Duality in potential curve crossing: Application to quantum coherence

TL;DR

This paper explores a duality in potential curve crossing problems using an $su(2)$ gauge transformation, revealing a symmetry between weak and strong interactions, and discusses implications for quantum coherence and perturbation theory.

Contribution

It introduces a gauge transformation-based duality in potential curve crossing, enabling perturbation theory in both weak and strong interaction regimes, and analyzes quantum coherence suppression.

Findings

Weak and strong potential crossing interactions are dual under the gauge transformation.

Landau-Zener formula is accurately described by simple perturbation theory.

Quantum coherence is suppressed by potential crossing effects, similar to dissipation.

Abstract

A field dependent $su(2)$ gauge transformation connects between the adiabatic and diabatic pictures in the (Landau-Zener-Stueckelberg) potential curve crossing problem. It is pointed out that weak and strong potential curve crossing interactions are interchanged under this transformation, and thus realizing a naive strong and weak duality. A reliable perturbation theory should thus be formulated in the both limits of weak and strong interactions. In fact, main characteristics of the potential crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well-described by simple (time-independent) perturbation theory without referring to Stokes phenomena. We also show that quantum coherence in a double well potential is generally suppressed by the effect of potential curve crossing, which is analogous to the effect of Ohmic dissipation on quantum coherence.