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Physical Review Letters

Quantum Beats in Superfluorescence in Atomic Cesium

Quirin H. F. Vrehen, H. M. J. Hikspoors, H. M. Gibbs

Published Apr 4, 1977• 110 citations
Publisher

Abstract

Superfluorescence has been observed at 3 \ensuremath{\mu}m on the $7P$-to-$7S$ transition in atomic cesium after 2-ns excitation of a $6S$-to-$7P$ transition. Both in a magnetic field and in zero field, quantum beats have been observed. The beat frequencies correspond not only to initial-level splittings but also to combinations of initial- and final-level splittings. Superfluorescence beats are therefore basically different from single-atom quantum beats.

DOI
10.1103/physrevlett.38.764

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Superfluorescence has been observed at 3 \ensuremath{\mu}m on the 7P7P7P-to-7S7S7S transition in atomic cesium after 2-ns excitation of a 6S6S6S-to-7P7P7P transition. Both in a magnetic field and in zero field, quantum beats have been observed. The beat frequencies correspond not only to initial-level splittings but also to combinations of initial- and final-level splittings. Superfluorescence beats are therefore basically different from single-atom quantum beats.
Photon-echo quantum beats arising from magnetic splitting of the cesium $7{P}_{\frac{3}{2}}\ensuremath{-}6{S}_{\frac{1}{2}}$ transition were observed in a dilute atomic vapor by means of a novel polarization-rotation technique. The quantum-beat spectrum contains frequencies generated by the hyperfine structure of the 7P327{P}_{\frac{3}{2}}7P23​​ level as well as those due to the Zeeman splitting of both ground and excited levels. Experimental data for both F=3F=3F=3 and F=4F=4F=4 hyperfine components of the 6S126{S}_{\frac{1}{2}}6S21​​ ground state and for several echo delay times were fitted to calculated spectra, including corrections arising from Faraday rotation of the echo pulses.
Quantum beats in the radiation field of "three-level" atoms are analyzed by means of a previously developed boson-second-quantization (BSQ) formalism. Two types of atoms are considered: type I, in which beats are due to transitions from each of two closely spaced upper levels to a single lower level, and type II, in which beats are due to transitions between a single upper level and each of two closely spaced lower levels. This classification is motivated by the claim found in the literature that semiclassical theory and quantum theory give qualitatively different results concerning the existence of beats in the case of type-II atoms. The terminology associated with beats is made precise by distinguishing between amplitude modulation at the beat frequency of the transition frequency field EEE, and the existence of a spectral component at the beat frequency in E2{E}^{2}E2. With respect to the former, no qualitative difference is found in the predictions from semiclassical theory and quantum theory; with respect to the latter, results that appear paradoxical from an intuitive viewpoint are discussed. It is shown that for the case in which the atoms are all in the same coherent superposition of energy states, with all levels occupied, semiclassical and quantum-mechanical results become equivalent as the number of atoms increases. Reference is made to the disturbance caused by the measurement processes in the case of a single atom. The essential difference in spontaneous emission beats between type-I and type-II atoms [with the ground state(s) unoccupied] is explained by the fact that the phase of the beat amplitude may be determined by preparation of the initial state in type-I atoms but may not be determined in type-II atoms.
A laser pulse two-photon resonant with the ${6S}_{1/2}\ensuremath{-}{6D}_{3/2}$ 442 nm transition in Cs vapor generates delayed superfluorescence (SF) on the upper ${6D}_{3/2}\ensuremath{-}{6P}_{1/2}$ 876 nm and lower ${6P}_{1/2}\ensuremath{-}{6S}_{1/2}$ 894 nm transitions. Yoked SF is observed in the forward (along the laser) direction as evidenced by the simultaneous appearance of SF on both transitions. Cascade SF is observed in the backward direction, where SF on the lower transition only evolves after it has terminated on the upper. The four SF signals exhibit quantum beats associated with the 6P1/2{6P}_{1/2}6P1/2​ hyperfine splitting.