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Abstract
When a photon with well-defined polarization and momentum passes through a focusing device, these properties are no longer well defined. Their loss is captured by describing polarization by a 3× 3 effective density matrix. Here we show that the effective density matrix corresponds to the actual photodetection model and we provide a simple formula to calculate it in terms of classical fields. Moreover, we explore several possible experimental consequences of the ‘longitudinal’ term: limits on single-photon detection efficiency, polarization-dependent atomic transitions rates and the implications on quantum information processing.
Acknowledgments
The work of NHL is supported by a grant from the Technion Graduate School. Parts of this research were done during the visit of NHL to the Perimeter Institute and of DRT to the University of Queensland. The importance of focusing effects was pointed out to us by Eli Yablonovich. We thank Gerard Milburn, Petra Scudo, Christine Silberhorn, Vlatko Vedral and Andrew White for useful discussions and helpful comments.