds Across the Quantum Rabi Transition
AU - Razmik G. Unanyan
AU - Michael Fleischhauer
AU - Nikolay V. Vitanov
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21556
UR - https://arxiv.org/abs/2610.21556
AB - We consider the quantum Rabi model, a fundamental model of quantum optics describing a two-level system coupled to a bosonic mode, including counter-rotating terms. In the limit of large separation between the two-level transition frequency and the bosonic mode frequency, the model exhibits a quantum phase transition at a critical coupling strength. Although the model is exactly solvable, simple analytic expressions for important physical quantities are generally unavailable. We derive rigorous upper and lower bounds for the ground-state energy and boson occupation number across the quantum phase transition at finite frequency ratios. Our results characterize the subcritical, critical, and supercritical regimes and establish the scaling behavior of the boson occupation near the critical point. Exact numerical diagonalization demonstrates the tightness of the derived bounds, while the resulting finite-frequency inequalities provide experimentally testable predictions for trapped-ion quantum simulators.
ER -