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Physical Review

Spontaneous Emission in the Presence of a Prescribed Classical Field

Maurice C. Newstein

Published Mar 5, 1968• 120 citations
Publisher

Abstract

The effect of the application of a classical driving field on the spectrum of spontaneous emission from a simple physical system is studied. The physical system consists of an ensemble of two-level atoms interacting with a relaxation mechanism. The single Lorentzian line-shape characteristic of the power spectrum of spontaneous emission for the undriven case is split into components by the driving field. This splitting is associated with the establishment of definite phase relations between the corresponding components of the field spectrum.

DOI
10.1103/physrev.167.89

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Physical Review A•Aug 1, 1990•284 citations
The effect of the application of a classical driving field on the spectrum of spontaneous emission from a simple physical system is studied. The physical system consists of an ensemble of two-level atoms interacting with a relaxation mechanism. The single Lorentzian line-shape characteristic of the power spectrum of spontaneous emission for the undriven case is split into components by the driving field. This splitting is associated with the establishment of definite phase relations between the corresponding components of the field spectrum.
A previously developed theory of spontaneous emission from driven systems has been applied to the case of a Doppler broadened gas of two level atoms radiating into free space. The power spectrum of those photons radiated nearly parallel to the propagation vector of the driving field is predicted to differ from that of the undriven system. The case of zero attenuation coefficient (population equality in the two resonance levels) and the driving field tuned to the center of the Doppler line, is investigated in particular. When the saturation parameter is large there is strong suppression, in an interval about the central frequency comparable to the saturated width, of the spontaneous emission whose spectral components are phased for amplitude modulation relative to the driving field. An amount of power equal to that suppressed, but with spectral components phased for phase modulation relative to the driving field, is radiated in an interval about the central frequency comparable to the homogeneous width.
The quantum interference in the spontaneous-emission spectrum of a driven atom, when the upper level of the atomic transition is coupled to a third level via a classical driving field, results in a dark line in the absence of the atomic decays. The existence of the dark line is independent of the Rabi frequency associated with the driving field. There is no such dark line in the spontaneous-emission spectrum when, instead of the upper level, the lower level is coupled to a third level via a driving field. In this paper, we include the level decays, incoherent pumping, and the finite bandwidth of the driving field in our analysis and study their role in the spontaneous-emission spectrum in the two configurations.
The spontaneous emission spectrum from a driven three-level atom placed inside a double-band photonic crystal has been investigated. We use the model which assumes the upper levels of the atomic transition are coupled via a classical driving field. The transition from one of the upper levels to lower level couples to the modes of the modified reservoir, and the transition from the other upper level to lower level interactwith the free vacuum modes. The effect of classical driving field on the spontaneous emission spectrum of this latter transition is investigated in detail. Most interestingly it is shown that only in the presence of the classical driving field; there is a black dark line in the spontaneous emission spectrum of free-space transition when the modified reservoir is of the photonic band gap type. This dark line is not seen in the case where the modified reservoir is of the free space type for relatively weak driving field.
We study the influence of quantum interference on the spontaneous emission from an excited two-level atom when either the atomic upper or lower level is coupled by a coherent field to a third, usually higher-lying, state. In the case of the upper level coupling, destructive quantum interference between two competing decay amplitudes produces a dark line in the emission spectrum, a phenomenon that should not be confused with the well known population trapping, and a narrowing of one of the two side lobes that make up the spectral profile. Quantum interference is absent, instead, in the case of the lower level coupling, and the spectrum modified by the external driving field is just the incoherent superposition of two Lorentzian lines. We suggest a physical interpretation of these results. In addition, we compare the analytic predictions of the simplest nontrivial versions of these models with more realistic but nonanalytic descriptions and show, numerically, that the interference effects persist in the upper level case even when additional complications are taken into account.
The modification of the spontaneous emission spectrum has been studied in this paper in a four-level doubly driven N-type atomic system. In the presence of two coherent fields, emphasis has been given to studying the spectral distribution of spontaneous emission in the relaxation process of the initially prepared excited level. The phenomenon of quantum interference dynamically induced in the system by these fields can significantly change the spontaneous emission spectrum. We have shown the emergence of a two-peak spectrum where two widely separated symmetric peaks are associated with a sharp dark line at their mid-position. At different dynamic conditions, we have also shown that two symmetric peaks may appear in the spectrum with an extended dark zone between them. Depending on the values of the Rabi frequencies and the detunings of the external fields, one can achieve a large enhancement of very narrow spectral components within the spontaneous emission line shape under different conditions. The phenomenon of suppression of spectral line and the selective cancellation of spontaneous emission have also been discussed. The results shown in various cases are analysed by considering all possible dressed states corresponding to the bare state model. The influence of collision-induced effects on the spontaneous emission spectrum is investigated as a conditional case.
We investigate the steady-state spontaneous emission spectrum of a three-level atom driven by two coherent fields and the absorption spectrum of a weak probe passing through a collection of such driven atoms. We find that the fluorescence spectrum is strongly affected by the decay rates of all the levels involved in the atomic evolution and not just by the decay parameters of the specific transition whose emission spectrum is being monitored. In particular, the spectral components can acquire very different widths and peak heights relative to the case of the standard resonance fluorescence in which a two-level system is driven by a single near-resonant field. An external probe signal passing through the gas of three-level atoms may be absorbed or amplified, as in the standard two-level case, but under specific operating conditions, amplification (or absorption) occurs over the entire range where the atomic response is appreciable. In this case the existence of amplification or absorption is controlled solely by the population difference between two dressed states of the system. We provide numerical results in support of our arguments for arbitrary values of the atomic and field parameters and also develop an analytic description in the limit of strong driving fields that leads to explicit line-shape and linewidth formulas.