Cross-phase modulation and population redistribution in a periodic tripod medium

Abstract

The cross-Kerr effect is studied for two weak beams, probe and trigger, propagating in an atomic medium in a tripod configuration, dressed by a strong standing wave coupling beam in a regime of electromagnetically induced transparency. The nonlinear phase shifts for both transmitted and reflected probe beams induced by the trigger's presence are found to depend on the probe detuning, the control beam's intensity, the relaxation rates and, in particular, on the redistribution of the population among the atomic levels. Such a quantitative analysis indicates that the transmitted and reflected probe beam components and their respective phase shifts can be easily controlled and optimized.

Keywords:

• electromagnetically induced transparency
• Kerr effect
• tripod configuration
• periodic medium
• phase gate

Acknowledgements

K. Słowik is grateful to G.C. La Rocca and Scuola Normale Superiore in Pisa for their kind hospitality. The work of K. Słowik was sponsored by a scholarship for doctoral students ZPORR 2008/2009 of the Marshal of the Kuyavian-Pomeranian Voivodeship. Financial support from Grant Azione Integrata IT09L244H5 of MIUR is also acknowledged.