Abstract

We study a system of two interacting, nonidentical quantum emitters driven by a coherent field. We focus on the particular condition of two-photon resonance and obtain analytical expressions for the stationary density matrix of the system and observables of the fluorescent emission. Importantly, our expressions are valid for the general situation of nonidentical emitters with different transition energies. Our results allow us to determine the regime of parameters in which coherent two-photon excitation, enabled by the coherent coupling between emitters, is dominant over competing, first-order processes. Using the formalism of quantum parameter estimation, we show that the features imprinted by the two-photon dynamics into the spectrum of resonance fluorescence are particularly sensitive to changes in the distance between emitters, making two-photon excitation the optimal driving regime for the estimation of interemitter distance. This can be exploited for applications such as super-resolution imaging of pointlike sources.

Highlights

  • The cooperative phenomena emerging from the interaction between multiple quantum emitters and a common electromagnetic mode are one of the central topics in quantum optics [1,2,3,4]

  • This is explained by the fact that the mechanism of two-photon excitation is strongly dependent on the coherent coupling between emitters, as we have seen in previous sections, and this is strongly modified by the interemitter distance kr12

  • We have studied a system of two interacting, nonidentical quantum emitters under coherent driving, focusing on the regime of two-photon excitation

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Summary

INTRODUCTION

The cooperative phenomena emerging from the interaction between multiple quantum emitters and a common electromagnetic mode are one of the central topics in quantum optics [1,2,3,4]. The emergence of an extra peak in the excitation spectrum due to this two-photon resonance has been demonstrated experimentally [28] and used as a method to quantify dipole coupling and, indirectly, estimate the distance between quantum emitters with nanometer resolution. We obtain general analytical expressions for the stationary density matrix of two interacting nonidentical quantum emitters under coherent driving at the two-photon resonance. This allows us to provide closed-form expressions in regimes that could not be described by previous analytical results [10], such as large driving strengths that saturate the two-photon transition and large coupling between quantum emitters. V, we use quantum parameter estimation theory to analyze the potential of spectrum measurements for the estimation of the interemitter distance

General model
Effective models
Model 2P
Model 1P
STEADY-STATE OBSERVABLES OF THE EMITTED LIGHT
Mean intensity
Second-order correlation function
SPECTRUM OF TWO-PHOTON RESONANCE FLUORESCENCE
QUANTUM PARAMETER ESTIMATION OF
CONCLUSIONS

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