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Physical Review Letters

Possibility of Direct Observation of Quantum Jumps

Richard J. Cook, Harry J. Kimble

Published Mar 11, 1985• 302 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 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.

DOI
10.1103/physrevlett.54.1023

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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.
A quantum-statistical theory is developed for a single-atom, three-state quantum system where a strong (1-3) and a weak (2-3) transition are driven resonantly by an incoherent field. From a second-order correlation function of the fluorescence intensity, it is concluded that a quantum jump can occur, in the sense that the single atom can undergo large fluctuations between a state of full emission in the strong transition to a state of no emission when the electron is shelved in the metastable state (2).
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.
We examine the intensity fluctuations in the fluorescence from a single three-level atom exhibiting quantum jumps. The macroscopic intensity fluctuations revealed in the quantum random telegraph signal of emitted light are the signature of transitions between rapidly emitting and metastable states. We calculate the Mandel Q parameter for such a three-level atom both for incoherent and coherent driving and demonstrate how it provides a sensitive measure of the jumps. We show that the Q parameter reflects the existence of periods of brightness and darkness in the telegraph signal more directly than the second-order intensity correlation function.
We detect the radiatively driven electric quadrupole transition to the metastable 2D52^{2}D_{\frac{5}{2}}2D25​​ state in a single, laser-cooled Hg II ion by monitoring the abrupt cessation of the fluorescence signal from the laser-excited $^{2}S_{\frac{1}{2}}\ensuremath{\rightarrow}^{2}P_{\frac{1}{2}}$ first resonance line. When the ion "jumps" back from the metastable DDD state to the ground SSS state, the $S\ensuremath{\rightarrow}P$ resonance fluorescence signal immediately returns. The statistical properties of the quantum jumps are investigated; for example, photon antibunching in the emission from the DDD state is observed with 100% efficiency.