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Physical Review Letters

Correlation of Photons in Cascade and the Coherence Time of the 6P13 State of Mercury

Gilbert H. Nussbaum, F. M. Pipkin

Published Nov 6, 1967• 40 citations
Publisher

Abstract

We have observed directly the time correlation between successively emitted photons in the $7^{3}S_{1}\ensuremath{-}6^{3}P_{1}\ensuremath{-}6^{1}S_{0}$ cascade of atomic mercury, and have deduced from it direct measurements of both the natural lifetime of the $6^{3}P_{1}$ state and the dependence of the mean correlation time (coherence time) on the density of the mercury vapor surrounding the primary radiation region. The density-dependent coherence time constitutes a direct observation of the imprisonment of resonance radiation and provides an experimental confirmation of the theory describing this phenomenon.

DOI
10.1103/physrevlett.19.1089

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Isotope Effect in the Imprisonment of Resonance Radiation

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On theoretical grounds it is expected that the decay time of imprisoned resonance radiation in the vapor of a single even isotope of mercury should be some six times larger than that observed with the natural samples of mixed isotopic constitution. To investigate this effect experimentally, decay measurements were carried out with samples of ${\mathrm{Hg}}^{198}$ (3 percent ${\mathrm{Hg}}^{199}$ and 0.1 percent ${\mathrm{Hg}}^{200}$). For vapor densities $N\ensuremath{\lesssim}\frac{{10}^{14}}{\mathrm{cc}}$, the predicted effect was verified. For $N>\frac{{10}^{14}}{\mathrm{cc}}$, the observed decay time drops below that predicted theoretically for pure ${\mathrm{Hg}}^{198}$. This secondary effect is here attributed to the transfer of excitation from ${\mathrm{Hg}}^{198}$ to ${\mathrm{Hg}}^{199}$ and ${\mathrm{Hg}}^{200}$ by collisions of the second kind. Comparison of experimental data with an appropriately generalized theory permits estimation of the cross section for such collisions. The value so obtained is ${10}^{\ensuremath{-}13}$ ${\mathrm{cm}}^{2}$, some twenty times the gas-kinetic cross section, and in order-of-magnitude agreement with theoretical expectations.

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Effect of Imprisonment of Radiation in Sodium Vapor on the Measured Lifetime of the 3 P2 States

B P Kibble, G. H. Copley, L. Krause

The effect of imprisonment of radiation in sodium vapor on the measured lifetime of the $3 ^{2}P$ states has been investigated in an experiment in which the atoms in the vapor were excited with 10-nsec pulses of resonance radiation and the elapsed times between the exciting and the fluorescent pulses were recorded using a time-to-amplitude converter and kicksorter. At vapor densities below ${10}^{10}$ atoms/${\mathrm{cm}}^{3}$, where there is no multiple scattering, the measured lifetime reaches a constant value of (1.63\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ sec, equal to the natural lifetime of the $3 ^{2}P$ states. In the density range ${10}^{9}$-${10}^{13}$ atoms/${\mathrm{cm}}^{3}$, the variation of the effective lifetime with the vapor density is in good agreement with the predictions of Milne's theory of radiation trapping; agreement with Holstein's theory is observed only in the range ${10}^{12}$-${10}^{13}$ atoms/${\mathrm{cm}}^{3}$. The results of a subsidiary Hanle experiment show that a multiply scattered photon of sodium resonance fluorescence loses its original polarization and that, at high sodium vapor pressure, coherence is not preserved.

Physical Review•Jan 5, 1967•114 citations

The Quenching of Mercury Resonance Radiation (2537A) by Nitrogen

C. G. Matland

When a mercury atom in the resonance $6^{3}P_{1}$ state collides with a nitrogen molecule, it may be transferred to the metastable $6^{3}P_{0}$ state. The cross section for this reaction has been measured by a new method. Mercury vapor, in the presence of a known pressure of nitrogen gas, is excited by 2537A radiation. After the source of the excitation is cut off, the decay time of the imprisoned radiation is observed. The quenching collision cross section ${\ensuremath{\sigma}}_{Q}$ is calculated from the measured decay time and the known value of the imprisonment time in the absence of the quenching gas. Measurements have been taken over the temperature range 325-525\ifmmode^\circ\else\textdegree\fi{}K; ${\ensuremath{\sigma}}_{Q}$ is found to increase from 5.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at the lower temperature to 1.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ at the upper temperature.

