Optical decay into CROW waveguides - an exact solution

Photonic quantum processing is a promising route towards large-scale quantum computation and communication, with a need for fully integrated devices. Recently we have proposed a microsystem (MS) made of two emitters strongly... [ view full abstract ]

Photonic quantum processing is a promising route towards large-scale quantum computation and communication, with a need for fully integrated devices. Recently we have proposed a microsystem (MS) made of two emitters strongly coupled to a two-mode cavity (Fig.1) as a source of directionally-entangled photons. Such a MS is potentially a solid state on demand electrically pumped source, ultrabright and integrable in a 2D photonic band gap circuit.

The MS principle relies on a fundamental symmetry plane (Fig.1), and an engineered degeneracy of the intermediate dressed states of the cascade from “two-quanta dressed states”. The photon pairs must be collected by narrow-band waveguides, indicating use of coupled-resonator optical waveguides (CROW) whose minibands selecting the photon pairs.

Here we explore the decay of a single MS transition into periodic CROW waveguide with a Weisskopf-Wigner approach. We have found a new closed form solution for the probability to remain in the excited state P (Fig.2), and even for the final emitted quantum state, valid for all parameter values. In Fig.2 the contours of P are displayed as a function of the coupling and the detuning. We clearly see that the parameter space is divided into three regions of fundamentally different behaviour. First, in the white region the asymptotic decay is always complete, and becomes faster (and progressively non-exponential) as coupling increases. Second, in the region hatched region P is not defined since the probability to stay in the excited state oscillates forever between two values: this is the strong coupling region with the CROW. Third, in the remaining area the asymptotic decay is never complete (P > 0), nor is it completely inhibited (P) < 1. 

These results may seem surprising, in particular the possibility of partial decay when the transition frequency is outside the channel bandwidth where the coupling constant vanishes, but constitutes a beautiful exact model for qualitative behaviour previously discussed in [1].

[1] A.G.Kofman et al., J. Mod. Opt. 41, p.353 (1994); P.R.Berman et al., Adv. At. Mol. and Opt. Phys. 59, p.175 (2010)