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Physical Review A

Intermittent atomic fluorescence

Harry J. Kimble, Richard J. Cook, Ann Laurie Wells

Published Oct 1, 1986• 84 citations
Publisher

Abstract

In a single-atom double-resonance experiment involving a strong and a weak transition, quantum jumps on the weak transition cause the resonance fluorescence of the strong transition to turn on and off randomly in time when observed over intervals long compared to the lifetime of the strong transition but short compared to that of the weak transition. Here we present a theory of this intermittent atomic fluorescence for the case of coherent excitation.

DOI
10.1103/physreva.34.3190

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IEEE Journal of Quantum Electronics•Jul 1, 1988•45 citations
In a single-atom double-resonance experiment involving a strong and a weak transition, quantum jumps on the weak transition cause the resonance fluorescence of the strong transition to turn on and off randomly in time when observed over intervals long compared to the lifetime of the strong transition but short compared to that of the weak transition. Here we present a theory of this intermittent atomic fluorescence for the case of coherent excitation.
In a single-atom double-resonance experiment involving a strong and a weak transition, quantum jumps on the weak transition cause the fluorescence of the strong transition to turn on and off abruptly. The fluorescence is off when the weak transition is excited and on when it is not. Thus quantum jumps on the weak transition can be directly monitored by observation of the random telegraph signal radiated by the strong transition. We present here a simple theory of this effect for the case of incoherent excitation.
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.
In a recent publication1 the question of the possibility of observing directly the quantum jumps associated with the excitation and deexcitation of an atomic electron in a three-level transition was considered. While the analysis of Ref. 1 reveals the manner in which the fluorescence from a strong transition of a lifetime T1 is modulated by the absorption and emission processes of a weak transition of lifetime T2 (T1 ≪ T2), it was restricted to the case of incoherent excitation of the two transitions. The purpose of the present work is to reconsider this problem for monochromatic excitation in which a variety of coherent effects come into play. The analysis proceeds in a straightforward fashion in the Heisenberg representation to yield expressions for field and atomic correlation functions representing probabilities for the detection of successive photons from the same transition as well as for cross correlations of emission probabilities. In the limit of T1 ≪ T2, a coarse graining of time with respect to the strong transition produces expressions analogous to those presented in Ref. 1. The roles of Autler-Townes splitting, frequency detuning, and saturation of the weak transition are discussed.
Phase-sensitive squeezing in the resonance fluorescence of two-level atoms, that are coherently driven by a near-resonant laser field in free space, was observed recently (Lu et al 1998 Phys. Rev .L ett. 81 3635). This was accomplished via homodyne detection at a phase near ±45 ◦ relative to the driving field for strong off-resonant excitation of ‘long-lived’ atoms (where th ea tomic lifetime far exceeded the laser–atom interaction time, meaning that relaxation effects could be ignored). On the other hand, traditional theoretical predictions of phase-sensitive squeezing in the resonance fluorescence from two-level atoms have emphasized in- and out-of-phase (i.e., 0 ◦ and 90 ◦ ) quadratures, and weak, on-resonant excitation of ‘short-lived’ atoms (where the observation time for laser–atom interaction fa re xceeded the natural atomic lifetime, meaning that relaxation effects dominate). Here, we calculate the probability of a delayed-coincidence detection in the interference field of a fluorescing dipole with a local oscillator (LO). We show that, despite the strikingly different conditions in which squeezing occurs in short- and long-lived atoms, squeezing in both cases can be shown to arise from a joint detection of two photons which are related by a quantum jump in the following way: the first photodetection precipitates a quantum jump of the atom to the ground state, and the second measures the mean amplitude of the fluorescent field subsequent to the quantum jump.
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{p}_{[0}p[0​,t)(t1{\mathrm{t}}_{1}t1​,t2{t}_{2}t2​,..., tn{t}_{n}tn​) which gives us the probability density that exactly n photons are emitted at times t1{t}_{1}t1​,t2{t}_{2}t2​,...,tn{t}_{n}tn​ by the atom in the time interval [0,t). We show that p[0{p}_{[0}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.''
The statistics of spontaneous photon emission times in single atom resonance fluorescence are investigated through the radiative cascade of the dressed atom. The delay function which gives the distribution of the delays between two successive emissions is calculated for a coherent as well as an incoherent laser excitation. For a two-level atom, various signals that reflect the fluorescence intensity (average value, photon counting, fluctuation spectrum, etc.) are reviewed by this method. For a three-level atom, this approach is applied to the analysis of the recently observed phenomenon of intermittent fluorescence and quantum jumps.>