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Physical Review A

Incoherent Resonance Fluorescence from a Rb Atomic Beam Excited by a Short Coherent Optical Pulse

Hyatt M. Gibbs

Published Jul 1, 1973• 63 citations
Publisher

Abstract

Fluorescence has been detected from Rb atoms following narrow-line excitation by a short coherent optical pulse. The fluorescence oscillates as a function of the pulse area $A$ with maxima for $A=\ensuremath{\pi},3\ensuremath{\pi},5\ensuremath{\pi},\dots{}$ and minima for $A=0,2\ensuremath{\pi},4\ensuremath{\pi},\dots{}$. In addition to demonstrating one of the simplest coherent optical effects, this experiment dramatizes the potential of the technique for determining dipole moments, pulse areas, relaxation times, and lifetimes. The details of the experimental apparatus are described. Results of a computer simulation of the experiment including the actuai excitation pulse shape, absorption frequency width, finite absorption (5-10% of pulse), and loss to a third level are given.

DOI
10.1103/physreva.8.446

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arXiv:2410.01703•Журнал Экспериментальной и Теоретической Физики•Nov 1, 2024•2 citations
Fluorescence has been detected from Rb atoms following narrow-line excitation by a short coherent optical pulse. The fluorescence oscillates as a function of the pulse area AAA with maxima for A=\ensuremathπ,3\ensuremathπ,5\ensuremathπ,…A=\ensuremath{\pi},3\ensuremath{\pi},5\ensuremath{\pi},\dots{}A=\ensuremathπ,3\ensuremathπ,5\ensuremathπ,… and minima for A=0,2\ensuremathπ,4\ensuremathπ,…A=0,2\ensuremath{\pi},4\ensuremath{\pi},\dots{}A=0,2\ensuremathπ,4\ensuremathπ,…. In addition to demonstrating one of the simplest coherent optical effects, this experiment dramatizes the potential of the technique for determining dipole moments, pulse areas, relaxation times, and lifetimes. The details of the experimental apparatus are described. Results of a computer simulation of the experiment including the actuai excitation pulse shape, absorption frequency width, finite absorption (5-10% of pulse), and loss to a third level are given.
Coherent excitation of an atomic excited state occurs during the propagation of near-resonant light pulses and is responsible for the induced polarization. Simultaneously, incoherent excitation occurs due to the relaxation processes described by the absorption coefficient. Here, the theory for the coherent and incoherent excitation is initially presented in terms of the traditional vector model. While a complete understanding of the two-level system is provided by the vector model, it is shown to be incomplete when the problem of directly monitoring the coherent and incoherent excitation is considered. This is because this latter problem involves more than two levels. For this more complicated multilevel problem, adiabatic states are introduced to gain further understanding. The adiabatic states are the stationary states of the atom in the presence of the near-resonant laser field; they help to explain the intimate connection between the coherent excitation and the two-photon resonance. Experimental measurements of the coherent and incoherent excitation associated with near-resonant pulse propagation in Rb vapor are presented. The double-resonance technique used a relatively strong pulsed dye laser tuned near the $5{S}_{\frac{1}{2}}\ensuremath{\leftrightarrow}5{P}_{\frac{1}{2}}$ transition (7948 \AA{}A) of Rb to produce the coherent and incoherent excitation, and a weak, tunable cw dye laser tuned in the region of the $5{P}_{\frac{1}{2}}\ensuremath{\leftrightarrow}6{D}_{\frac{3}{2}}$ transition (6206 \AA{}A) to monitor this excitation. In agreement with theory, the experimental results demonstrate that coherent excitation is responsible for two-photon absorption, while the incoherent excitation corresponds to one-photon absorption to the 5P125{P}_{\frac{1}{2}}5P21​​ state.
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.
Traditionally, the phenomenon of optical coherence has been observed by detecting coherent transients (i.e., optical nutation, FID, photon echoes) propagating along the laser beam following passage through an absorbing medium. Recently, we have demonstrated that detection of the incoherent (spontaneous) emission from selectively prepared states provides the optical coherence of the ensemble. Our observation of the nutation and the photon echo at right angles to the exciting beam gives directly optical T_1, T_2, and the moment of the laser excited transition. This technique is simple and not susceptible to some of the problems inherent in coherent absorption experiments. Details about this laser technique will be presented. We will also discuss the different dynamical information one obtains about excited states in gases, molecular beams and solids.
In an experiment on three-photon laser excitation 5S 1/2 → 5P 3/2 → 6S 1/2 → 37P 3/2 of a single 87 Rb, Rydberg atom in an optical dipole trap, we have observed for the first time three-photon Rabi oscillations between the ground and the Rydberg states. A single atom was detected optically by resonance fluorescence signal using a low-noise sCMOS video camera. The relative probability for the atom to remain in the trap after the action of three synchronized exciting laser pulses with durations varying from 100 ns to 2 µs was measured. A distinctive feature of the experiment was the use of intense laser radiation with a wavelength of 1367 nm at the second excitation step, providing a single-photon Rabi frequency up to 2 GHz to control the effective detunings of intermediate levels of the three- photon transition due to the dynamic Stark effect. Rabi oscillations with frequencies from 1 to 5 MHz were registered depending on the intensity of laser pulses of the first and second excitation steps with coherence time 0.7–0.8 µs. Ways to increase the coherence time and contrast of three-photon Rabi oscillations for applications in quantum information with Rydberg atoms are discussed.