Abstract
We present a quantum theory for the interaction of a two level emitter with surface plasmon polaritons confined in single-mode waveguide resonators. Based on the Green's function approach, we develop the conditions for the weak and strong coupling regimes by taking into account the sources of dissipation and decoherence: radiative and non-radiative decays, internal loss processes in the emitter, as well as propagation and leakage losses of the plasmons in the resonator. The theory is supported by numerical calculations for several quantum emitters, GaAs and CdSe quantum dots and NV centers together with different types of resonators constructed of hybrid, cylindrical or wedge waveguides. We further study the role of temperature and resonator length. Assuming realistic leakage rates, we find the existence of an optimal length at which strong coupling is possible. Our calculations show that the strong coupling regime in plasmonic resonators is accessible within current technology when working at very low temperatures (<4K). In the weak coupling regime our theory accounts for recent experimental results. By further optimization we find highly enhanced spontaneous emission with Purcell factors over 1000 at room temperature for NV-centers. We finally discuss more applications for quantum nonlinear optics and plasmon-plasmon interactions.
Highlights
Cavity quantum electrodynamics was invented to study and control the simplest light-matter interaction: a two-level emitter coupled to a light monomode.1 At first associated with quantum optics, the emitter was an atom or a collection of them, while the electromagnetic (EM) field was confined in a high-finesse cavity.2 Nowadays, cavity QED experiments cover quite a lot of implementations
The theory is supported by numerical calculations for several quantum emitters, GaAs and CdSe quantum dots, and nitrogen vacancy (NV) centers together with different types of resonators constructed of hybrid, cylindrical, or wedge waveguides
We have reported a quantum theory for plasmonic resonators coupled to single quantum emitters
Summary
Cavity quantum electrodynamics (cavity QED) was invented to study and control the simplest light-matter interaction: a two-level emitter (called TLS or emitter throughout this paper) coupled to a light monomode. At first associated with quantum optics, the emitter was an atom or a collection of them, while the electromagnetic (EM) field was confined in a high-finesse cavity. Nowadays, cavity QED experiments cover quite a lot of implementations. Losses dominate and the emission spectrum consists of a single peak around the dressed TLS resonant transition while the lifetime is modified because of the field confinement inside the cavity. This modification is nothing but the Purcell effect. We first summarize the quantum theory for the coupling between quantum dipoles and resonators made out of one-dimensional (1D) plasmonic waveguides Within this theoretical framework, we properly include the losses and map to a Jaynes-Cummings model and, to the physics and applications of traditional cavity QED.
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