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Physical Review A

Coherence with incoherent light: A new type of quantum beat for a single atom

Gerhard C. Hegerfeldt, Martin Bodo Plenio

Published Mar 1, 1993• 67 citations
Publisher

Abstract

Even with incoherent driving, coherence effects may show up in the spontaneous emissions of an atom. We derive a general master equation and predict that for both the three-level V and \ensuremath{\Lambda} systems the intensity correlation function ${\mathit{g}}^{(2)}$(\ensuremath{\tau}) may exhibit pronounced oscillations with frequency \ensuremath{\delta}\ensuremath{\omega} if the level separation \ensuremath{\Elzxh}\ensuremath{\delta}\ensuremath{\omega} is small. We obtain a marked difference in the beat amplitude for a single \ensuremath{\Lambda} system as compared to a beam or gas. If \ensuremath{\delta}\ensuremath{\omega} is much smaller than the natural linewidth we find dark and light periods in the spontaneous emission.

DOI
10.1103/physreva.47.2186

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Even with incoherent driving, coherence effects may show up in the spontaneous emissions of an atom. We derive a general master equation and predict that for both the three-level V and \ensuremath{\Lambda} systems the intensity correlation function g(2){\mathit{g}}^{(2)}g(2)(\ensuremath{\tau}) may exhibit pronounced oscillations with frequency \ensuremath{\delta}\ensuremath{\omega} if the level separation \ensuremath{\Elzxh}\ensuremath{\delta}\ensuremath{\omega} is small. We obtain a marked difference in the beat amplitude for a single \ensuremath{\Lambda} system as compared to a beam or gas. If \ensuremath{\delta}\ensuremath{\omega} is much smaller than the natural linewidth we find dark and light periods in the spontaneous emission.
Abstract It has been shown that coherence effects have a marked influence in the spontaneous emission spectrum of a three-level Λ -type atom driven by weak coherent and incoherent fields. Phase dependent evolution of interference effects leading to spectral narrowing, generation of spectral hole and dark line are exhibited in the present scheme when the atom does not interact with the incoherent fields. The basic mechanism underlying this scheme seems to be appropriate for a phaseonium. Apart from phase-coherence introduced in the system the phenomenon of line narrowing, in the presence of weak incoherent pumping, can be achieved in a different way as a consequence of two competitive resonant effects: sharp non-Lorentzian and symmetric Fano-like-resonance contributions to the line shape. In both the situations, the evolution of narrow structures in the line shape can be achieved even when the emission is influenced by the dephasing of Raman coherence.
Advances in trap technology have made feasible experiments on single, or a few, atoms and ions. Photon counts from a single atom may exhibit new features that are washed out in ensembles. Wilser and I recently proposed a theoretical approach based on repeated gedanken measurements, which was then also independently proposed by Dalibard et al. and by Carmichael. The optical Bloch equations are not used but rather follow as a consequence. The approach is applied to a three-level V-system with small separation of the upper levels having parallel dipole moments. Macroscopic dark periods are predicted for such a laser-driven system, although none of the levels is metastable as in the Dehmelt system. The reason is a coherence effect. For particular values the dark period may become arbitrarily long. A similar result holds for A-systems. This explains the observed dark resonances in ensembles of such systems by increasingly long dark periods of individual atoms. The approach is then applied to atoms driven by incoherent light, and nonrate equations with off-diagonal terms are derived. It is shown that these may lead to coherence effects.
Spontaneous emission from a multilevel atom is studied from the viewpoint of quantum beats. The master equation describing the atomic dynamics is shown to have some parameters that oscillate at the beat frequencies, and because of this a Pauli type of master equation for the diagonal elements of the density matrix is not obtained. As a result, the transition rates in the atomic system show the characteristic beats. The relation of the rate of change of the energy of the atomic system to the total power radiated in the far zone is also established. The normally and antinormally ordered correlation functions of the spontaneously emitted radiation are calculated under the approximation that the level widths are much smaller than the beat frequencies. The contribution arising from the interference of the free field and the source terms to antinormally ordered correlations is carefully evaluated. The nature of beats present in normally and antinormally ordered correlations is discussed, and their detection from the viewpoint of causing transitions in another atom is considered. The change in the nature of beats due to atomic collective effects is studied. Finally, it is shown that because of quantum effects, intensity correlations do not show any beats.
The term quantum beats refers to a superposed oscillatory behaviour in the light intensity emitted by some suddenly excited atomic systems in their subsequent decay. In this paper we reinvestigate quantum beats for systems where two upper levels may decay to a common ground state by using the recently developed approach of quantum jumps. The treatment turns out to be very simple and intuitive. It gives explicit expressions for the time-dependent intensity of the radiating system and allows us to exhibit several phenomena which so far seem to have been overlooked. We show that quantum beats may also occur if only one of the upper levels is initially excited, a superposition is not needed. A possible experimental set-up for the verification of this effect is proposed. It is also shown that in some cases the beat frequency may differ considerably from the separation delta omega of the upper levels. For equal Einstein coefficients of the upper levels the beats are shown to be unexpectedly absent for small delta omega .
We represent two groups of excited atoms which radiate at slightly different frequencies by means of a pair of inverted harmonic oscillators coupled to the radiation field. The radiation emitted spontaneously by these oscillators is amplified exponentially and the field generated by each exerts a strong dynamical influence on the other. For the regime in which the amplification rate is large compared to the frequency difference of the uncoupled oscillators, the indirect coupling via the field tends to lock the two systems in phase so that they radiate in unison. When the amplification rate is small compared to the frequency difference, however, each oscillator undergoes, in addition to its own spontaneous oscillation, a partially coherent oscillation forced at the frequency of the other oscillator. These mutually induced oscillations give rise to intensity beats in the radiated field. Such beats have predetermined phases which are independent of the random initial phases of the oscillator amplitudes. The beats can be present and detectable in statistical terms even before a single photon has been emitted on the average.