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Physical Review A

Quantum jumps via spontaneous Raman scattering

Randall G. Hulet, David J. Wineland

Published Sep 1, 1987• 12 citations
Publisher

Abstract

A single laser, which is used to induce and detect spontaneous Raman transitions, can be used to observe quantum jumps in a single atom. The population dynamics of a particular system, consisting of two $^{2}\mathrm{S}_{1/2}$ ground-state levels and four $^{2}\mathrm{P}_{3/2}$ excited-state levels split by a magnetic field, is analyzed for a laser tuned near a particular transition. We find that the statistics of the fluorescence emitted by this system are described by the same formalism developed for the three-level V configuration irradiated by two light sources. Over a wide range of observation times, the fluorescence intensity will be two valued, either off or on, as has been verified for the V configuration. Some surprising and elegant features of this new system are described.

DOI
10.1103/physreva.36.2758

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A single laser, which is used to induce and detect spontaneous Raman transitions, can be used to observe quantum jumps in a single atom. The population dynamics of a particular system, consisting of two 2S1/2^{2}\mathrm{S}_{1/2}2S1/2​ ground-state levels and four 2P3/2^{2}\mathrm{P}_{3/2}2P3/2​ excited-state levels split by a magnetic field, is analyzed for a laser tuned near a particular transition. We find that the statistics of the fluorescence emitted by this system are described by the same formalism developed for the three-level V configuration irradiated by two light sources. Over a wide range of observation times, the fluorescence intensity will be two valued, either off or on, as has been verified for the V configuration. Some surprising and elegant features of this new system are described.
Quantum jumps due solely to spontaneous Raman scattering between the Zeeman sublevels of a single 24Mg+^{24}\mathrm{Mg}^{+}24Mg+ ion have been observed in the fluorescence emitted by the ion. A theory of quantum jumps for this system predicts that coherences between excited levels cause the ratio of the mean duration of the "fluorescence-on periods" to the mean duration of the "fluorescence-off periods" to be independent of laser intensity. The measured value agrees with the predicted one to within the measurement precision of 2%. The distribution of the durations of the off periods also agrees with theory.
Several experiments performed at NBS using a single (or few) trapped atomic ions are described. We recently observed the ‘‘quantum jumps’’ in the fluorescence from a single ion of Mg+ due to spontaneous Raman transitions between the energy levels of the ion. In this system, a single laser is used to induce transitions between Zeeman sub‐levels of the ion. As with other realizations of quantum jumps, the dynamics of the population evolution is governed by an effective two‐level rate equation. A novel coherence phenomenon between excited state sub‐levels makes this system ideally suited for quantitatively testing the quantum jump theory. Our data are consistent with theory to within the measurement precision of 2%. Images of two to four ions which have been laser‐cooled until they ‘‘crystallize’’ are displayed and several other recent single ion experiments are mentioned.
A theory of the discrete photodetection of quantum jumps on the V configuration of atomic levels has been developed. A three-level source atom is placed in a cavity excited by a resonance fluorescence field. The cavity is tuned to exact resonance with an atomic transition. The cavity mode state is tested by a flux of unexcited (at the entrance) probe atoms passing through the cavity. The energy states of the outgoing probe atoms are detected by ionization chambers, which are assumed ideal. This a posteriori statistical information is indirectly related to the numerical characteristics of a measured quantum system consisting of the source atom and cavity mode. The “tuning” conditions for a discrete photodetector, i.e., the rules for choosing the parameters and durations of the interactions of the cavity mode with the probe and source atoms, intensities of the pump and probe fields that are necessary for observing quantum jumps from the “bright” state to the “dark” one and vice versa, have been determined. A two-state model that describes the dynamics of a quantum jump has been analyzed. The formulas have been obtained for the observable characteristics of quantum jumps: the mean residence time of the quantum system in quasistationary states (durations of the bright and dark periods), probabilities of quantum jumps, mean excitation levels of the quantized cavity mode, etc.
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.>
Complete density-matrix equations and a one-photon counting probability are used to examine the photon statistics of fluorescence light of a single three-level atom, weakly coupled to an external cavity of low QQQ value. The internal structure of the atom is supposed to be characterized by a weak and a strong transition. The strong transition is coherently driven by an external laser field, whereas no external field is acting on the weak transition. In free space the system exhibits quantum jumps. By placing the atom within the mirrors of an external cavity, tuned close to the transition frequency of the two upper levels, modifications in the quantum jump behavior of the atom are shown due to a modified spontaneous decay rate between the two states. In particular, it is demonstrated that the effect of the cavity is to modify the repetition rate of quantum jumps into the metastable dark state and the average duration of bright periods of fluorescence, whereas the average duration of dark periods is not changed in first order of the spontaneous decay rates involved. In view of current experiments in our laboratory a quantitative analysis is presented for the special case of a single indium ion located between the mirrors of a high-order symmetric confocal cavity.
Recent experiments with single atomic ions isolated in electromagnetic traps have demonstrated abrupt changes in observed fluorescence intensities, which have been interpreted as evidence for quantum jumps as the atom changes energy levels. This presents the seeming paradox of discontinuously changing observables from a system whose dynamical evolution is governed by the continuous optical Bloch equations. In this paper I present an analysis of the dynamics of a model three-level atom interacting with two laser fields in terms of the dressed states of the atom-laser system. These dressed states are eigenstates of a Hamiltonian which includes laser-atom interactions, and thus they simplify the discussion of the time evolution of the combined laser-atom system. This dressed-state description is particularly useful in the regime in which both laser intensities are strong enough to saturate their respective transitions. I calculate the radiative lifetimes of the different species of dressed states and the branching ratios for decay to other dressed states, and demonstrate the consequences of these quantities for the observed fluorescence pattern. The calculated duration of bright and dark periods shows a pronounced dependence on the detunings of the lasers.