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Optics Letters

Numerical approach to statistical properties of resonance fluorescence

Matthew Bradford, Jung‐Tsung Shen

Published Sep 17, 2014• 15 citations
Publisher

Abstract

We formulate a numerical scheme to investigate the correlation of photons scattered by a two-level atom coupled to a waveguide, and compute the second-order correlation function. We also show that a three-dimensional resonance fluorescence experiment can be mapped into the one-dimensional situation studied here. The correlation functions for both cases show excellent agreement.

DOI
10.1364/ol.39.005558

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We formulate a numerical scheme to investigate the correlation of photons scattered by a two-level atom coupled to a waveguide, and compute the second-order correlation function. We also show that a three-dimensional resonance fluorescence experiment can be mapped into the one-dimensional situation studied here. The correlation functions for both cases show excellent agreement.
We show how to calculate the first- and second-order statistics of the scattered fields for an arbitrary intensity coherent-state light field interacting with a two-level system in a waveguide geometry. Specifically, we calculate the resonance fluorescence from the qubit, using input-output formalism. We derive the transmission and reflection coefficients, and illustrate the bunching and antibunching of light that is scattered in the forward and backward directions, respectively. Our results agree with previous calculations on one- and two-photon scattering as well as those that are based on the master equation approach.
We suggest that the statistical properties of the scattered radiation in resonance-fluorescence experiments may be affected significantly by the existence of atomic correlations. The scattered light spectrum from two- and three-atom collective systems has been calculated and compared with the one-atom spectrum. The differences are quite significant for weak fields, but become less pronounced as the intensity of the driving field is increased. In addition, we have calculated the scattered intensity correlation function for collectively interacting systems, and found that its behavior is very different from that of the single-atom intensity correlation function, both for weak and strong incident fields. The implications of our findings for the observation of photon antibunching are also discussed.
Resonance fluorescence and photon correlations are areas that have long been studied, and are integral to the field of quantum optics. Recently frequency filtered photon correlations and the method of frequency filtering have had a surge of interest [1]–[4]. In this work we develop a novel method of calculating frequency filtered photon correlations by coupling the atomic fluorescence - in this case, from a three-level ladder type atom [5], [6] - into an array of single-mode cavity filters. This coupling, modelled with an open cascaded systems approach [7], [8] is entirely unidirectional, allowing us to derive a closed set of coupled moment equations for the filter source operators. This provides an extremely efficient method for calculating frequency filtered second-order correlation functions.
In the framework of the signal processing approach to single-atom resonance fluorescence with spectral resolution, we diagrammatically derive an analytical formula for arbitrary-order spectral correlation functions of the scattered fields that pass through Fabry-Perot interferometers. Our general expression is then applied to study correlation signals in the limit of well separated spectral lines of the resonance fluorescence spectrum. In particular, we study the normalized second-order temporal intensity correlation functions in the case of the interferometers tuned to the components of the spectrum and obtain interferential corrections to the approximate results derived in the secular limit. In addition, we explore purely spectral correlations and show that they can fully be understood in terms of the two-photon cascades down the dressed state ladder.
We present analytical solutions for the second-order correlation function [ g (2 )( τ )] for light scattered from a two-level atom driven by laser light with arbitrary detuning and the Rabi frequency. By solving the optical Bloch equations for a two-level atom, we obtain analytical solutions for the populations that are subsequently used for calculating g (2 )( τ ). We also obtain g (2)( τ ) for special cases, such as zero detuning or weak laser intensity, directly from the general analytical solutions for g (2 )( τ ).