Abstract

We characterize, for the first time to our knowledge, the laser-induced backward fluorescence (retrofluorescence) spectra that result from energy-pooling collisions between Cs atoms near a dissipative thin Cs layer on a glass substrate. We resolve, experimentally and theoretically, the laser spectroscopic problem of energy-pooling processes related to the nature of the glass–metallic vapor interface. Our study focused on the integrated laser-induced retrofluorescence spectra for the 455.5-nm (72P3/262S1/2) and 852.2-nm (62P3/262S1/2) lines as a function of laser scanning through pumping resonance at the 852.2-nm line. We experimentally investigate the retrofluorescence from 420 to 930 nm, induced by a diode laser tuned either in the wings or in the center of the pumping resonance line. We present a detailed theoretical model of the retrofluorescence signal based on the radiative transfer equation, taking into account the evanescent wave of the excited atomic dipole strongly coupled with a dissipative surface. Based on theoretical and experimental results, we evaluate the effective nonradiative transfer rate A¯62P3/262S1/2sf for atoms in the excited 62P3/2 level located in the near-field region of the surface of the cell. Values extracted from the energy-pooling process analysis are equivalent to those found directly from the 852.2-nm resonance retrofluorescence line. We show that the effective energy-pooling coefficients k˜72P3/2 and k˜72P1/2 are approximately equal. The agreement between theory and experiment is remarkably good, considering the simplicity of the model.

© 2002 Optical Society of America

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References

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  1. M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. (Paris) II 2, 631–657 (1992).
  2. K. Zhao, Z. Wu, and H. M. Lai, “Optical determination of alkali metal vapor number density in the vicinity (~10−5 cm) of cell surfaces,” J. Opt. Soc. Am. B 18, 1904–1910 (2001).
    [CrossRef]
  3. V. G. Bordo, J. Loerke, L. Jozefowski, and H.-G. Rubahn, “Two-photon laser spectroscopy of the gas boundary layer in crossed evanescent and volume waves,” Phys. Rev. A 64, 012903/1–11 (2001).
    [CrossRef]
  4. K. Le Bris, J.-M. Gagné, F. Babin, and M.-C. Gagné, “Characterization of the retrofluorescence inhibition at the interface between glass and optically thick Cs vapor,” J. Opt. Soc. Am. B 18, 1701–1710 (2001).
    [CrossRef]
  5. F. de Tomasi, S. Milosevic, P. Verkerk, A. Fioretti, M. Allegrini, Z. J. Jabbour, and J. Huennekens, “Experimental study of caesium 6PJ+6PJ→7PJ+6S energy pooling collisions and modelling of the excited atom density in the presence of optical pumping and radiation trapping,” J. Phys. B 30, 4991–5008 (1997).
    [CrossRef]
  6. R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” J. Chem. Phys. 62, 2245–2253 (1975).
    [CrossRef]
  7. Z. J. Jabbour, R. K. Namiotka, J. Huennekens, M. Allegrini, S. Milosevic, and F. de Tomasi, “Energy-pooling collisions in cesium: 6PJ+6PJ→6S+(nl=7P,  6D,  8S, 4F),” Phys. Rev. A 54, 1372–1384 (1996).
    [CrossRef] [PubMed]
  8. J. B. Taylor and I. Langmuir, “Vapour pressure of Caesium by the positive ion method,” Phys. Rev. 51, 753–760 (1937).
    [CrossRef]
  9. L. Krause, “Sensitized fluorescence and quenching,” The Excited State in Chemical Physics, J. W. McGowan, ed. (Wiley, New York, 1975), pp. 267–316.
  10. M. Zinkin, MFIT version 0.3 (1997), http://www.ill.fr/tas/matlab/.

2001 (3)

1997 (1)

F. de Tomasi, S. Milosevic, P. Verkerk, A. Fioretti, M. Allegrini, Z. J. Jabbour, and J. Huennekens, “Experimental study of caesium 6PJ+6PJ→7PJ+6S energy pooling collisions and modelling of the excited atom density in the presence of optical pumping and radiation trapping,” J. Phys. B 30, 4991–5008 (1997).
[CrossRef]

1996 (1)

Z. J. Jabbour, R. K. Namiotka, J. Huennekens, M. Allegrini, S. Milosevic, and F. de Tomasi, “Energy-pooling collisions in cesium: 6PJ+6PJ→6S+(nl=7P,  6D,  8S, 4F),” Phys. Rev. A 54, 1372–1384 (1996).
[CrossRef] [PubMed]

1992 (1)

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. (Paris) II 2, 631–657 (1992).

