Minimum uncertainty solutions for partially coherent fields and quantum mixed states

• Published in: New journal of physics Vol. 16; no. 12; pp. 123023 - 19
• Main Authors: Alonso, M, Setälä, T, Friberg, A T
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 08.12.2014
• Subjects: Beams (radiation); Coherence; Coherent light; Lower bounds; Physics; Pulse propagation; Purity; quantum states; Representations; Spreads; Uncertainty; uncertainty relations
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/16/12/123023

A general prescription is given for finding uncertainty relations that dictate the lower bounds on the measures of spread corresponding to two different representations of a partially coherent wave field or mixed quantum state, for a given measure of overall coherence or purity. In particular it is shown that the coherent modes of the fields/states that achieve the lower bounds are independent of the measure of purity being used, and that this measure determines only the amount in which these modes contribute. Our results are important in the design of optical systems with partially coherent light and in quantum mixed states, for which maximal joint localization is desired. These ideas are illustrated for the case of optical beams, pulses propagating in dispersive media and quantum phase.