Gauge theory and two level systems

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.

7 pages

References in corpus (7)

• Cosmological Experiments in Condensed Matter Systems
• Optimized Dynamical Decoupling in a Model Quantum Memory
• The role of the electromagnetic field in the formation of domains in the process of symmetry breaking phase transitions
• Entangled Quantum Fields near the Event Horizon and Entropy
• Non-abelian gauge structure in neutrino mixing
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• Analysis of Kak's Quantum Cryptography Protocol from the Perspective of Source Strength