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Physical Review A

Quantum interference effects in spontaneous atomic emission: Dependence of the resonance fluorescence spectrum on the phase of the driving field

M. A. G. Martinez, Peter R. Herczfeld, Charles Samuels, L. M. Narducci, C. H. Keitel

Published Jun 1, 1997• 122 citations
Publisher

Abstract

We discuss quantum interference effects in the resonance fluorescence spectrum of a \ensuremath{\Lambda} three-level atom when the lower-level doublet is driven by a coherent field. The interfering pathways that lead to the same final state involve both spontaneous decays and stimulated transitions, and differ from one another by an odd number of stimulated processes induced by the driving field. As a consequence, the interference structures depend upon the phase of the coherent field, an effect that is absent in other resonance fluorescence phenomena. The phase dependence of the quantum interference contribution is especially significant when the level splitting of the driven doublet is comparable to the spontaneous decay rates of the competing optical paths.

DOI
10.1103/physreva.55.4483

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We discuss quantum interference effects in the resonance fluorescence spectrum of a \ensuremath{\Lambda} three-level atom when the lower-level doublet is driven by a coherent field. The interfering pathways that lead to the same final state involve both spontaneous decays and stimulated transitions, and differ from one another by an odd number of stimulated processes induced by the driving field. As a consequence, the interference structures depend upon the phase of the coherent field, an effect that is absent in other resonance fluorescence phenomena. The phase dependence of the quantum interference contribution is especially significant when the level splitting of the driven doublet is comparable to the spontaneous decay rates of the competing optical paths.
We investigate the spontaneous emission spectrum of a three-level atom coherently driven by a microwave field. The microwave excitation establishes a coherent link between the bottom two levels, and as a consequence induces the quantum interference of previously independent decay pathways. As the decay pathways differ from one another by an odd number of stimulated emission processes, the spontaneous emission spectrum acquires a dependence on the phase of the excitation field, a feature that is absent in other resonance fluorescence phenomena.
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.
We discuss the spontaneous emission from a coherently prepared and microwave-driven doublet of potentially closely spaced excited states to a common ground level. Multiple interference mechanisms are identified that may lead to fluorescence inhibition in well-separated regions of the spectrum or act jointly in canceling the spontaneous emission. In addition to phase-independent quantum interferences due to combined absorptions and emissions of driving field photons, we distinguish two competing phase-dependent interference mechanisms as means of controlling the fluorescence. The indistinguishable quantum paths may involve the spontaneous emission from the same state of the doublet, originating from the two different components of the initial coherent superposition. Alternatively the paths involve a different spontaneous photon from each of two decaying states, necessarily with the same polarization. This makes these photons indistinguishable in principle within the uncertainty of the two decay rates. The phase dependence arises for both mechanisms because the interfering paths differ by an unequal number of stimulated absorptions and emissions of the microwave field photons.
The resonance fluorescence from a four-level atom driven by two coherent fields is studied. If the dipole moments between the two upper levels and each of the two lower levels are parallel, the spontaneous emission paths from the upper levels to the lower levels will have strongly or even completely destructive quantum interference. We show that this quantum interference will result in a complete inhibition of the fluorescence when one of the driving fields is tuned at the middle point of the upper levels. The quantum interference will lead to the dependence of atomic populations at steady state on the initial condition, when both of the driving fields are tuned to the middle point of the upper levels. When the dipole moments are close to but not exactly parallel, or none of the driving fields is tuned at the middle point of the upper levels and there is a small difference between detunings of the two driving fields to the uppermost level, ultranarrow lines at the spectral center appear because of the destructive quantum interference.
We study the resonance fluorescence from a coherently driven four-level atom in the Y-type configuration. The effects of quantum interference induced by spontaneous emission on the fluorescence properties of the atom are investigated. It is found that the quantum interference resulting from cascade emission decays of the atom leads to a splitting of resonances in the excited-level populations calculated as a function of light detuning. For some parameters, interference-assisted enhancement of inner sidebands and narrowing of central peaks may also occur in the fluorescence spectrum. We present a physical understanding of our numerical results using the dressed-state description of the atom-light interaction.
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.