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Physical Review A

Time-delayed second-harmonic generation in cesium vapor

Alexander I. Lvovsky, Sven R. Hartmann

Published Nov 1, 1997• 0 citations
Publisher

Abstract

Refined measurements and analysis of time-delayed second-harmonic generation on the ${6D}_{3/2}{\ensuremath{-}6S}_{1/2}$ transition in Cs vapor are presented that resolve the disparity between the measured and calculated time delays reported in its initial observation. We extend our work to the ${6D}_{5/2}{\ensuremath{-}6S}_{1/2}$ transition which, in agreement with our analysis, is characterized by a slightly smaller delay. For both transitions we also measure the amplitude of the second-harmonic intensity and find it close to what we estimate it should be.

DOI
10.1103/physreva.56.4254

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Refined measurements and analysis of time-delayed second-harmonic generation on the 6D3/2\ensuremath−6S1/2{6D}_{3/2}{\ensuremath{-}6S}_{1/2}6D3/2​\ensuremath−6S1/2​ transition in Cs vapor are presented that resolve the disparity between the measured and calculated time delays reported in its initial observation. We extend our work to the 6D5/2\ensuremath−6S1/2{6D}_{5/2}{\ensuremath{-}6S}_{1/2}6D5/2​\ensuremath−6S1/2​ transition which, in agreement with our analysis, is characterized by a slightly smaller delay. For both transitions we also measure the amplitude of the second-harmonic intensity and find it close to what we estimate it should be.
Time-delayed second harmonic generation has recently been reported in an atomic vapor of Cs at a temperature near 180 degrees Celsius and situated in a magnetic field of the order of a killogauss. Short 10 ps excitation laser pulses at 885 nm were used to excite a macroscopic electric quadrupole density which was then observed to radiate at 442 nm after a delay of a few hundred picoseconds. The experiment is complicated by the presence of several superfluorescence transitions some of which radiate close to the 442 nm wavelength. These emissions are also delayed and our strategy is to set the experimental conditions so that they only become appreciable after the second harmonic emission is complete. In this paper we show how the second harmonic develops by considering the evolution of the radiation pattern of an isolated atomic radiator (not forbidden to radiate at the second harmonic even in the absence of a magnetic field). We estimate the intensity of the superradiant second harmonic emission and obtain agreement with experiment. Excellent agreement is also obtained between measured and calculated delay.
Second harmonic generation has hitherto been thought of as simultaneous with the excitation pulse which generates it. Recent experiments in Cs vapor demonstrate otherwise. A short two-photon 6D - 6S resonant excitation pulse in Cs vapor generates a superposition state which would radiate immediately were it not for destructive interference arising from the sample being large compared to the radiation wavelength. The radiation pattern of an isolated radiator (atom) starts out with a null in the plane transverse to the polarization (linear) direction but then rotates about the applied transverse magnetic field developing a radiation component along the phase matched direction which we detect. Experimental results are presented in excellent agreement with theory. Previous delay discrepancies have been resolved by using a nonmetallic sample cell. Cascade and yoked superfluorescence take place but not significantly until after the second harmonic emissions. Quantitative measurements of signal intensity are also presented.
Second harmonic generation in Cs vapor is produced by the combined action of a polarized laser pulse and a magnetic field. It is delayed from the 10 ps excitation pulse by several hundred ps. The laser is two-photon resonant with the $6{S}_{\frac{1}{2}}\ensuremath{-}6{D}_{\frac{3}{2}}$ transition and initially induces a macroscopic quadrupole moment whose radiation pattern has a null in the forward direction. The magnetic field reshapes this pattern to produce second harmonic light, which is simply a free polarization decay signal evolving in a manner akin to the free induction decay following an adiabatic demagnetization.
A 10 ps transform limited optical pump pulse two-photon-resonant with the 6 S1/2-6 D32 442 nm transition in Cs vapor generates a coherent state superposition which, after a delay exceeding the pulse width, gives rise to second harmonic emission (when a transverse magnetic field is present) and superfluorescence (SF) directed against the pump on the upper 6 D3/2-6 P1/2 transition, followed by cooperative SF along the pump simultaneously on both the upper and lower 6 P3/2 − 6 P1/2 transitions, followed in turn by SF against the pump on the lower transition. Phase locked quantum beats associated with the 1.17 GHz hyperfine splitting of the 6 P1/2 appear on all SF emissions.
Resonant enhancement of optical third-harmonic generation in cesium vapor has been observed when twice the energy of the fundamental photon becomes equal to the energy difference between the 9d2D329d^{2}D_{\frac{3}{2}}9d2D23​​ level and the ground state of the cesium atom. The measured, effective coefficient is ${10}^{\ensuremath{-}30}$ esu/atom, which is more than a factor 108{10}^{8}108 larger than the corresponding coefficient for the helium atom. An effective coefficient is synthesized by first calculating the coefficient for a single cesium atom at rest and then including the effects of Doppler broadening and the fundamental laser spectrum. The calculated value is in satisfactory agreement with experiment.