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Physical Review A

Conditional resonance-fluorescence spectra of single atoms

Gerhard C. Hegerfeldt, Martin Bodo Plenio

Published Feb 1, 1996• 22 citations

Abstract

The temporal behavior of a single quantum system may contain information, for instance, about macroscopic dark periods in electron shelving, which is washed out or even lost in ensemble averages. The same is true in principle for spectral information. For example, for an atom with light and dark periods one might try to spectrally analyze the light emitted in a light period of given length or, more generally, the light emitted into one solid angle while monitoring the temporal emission in another solid angle. Considering different emission behaviors one may get different spectra, i.e., spectra that are dependent on the conditions imposed. In this paper, such questions, in particular the notion of spectrum in a light period, are studied. To this end we generalize the recent quantum jump approach to include resonance-fluorescence spectra of single atoms. We explicitly show that the theory developed in this paper easily generalizes, e.g., to absorption spectra. We apply the theory to a V system that has one metastable level and that may exhibit intermittent fluorescence when driven by two lasers. We show that the spectrum of resonance fluorescence of the complete ensemble differs substantially from that observed in a light period. A physical explanation of this behavior is presented. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physreva.53.1164

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The temporal behavior of a single quantum system may contain information, for instance, about macroscopic dark periods in electron shelving, which is washed out or even lost in ensemble averages. The same is true in principle for spectral information. For example, for an atom with light and dark periods one might try to spectrally analyze the light emitted in a light period of given length or, more generally, the light emitted into one solid angle while monitoring the temporal emission in another solid angle. Considering different emission behaviors one may get different spectra, i.e., spectra that are dependent on the conditions imposed. In this paper, such questions, in particular the notion of spectrum in a light period, are studied. To this end we generalize the recent quantum jump approach to include resonance-fluorescence spectra of single atoms. We explicitly show that the theory developed in this paper easily generalizes, e.g., to absorption spectra. We apply the theory to a V system that has one metastable level and that may exhibit intermittent fluorescence when driven by two lasers. We show that the spectrum of resonance fluorescence of the complete ensemble differs substantially from that observed in a light period. A physical explanation of this behavior is presented. \textcopyright{} 1996 The American Physical Society.

We consider a three-level atomic system driven strongly on one transition and weakly on the other. The excited state on the weak transition is assumed to be metastable. We give an analysis of the fluorescence from the strong transition in terms of the elementary probability density

{p}_{[0}

,t)(

{\mathrm{t}}_{1}

,

{t}_{2}

,...,

{t}_{n}

) which gives us the probability density that exactly n photons are emitted at times

{t}_{1}

,

{t}_{2}

,...,

{t}_{n}

by the atom in the time interval [0,t). We show that

{p}_{[0}

,t) essentially factorizes into products of conditional densities c\ifmmode \tilde{}\else \~{}\fi{}(\ensuremath{\tau}) that, given a photon is emitted at time zero, the next photon emission occurs at time \ensuremath{\tau}. This enables a simulation of the individual photon emissions to be given which shows directly the existence of prolonged dark windows in the fluorescence corresponding to the shelving of the electron in the metastable state or ``quantum jumps.''

We investigate the spectrum of resonance fluorescence of laser-driven three-level systems in the V or $\ensuremath{\Lambda}$ configuration where one transition is metastable. If the laser driving the weak transition has a sufficiently small Rabi frequency we find an extremely narrow structure in the resonance fluorescence spectrum of the strong transition. Analytical expressions approximating the spectrum are given and the properties of the spectrum are discussed. With the help of a simplified model of resonance fluorescence emitted on the strong transition we are able to show that the origin of the narrow peak can be traced back to electron shelving, i.e., to the existence of light and dark periods in the resonance fluorescence emitted on the strong transition.

We investigate time-dependent spectra of the intermittent resonance fluorescence of a single, laser-driven, three-level atom due to electron shelving. After a quasistationary state of the strong transition, a slow decay due to shelving leads to the steady state of the three-level system. The long-term stationary spectrum consists of a coherent peak, an incoherent Mollow-like structure, and a very narrow incoherent peak at the laser frequency. We find that in the ensemble-average dynamics, the narrow peak emerges during the slow decay regime, after the Mollow spectrum has stabilized but well before an average dark time has passed. The coherent peak, being a steady-state feature, is absent during the time evolution of the spectrum.

One of the experiments made possible by the trapping and cooling of a single atom is to observe the quantum jumps to a metastable state in the atom by monitoring the resonance fluorescence of a strong transition in which at least one of the states is coupled to the metastable state. When the atomic electron moves to the metastable state, the fluorescence from the strongly driven transition disappears. When the electron drops back into the strongly driven transition, the fluorescence abruptly returns. Statistical analysis of these random interruptions to the fluorescence signal implies photon antibunching in the emission of the weak photon.