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arXiv:quant-ph/0301145

Two-Level System and Some Approximate Solutions in the Strong Coupling Regime

Kazuyuki Fujii

Published Jan 27, 2003• 9 citations
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Abstract

In this paper we treat the 2--level system interacting with external fields without the rotating wave approximation and construct some approximate solutions in the strong coupling regime.
DOI
10.48550/arxiv.quant-ph/0301145

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The Bloch vector's path of a two-level system exposed to a monochromatic field exhibits, in the regime of strong coupling, complex corkscrew trajectories. By considering the infinitesimal evolution of the two-level system when the field is treated as a classical object, we show that the Bloch vector's rotation speed oscillates between zero and twice the rotation speed predicted by the rotating wave approximation. Cusps appear when the rotation speed vanishes. We prove analytically that in correspondence to cusps the curvature of the Bloch vector's path diverges. On the other hand, numerical data show that the curvature is very large even for a quantum field in the deep quantum regime with mean number of photons $\overline{n}\ensuremath{\lesssim}1$. We finally compute numerically the typical error size in a quantum gate when the terms beyond rotating wave approximation are neglected.