Abstract
We show that metrological resolution in the detection of small phase shifts provides a suitable generalization of the degrees of coherence and polarization. Resolution is estimated via Fisher information. Besides the standard two-beam Gaussian case, this approach provides also good results for multiple field components and nonGaussian statistics. This works equally well in quantum and classical optics.
Highlights
Interference and polarization are leading manifestations of coherence [1, 2]
The standard definitions of the degrees of coherence and polarization in Eqs. (1) and (2) hold provided that three conditions are satisfied: i) we are restricted to two scalar electromagnetic fields, ii) we perform statistical evaluations of second order in the amplitudes, and iii) the fields obey Gaussian statistics
The key point is the idea of coherence as equivalent to good interference. This idea emerges after Eq (1), where coherence is the maximum fringe visibility, as well as after Eq (4), where visibility reaches its maximum provided that the unitary transformation U is properly chosen
Summary
Interference and polarization are leading manifestations of coherence [1, 2]. In spite of being a very basic topic the complete relationship between coherence, interference and polarization for arbitrary fields is still an open question and is currently the subject of very active investigation [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. (1) and (2) hold provided that three conditions are satisfied: i) we are restricted to two scalar electromagnetic fields, ii) we perform statistical evaluations of second order in the amplitudes, and iii) the fields obey Gaussian statistics Beyond these three restrictions the standard approach may be undetermined or lack usefulness when applied to more general situations involving either more than two electric fields or nonGaussian statistics, as it is the case of the problems addressed in Refs. This idea emerges after Eq (1), where coherence is the maximum fringe visibility, as well as after Eq (4), where visibility reaches its maximum provided that the unitary transformation U is properly chosen This suggests that the degrees of coherence and polarization indicate the best interference that can be achieved with a suitable preparation of the interference for a given input field state. It is worth pointing out that the Fisher information has been extensively used to provide original analyses and interpretations of many different problems in science, from the formation of basic physical laws, to biology and financial economy, for example [36, 37]
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