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Free keywords:
Quantum Physics, quant-ph
MPINP:
Research group K. Z. Hatsagortsyan – Division C. H. Keitel
Abstract:
We investigate the applicability of the two major approximations which are
most commonly employed in the study of the quantum Rabi model, namely the
description of a resonant cavity mode as a single-mode quantized field and the
use of the rotating wave approximation. Starting from the Hamiltonian of a
two-level system interacting with a multi-mode quantized field, we perform the
canonical transformation of the field operators. This allows one to partition
the Hamiltonian of the system into two parts. The first part is the interaction
of the two-level system with a single collective field mode, while the second
one describes the interaction with field fluctuations. The first part is
usually associated with the resonant cavity mode. This division enables us to
determine the applicability condition of the single-mode approximation. In
addition we identify simple approximate relations for the description of the
eigenstates, eigenfunctions and the time evolution of the quantum Rabi model
beyond the rotating wave approximation.
