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Physical Review A

Quantum beats in two-atom resonance fluorescence

Z. Ficek, Barry C. Sanders

Published Jan 1, 1990• 39 citations
Publisher

Abstract

We study the resonance fluorescence emitted by two laser-driven coupled identical two-level atoms and allow for an arbitrary separation between the atoms and an arbitrary orientation of the interatomic axis in the laser field. Quantum beats arise in the resonance fluorescence intensity profile when an interatomic axis orientation is not perpendicular to the driving field propagation direction and are well resolved for an interatomic separation comparable to the resonant wavelength. These beats vanish for noninteracting atoms as well as for atoms separated by distances much smaller than the resonant wavelength. We also consider the time-dependent resonance fluorescence photon statistics that also exhibit quantum beats. Sub-Poissonian photon statistics occur for large interatomic separations and, for small separations, sub- and super-Poissonian statistics arise depending on the atomic orientation in the external driving field.

DOI
10.1103/physreva.41.359

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We study the resonance fluorescence emitted by two laser-driven coupled identical two-level atoms and allow for an arbitrary separation between the atoms and an arbitrary orientation of the interatomic axis in the laser field. Quantum beats arise in the resonance fluorescence intensity profile when an interatomic axis orientation is not perpendicular to the driving field propagation direction and are well resolved for an interatomic separation comparable to the resonant wavelength. These beats vanish for noninteracting atoms as well as for atoms separated by distances much smaller than the resonant wavelength. We also consider the time-dependent resonance fluorescence photon statistics that also exhibit quantum beats. Sub-Poissonian photon statistics occur for large interatomic separations and, for small separations, sub- and super-Poissonian statistics arise depending on the atomic orientation in the external driving field.
Resonance fluorescence of two two-level atoms driven by a coherent laser field propagating parallel to the interatomic axis is examined, taking into account the dipole-dipole interaction. We show that the number of peaks in the fluorescence intensity depends on the direction of observation with respect to the interatomic axis and on whether the system is driven by a standing-wave or a running-wave laser field. When the system is driven by the standing-wave field the fluorescence intensity shows two peaks and a dip for an observation direction perpendicular to the interatomic axis and three peaks in the direction parallel to it. When the system is driven by the running-wave field only two peaks are observed for the perpendicular direction. We explain these features in terms of the collective states of the system and show that the directional effect can be attributed to the fact that the antisymmetric state of the system does not radiate in the direction perpendicular to the interatomic axis. Photon statistics also demonstrate the directional effect for the standing-wave field. Frequency regimes are found where sub-Poissonian photon statistics occur. Depending on the direction of the observation, a state close to a Fock state can occur for one or two frequencies of the driving field, corresponding to zero-photon-number fluctuations or maximum sub-Poissonian behavior. The fluorescence spectrum is found to depend on the direction of observation and the interatomic separation. For small interatomic separations and a standing-wave driving field the spectrum exhibits seven lines for the perpendicular direction and 13 lines in the direction parallel to the interatomic axis. For the running-wave field the spectrum shows 13 lines independent of the direction of observation. Moreover, we show that for particular interatomic separations dark regimes appear in the spectrum. We discuss the effect of the dipole-dipole interaction on the dark states and explain the spectral features in terms of the dressed-atom model. We also consider the absorption spectrum of a weak probe beam illuminating the two-atom system. We show that apart from a weak dispersion structure, the spectrum shows large peaks as one of the atoms is moved to successive nodes of the field.
The phenomenon of resonance fluorescence provides an interesting manifestation of the quantum theory of light and is a “real world” application of the material of the Chapters 8 and 9. In this process, a two-level atom is typically driven by a resonant continuous-wave laser field and the spectral and quantum statistical properties of the fluorescent light emitted by the atom are measured. Experimentally this can be achieved by scattering a laser off a collimated atomic beam such that the directions of the laser beam, atomic beam, and detector axis are mutually perpendicular as shown in Fig. 10.1. If the driving field is monochromatic, then at low excitation intensity the atom absorbs a photon at the excitation frequency and reemits it at the same frequency as a consequence of conservation of energy. The spectral width of the fluorescent light is therefore very narrow. The situation, however, is considerably more complicated when the excitation intensity increases and the Rabi frequency associated with the driving field becomes comparable to, or larger than, the atomic linewidth. At such intensity levels, the Rabi oscillations show up as a modulation of the quantum dipole moment and sidebands start emerging in the spectrum of the emitted radiation. This so-called dynamic Stark splitting is an interesting feature of the atom–field interaction. In addition to that, the fluorescent light exhibits certain nonclassical properties including photon antibunching and squeezing. In this chapter, we develop a theory of resonance fluorescence to explain these phenomena.
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The two-time second-order correlation function of the electric field spontaneously emitted by a system of two non-identical two-level atoms with different transition frequencies and different natural linewidths is calculated from the viewpoint of quantum beats and photon anticorrelation effects. Our analytical solution shows that the intensity correlation exhibits quantum beats. The quantum beats are shown to appear even if the two atoms are independent. For identical atoms, beats appear only if dipole–dipole interaction between the atoms is included, and they are then strongly dependent on the direction of observation with respect to the line connecting the two atoms. The anticorrelation effect between the photons emitted in different directions is also discussed. It is shown that for a single-time correlation function the condition for anticorrelation is independent of interatomic interactions. For a two-time correlation function, interatomic interactions reduce the anticorrelation effect.
We study analytically the effect of the dipole-dipole interaction on the statistics of the fluorescent radiation emitted from a system of two two-level atoms resonantly driven by a coherent field. For some interatomic separations, an inhibition of fluorescence occurs, which is reminiscent of the recently discussed quantum-jump phenomenon in a single three-level atom. This is reflected in the behaviors of the intensity correlation function, Mandel's Q parameter, and the time-dependent fluorescence spectrum. It is argued that this quantum-jump-like behavior arises from the coupling between the symmetric states and the antisymmetric state caused by the dipole-dipole interaction.