Analytical solutions for the Rabi model
Abstract
The Rabi model that describes the fundamental interaction between a two-level system with a quantized harmonic oscillator is one of the simplest and most ubiquitous models in modern physics. However, this model has not been solved exactly because it is hard to find a second conserved quantity besides the energy. Here we present a unitary transformation to map this unsolvable Rabi model into a solvable Jaynes-Cummings-like model by choosing a proper variation parameter. As a result, the analytical energy spectrums and wavefunctions including both the ground and the excited states can be obtained easily. Moreover, these explicit results agree well with the direct numerical simulations in a wide range of the experimental parameters. In addition, based on our obtained energy spectrums, the recent experimental observation of Bloch-Siegert in the circuit quantum electrodynamics with the ultrastrong coupling can be explained perfectly. Our results have the potential application in the solid-state quantum information processing.
Keywords
Cite
@article{arxiv.1203.5408,
title = {Analytical solutions for the Rabi model},
author = {Lixian Yu and Shiqun Zhu and Qifeng Liang and Gang Chen and Suotang Jia},
journal= {arXiv preprint arXiv:1203.5408},
year = {2015}
}
Comments
5 pages, 4 figures