The Davydov D1.5 Ansatz for the quantum Rabi model**This paper is dedicated to Wolfgang Schleich on the occasion of his 60th birthday.

Abstract

We propose a new version of the Davydov Ansatz for the approximate solution of the time-dependent Schrödinger equation (TDSE) and apply it to a spin 1/2 system coupled to a single bosonic mode. In complexity the new Ansatz is between the well-studied D1 and D2 Ansätze and is therefore termed D1.5 Ansatz. It is tailored to specific but still rather general initial conditions and is free of numerical inconsistencies that plague the D1 Ansatz. Finally, a generalization to nontrivial multiplicity in the oscillator state space is given that leads, in principle, to an exact solution of the TDSE for arbitrary system parameters. By employing Bargmann coherent states, the equations of motion could be made explicit, which is a big advantage, computationally.