Gauge theory and two level systems

TL;DR

This paper introduces a gauge-invariant framework for describing the time evolution of two-level quantum systems, linking it to optical birefringence and quantum phases, with implications for entropy and environment effects.

Contribution

It develops a novel gauge-invariant formalism for two-level systems and relates it to optical phenomena and quantum phase concepts.

Findings

Gauge-invariant evolution equation for two-level systems

Analogy between gauge invariance and optical birefringence

Discussion of entropy, environment effects, and state distance

Abstract

We consider the time evolution of a two level system (a two level atom or a qubit) and show that it is characterized by a local (in time) gauge invariant evolution equation. The covariant derivative operator is constructed and related to the free energy. We show that the gauge invariant characterization of the time evolution of the two level system is analogous to the birefringence phenomenon in optics. The relation with Berry-like and Anandan--Aharonov phase is pointed out. Finally, we discuss entropy, environment effects and the distance in projective Hilbert space between two level states in their evolution.