Physical Review•Nov 1, 1953•32 citations
We have observed directly the time correlation between successively emitted photons in the 73S1\ensuremath−63P1\ensuremath−61S07^{3}S_{1}\ensuremath{-}6^{3}P_{1}\ensuremath{-}6^{1}S_{0}73S1​\ensuremath−63P1​\ensuremath−61S0​ cascade of atomic mercury, and have deduced from it direct measurements of both the natural lifetime of the 63P16^{3}P_{1}63P1​ state and the dependence of the mean correlation time (coherence time) on the density of the mercury vapor surrounding the primary radiation region. The density-dependent coherence time constitutes a direct observation of the imprisonment of resonance radiation and provides an experimental confirmation of the theory describing this phenomenon.
We report the first observation of the atomic cascade $9^{1}P_{1}\ensuremath{-}7^{3}S_{1}\ensuremath{-}6^{3}P_{1}$ in mercury. The exponential distribution of time delays between detection of the $9^{1}P_{1}\ensuremath{-}7^{3}S_{1}$ (5676-\AA{}) photon and the $7^{3}S_{1}\ensuremath{-}6^{3}P_{1}$ (4358-\AA{}) photon was measured, and a value of 8.2(0.2) nsec was obtained for the mean lifetime of the 73S17^{3}S_{1}73S1​ level.
The decay of imprisoned resonance radiation in mercury has been studied using delayed-coincidence techniques. It is characterized by two exponentially decaying components, whose relative amplitudes depend on the direction of linear polarization of the incident radiation. When this direction makes an angle of 54.7° to the direction of observation, only one component is observed. Classical and quantum-mechanical theories are presented which show that the geometry of the scattering cell plays an important role at low atomic densities. Experimental values are presented for the average degree of coherence transferred in the scattering process and for the natural lifetime of the 63P1 state of mercury.
On theoretical grounds it is expected that the decay time of imprisoned resonance radiation in the vapor of a single even isotope of mercury should be some six times larger than that observed with the natural samples of mixed isotopic constitution. To investigate this effect experimentally, decay measurements were carried out with samples of Hg198{\mathrm{Hg}}^{198}Hg198 (3 percent Hg199{\mathrm{Hg}}^{199}Hg199 and 0.1 percent Hg200{\mathrm{Hg}}^{200}Hg200). For vapor densities $N\ensuremath{\lesssim}\frac{{10}^{14}}{\mathrm{cc}}$, the predicted effect was verified. For N>1014ccN>\frac{{10}^{14}}{\mathrm{cc}}N>cc1014​, the observed decay time drops below that predicted theoretically for pure Hg198{\mathrm{Hg}}^{198}Hg198. This secondary effect is here attributed to the transfer of excitation from Hg198{\mathrm{Hg}}^{198}Hg198 to Hg199{\mathrm{Hg}}^{199}Hg199 and Hg200{\mathrm{Hg}}^{200}Hg200 by collisions of the second kind. Comparison of experimental data with an appropriately generalized theory permits estimation of the cross section for such collisions. The value so obtained is ${10}^{\ensuremath{-}13}$ cm2{\mathrm{cm}}^{2}cm2, some twenty times the gas-kinetic cross section, and in order-of-magnitude agreement with theoretical expectations.
The effect of imprisonment of radiation in sodium vapor on the measured lifetime of the 32P3 ^{2}P32P states has been investigated in an experiment in which the atoms in the vapor were excited with 10-nsec pulses of resonance radiation and the elapsed times between the exciting and the fluorescent pulses were recorded using a time-to-amplitude converter and kicksorter. At vapor densities below 1010{10}^{10}1010 atoms/cm3{\mathrm{cm}}^{3}cm3, where there is no multiple scattering, the measured lifetime reaches a constant value of (1.63\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ sec, equal to the natural lifetime of the 32P3 ^{2}P32P states. In the density range 109{10}^{9}109-1013{10}^{13}1013 atoms/cm3{\mathrm{cm}}^{3}cm3, the variation of the effective lifetime with the vapor density is in good agreement with the predictions of Milne's theory of radiation trapping; agreement with Holstein's theory is observed only in the range 1012{10}^{12}1012-1013{10}^{13}1013 atoms/cm3{\mathrm{cm}}^{3}cm3. The results of a subsidiary Hanle experiment show that a multiply scattered photon of sodium resonance fluorescence loses its original polarization and that, at high sodium vapor pressure, coherence is not preserved.
When a mercury atom in the resonance 63P16^{3}P_{1}63P1​ state collides with a nitrogen molecule, it may be transferred to the metastable 63P06^{3}P_{0}63P0​ state. The cross section for this reaction has been measured by a new method. Mercury vapor, in the presence of a known pressure of nitrogen gas, is excited by 2537A radiation. After the source of the excitation is cut off, the decay time of the imprisoned radiation is observed. The quenching collision cross section ${\ensuremath{\sigma}}_{Q}$ is calculated from the measured decay time and the known value of the imprisonment time in the absence of the quenching gas. Measurements have been taken over the temperature range 325-525\ifmmode^\circ\else\textdegree\fi{}K; ${\ensuremath{\sigma}}_{Q}$ is found to increase from 5.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ cm2{\mathrm{cm}}^{2}cm2 at the lower temperature to 1.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ cm2{\mathrm{cm}}^{2}cm2 at the upper temperature.