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GAUGE THEORY AND TWO LEVEL SYSTEMS

Dipartimento di Fisica "E. R. Caianiello" and INFN, Università di Salerno, I-84100 Salerno, Italy

Dipartimento di Matematica e Informatica, Università di Salerno and INFN, Gruppo Collegato Salerno, I-84100 Salerno, Italy

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S. KAK

Department of Computer Science, Oklahoma State University, Stillwater, OK 74078, USA

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G. RAIMONDO

Dipartimento di Fisica "E. R. Caianiello" and INFN, Università di Salerno, I-84100 Salerno, Italy

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G. VITIELLO

Dipartimento di Matematica e Informatica, Università di Salerno and INFN, Gruppo Collegato Salerno, I-84100 Salerno, Italy

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https://doi.org/10.1142/S021798491102698XCited by:11 (Source: Crossref)

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.

This paper is dedicated to Professor Mario Rasetti on the occasion of his 70th birthday.

Keywords:

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