Quantum limits to resolution and discrimination of spontaneous emission lifetimes

In this paper we investigate the quantum information theoretical limits to several tasks related to lifetime estimation and discrimination of a two-level spontaneous optical emitter. We focus, in particular, on the model problem of resolving two mutually incoherent exponential decays with highly overlapping temporal probability profiles. Mirroring recent work on quantum-inspired super-resolution of point emitters, we find that direct lifetime measurement suffers from an analog of "Rayleigh's curse"when the time constants of the two decay channels approach one another. We propose alternative measurement schemes that circumvent this limit and demonstrate superiority to direct measurement for a related binary hypothesis test. Our findings add to a growing list of examples in which a quantum analysis uncovers significant information gains for certain tasks in optomolecular metrology that do not rely on multiphoton interference but evidently do benefit from a more thorough exploitation of the coherence properties of single photons.