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arXiv:quant-ph/0205154 · Journal of Optics B Quantum and Semiclassical Optics

The intensity correlation function of $lquot$blinking$rquot$ quantum systems

Gerhard C. Hegerfeldt, Dirk Seidel

Published Jun 19, 2002• 7 citations
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Abstract

Explicit expressions are determined for the photon correlation function of ``blinking'' quantum systems, i.e. systems with different types of fluorescent periods. These expressions can be used for a fit to experimental data and for obtaining system parameters therefrom. For two dipole-dipole interacting $V$ systems the dependence on the dipole coupling constant is explicitly given and shown to be particularly pronounced if the strong driving is reduced. We propose to use this for an experimental verification of the dipole-dipole interaction.

DOI
10.1088/1464-4266/4/5/303

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The intensity correlation function of lquotlquotlquotblinkingrquotrquotrquot quantum systems
Explicit expressions are determined for the photon correlation function of ``blinking'' quantum systems, i.e. systems with different types of fluorescent periods. These expressions can be used for a fit to experimental data and for obtaining system parameters therefrom. For two dipole-dipole interacting VVV systems the dependence on the dipole coupling constant is explicitly given and shown to be particularly pronounced if the strong driving is reduced. We propose to use this for an experimental verification of the dipole-dipole interaction.
If an atom is able to exhibit macroscopic dark periods, or electron shelving, then a driven system of two atoms has three types of fluorescence periods (dark, single, and double intensity). We propose to use the average durations of these fluorescence types as a simple and easily accessible indicator of cooperative effects. As an example, we study two dipole-interacting V systems by simulation techniques. We show that the durations of the two types of light periods exhibit marked separation-dependent oscillations and that they vary in phase with the real part of the dipole-dipole coupling constant.
The excitation spectrum arising from photon density-density correlations has been considered in a system of two interacting identical atoms. The two-level atoms are pumped near resonance by a strong electromagnetic field while they interact through their dipole-dipole interaction and radiate to each other as well. In such a system the photon density-density correlations arise from the interference spectrum due to the beating of the frequency of the pump field and the atomic transition frequency, as well as from the spectrum induced by the dipole-dipole and radiative interactions between the atoms. The spectral function of this system has been calculated in the limit of high photon densities. It consists of four terms describing four bands which are similar to those appearing in the two-atom resonance fluorescence spectrum for the symmetric modes when the central peak is missing. The collective behavior as well as the dynamics of the system are discussed in detail. By using the spectral function, an expression for the photon density-density correlation function at different times has been derived where thermal effects have been also included.
We study analytically the effect of the dipole-dipole interaction on the statistics of the fluorescent radiation emitted from a system of two two-level atoms resonantly driven by a coherent field. For some interatomic separations, an inhibition of fluorescence occurs, which is reminiscent of the recently discussed quantum-jump phenomenon in a single three-level atom. This is reflected in the behaviors of the intensity correlation function, Mandel's Q parameter, and the time-dependent fluorescence spectrum. It is argued that this quantum-jump-like behavior arises from the coupling between the symmetric states and the antisymmetric state caused by the dipole-dipole interaction.
We investigate the effect of blinking on the two-photon interference measurement from two independent quantum emitters. We find that blinking significantly alters the statistics in the Hong-Ou-Mandel second-order intensity correlation function ${\mathrm{g}}^{(2)}(\ensuremath{\tau})$ and the outcome of two-photon interference measurements performed with independent quantum emitters. We theoretically demonstrate that the presence of blinking can be experimentally recognized by a deviation from the gD(2)(0)=0.5{\mathrm{g}}_{D}^{(2)}(0)=0.5gD(2)​(0)=0.5 value when distinguishable photons from two emitters impinge on a beam splitter. Our findings explain the significant differences between linear losses and blinking for correlation measurements between independent sources and are experimentally verified using a parametric down-conversion photon-pair source. We show that blinking imposes a mandatory cross-check measurement to correctly estimate the degree of indistinguishability of photons emitted by independent quantum emitters.
We consider the effect of dipole-dipole interaction on the quantum jumps in a system of two three-level atoms in a ssV configuration interacting with coherent fields. We show that the intensity-intensity correlation for the strong transition shows additional fluctuations for some interatomic separations between the atoms signifying three levels of fluorescence. It is argued that the intermediate level of fluorescence arises from the coupling between the symmetric and antisymmetric states caused by the dipole-dipole interaction.
We apply a general formalism for the separation of rapid and slow time scales in linear evolution equations to three-state atoms with a strong and a weak radiative transition. This leads to an expression for the intensity correlation function that constitutes a good approximation on both time scales. This result can also be translated into an expression for the waiting-time distribution for the next photon emission after a previous one. The slow evolution is expressed in two rate constants, which determine the statistical distribution for dark and bright periods in the fluorescent emission. The result is applied to various configurations of the radiative couplings between the three states.