On an optical realization of the SU(1,1) geometric phase, and the Bolyai-Lobachevsky plane
Department of Theoretical Physics,
Attila József University, Szeged,
Tisza L. krt 84, H-6720, Hungary
Accepted: 9 July 1997
We introduce and analyze the SU(1,1) geometric phase emerging in a series of discrete transformations in an optical ring cavity containing partial reflectors. In the theoretical description the underlying projective space is the Bolyai-Lobachevsky (B-L) plane. We show that the resulting geometric phase is equal to half of the area of an object on this plane, determined by the experimental parameters. In the case of three transformations this object is a triangle, and its sides and angles can be related to the reflection and transmission coefficients of the applied mirrors.
PACS: 03.65.Bz – Foundations, theory of measurement, miscellaneous theories (including Aharonov-Bohm effect, Bell inequalities, Berry's phase) / 42.79.-e – Optical elements, devices, and systems
© EDP Sciences, 1997