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Abstract
The Shannon entropy as a measure of information contents is investigated around an exceptional point (EP) in an open elliptical microcavity as a non-Hermitian system. The Shannon entropy is maximized near the EP in the parameter space for two interacting modes, but the exact maximum position is slightly off the EP toward the weak interaction region while the slopes of the Shannon entropies diverge at the EP. The Shannon entropies also show discontinuity across a specific line in the parameter space, directly related to the exchange of the Shannon entropy as well as the mode patterns with that line as a boundary. This feature results in a nontrivial topological structure of the Shannon entropy surfaces.
Highlights
The Shannon entropy as a measure of information contents is investigated around an exceptional point (EP) in an open elliptical microcavity as a non-Hermitian system
There is a conflicting theory suggesting negligible enhancement in spontaneous emission at an EP due to coherent perfect cancellation of two diverging Petermann factors associated with two cavity m odes[30]; the theory is classical in parts, and only the bi-orthogonality of the cavity modes is taken into account whereas the spatial distributions of the cavity modes are neglected
One is led to ask how the information contents associated with the mode distribution behave near an EP in an open physical system in term of the Shannon entropy, which as a measure of average information contents is directly related to the degree of the irregular[31] or disorder physical quantities[32]
Summary
The Shannon entropy as a measure of information contents is investigated around an exceptional point (EP) in an open elliptical microcavity as a non-Hermitian system. There is a conflicting theory suggesting negligible enhancement in spontaneous emission at an EP due to coherent perfect cancellation of two diverging Petermann factors associated with two cavity m odes[30]; the theory is classical in parts, and only the bi-orthogonality of the cavity modes is taken into account whereas the spatial distributions of the cavity modes are neglected. The reason why this conflict arises and which interpretation of the spontaneous emission near EP is valid are still open questions. One is led to ask how the information contents associated with the mode distribution behave near an EP in an open physical system in term of the Shannon entropy, which as a measure of average information contents is directly related to the degree of the irregular[31] or disorder physical quantities[32]
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