Abstract
The local observables of the quantised electromagnetic field near a mirror-coated interface depend strongly on the properties of the media on both sides. In macroscopic quantum electrodynamics, this fact is taken into account with the help of optical Green’s functions which correlate the position of an observer with all other spatial positions and photon frequencies. Here we present an alternative, more intuitive approach and obtain the local field observables with the help of a quantum mirror image detector method. In order to correctly normalise electric field operators, we demand that spontaneous atomic decay rates simplify to their respective free space values far away from the reflecting surface. Our approach is interesting, since mirror-coated interfaces constitute a common basic building block for quantum photonic devices.
Highlights
The fluorescence properties of an atomic dipole depend primarily on the so-called local density of states of the electromagnetic (EM) field, i.e., on the number of EM mode decay channels available at the same location (van Tiggelen and Kogan, 1994; Sprik et al, 1996; Kwadrin and Koenderink, 2013)
Carniglia and Mandel (Carniglia and Mandel, 1971) modeled semitransparent mirrors by only considering stationary photon modes which contain incoming as well as reflected and transmitted contributions. Their so-called triplet modes depend on reflection and transmission rates and are a subset of the free space photon modes of the EM field
The fluorescence properties of an atomic dipole depend on the socalled local density of states of the quantised EM field which itself depends in a complex way on the properties of all of its surroundings
Summary
The fluorescence properties of an atomic dipole depend primarily on the so-called local density of states of the electromagnetic (EM) field, i.e., on the number of EM mode decay channels available at the same location (van Tiggelen and Kogan, 1994; Sprik et al, 1996; Kwadrin and Koenderink, 2013). Deriving the local density of states of the EM field in more complex scenarios, which involves the calculation of the imaginary parts of the dyadic Green’s function (Novotny and Hecht, 2006; Scheel and Buhmann, 2008; Bennett and Buhmann, 2020; Stourm et al, 2020), can be computationally challenging Such calculations can aid the design of photonic devices, they do not provide much physical intuition. Carniglia and Mandel (Carniglia and Mandel, 1971) modeled semitransparent mirrors by only considering stationary photon modes which contain incoming as well as reflected and transmitted contributions Their so-called triplet modes depend on reflection and transmission rates and are a subset of the free space photon modes of the EM field. If one wants to avoid such interference problems, adjustments have to be made (Khosravi and Loudon, 1991; Creatore and Andreani, 2008), for example by doubling the usual Hilbert space of the quantised EM field in the presence of a semi-
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