1975 (1)

R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” J. Chem. Phys. 62, 2245–2253 (1975).
[CrossRef]

1937 (1)

J. B. Taylor and I. Langmuir, “Vapour pressure of Caesium by the positive ion method,” Phys. Rev. 51, 753–760 (1937).
[CrossRef]

Allegrini, M.

F. de Tomasi, S. Milosevic, P. Verkerk, A. Fioretti, M. Allegrini, Z. J. Jabbour, and J. Huennekens, “Experimental study of caesium 6PJ+6PJ→7PJ+6S energy pooling collisions and modelling of the excited atom density in the presence of optical pumping and radiation trapping,” J. Phys. B 30, 4991–5008 (1997).
[CrossRef]

Z. J. Jabbour, R. K. Namiotka, J. Huennekens, M. Allegrini, S. Milosevic, and F. de Tomasi, “Energy-pooling collisions in cesium: 6PJ+6PJ→6S+(nl=7P,  6D,  8S, 4F),” Phys. Rev. A 54, 1372–1384 (1996).
[CrossRef] [PubMed]

Babin, F.

Bloch, D.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. (Paris) II 2, 631–657 (1992).

Bordo, V. G.

V. G. Bordo, J. Loerke, L. Jozefowski, and H.-G. Rubahn, “Two-photon laser spectroscopy of the gas boundary layer in crossed evanescent and volume waves,” Phys. Rev. A 64, 012903/1–11 (2001).
[CrossRef]

Chance, R. R.

R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” J. Chem. Phys. 62, 2245–2253 (1975).
[CrossRef]

Chevrollier, M.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. (Paris) II 2, 631–657 (1992).

de Tomasi, F.

F. de Tomasi, S. Milosevic, P. Verkerk, A. Fioretti, M. Allegrini, Z. J. Jabbour, and J. Huennekens, “Experimental study of caesium 6PJ+6PJ→7PJ+6S energy pooling collisions and modelling of the excited atom density in the presence of optical pumping and radiation trapping,” J. Phys. B 30, 4991–5008 (1997).
[CrossRef]

Z. J. Jabbour, R. K. Namiotka, J. Huennekens, M. Allegrini, S. Milosevic, and F. de Tomasi, “Energy-pooling collisions in cesium: 6PJ+6PJ→6S+(nl=7P,  6D,  8S, 4F),” Phys. Rev. A 54, 1372–1384 (1996).
[CrossRef] [PubMed]

Ducloy, M.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. (Paris) II 2, 631–657 (1992).

Fichet, M.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. (Paris) II 2, 631–657 (1992).

Fioretti, A.

F. de Tomasi, S. Milosevic, P. Verkerk, A. Fioretti, M. Allegrini, Z. J. Jabbour, and J. Huennekens, “Experimental study of caesium 6PJ+6PJ→7PJ+6S energy pooling collisions and modelling of the excited atom density in the presence of optical pumping and radiation trapping,” J. Phys. B 30, 4991–5008 (1997).
[CrossRef]

Gagné, J.-M.

Gagné, M.-C.

Huennekens, J.

F. de Tomasi, S. Milosevic, P. Verkerk, A. Fioretti, M. Allegrini, Z. J. Jabbour, and J. Huennekens, “Experimental study of caesium 6PJ+6PJ→7PJ+6S energy pooling collisions and modelling of the excited atom density in the presence of optical pumping and radiation trapping,” J. Phys. B 30, 4991–5008 (1997).
[CrossRef]

Z. J. Jabbour, R. K. Namiotka, J. Huennekens, M. Allegrini, S. Milosevic, and F. de Tomasi, “Energy-pooling collisions in cesium: 6PJ+6PJ→6S+(nl=7P,  6D,  8S, 4F),” Phys. Rev. A 54, 1372–1384 (1996).
[CrossRef] [PubMed]

Jabbour, Z. J.

F. de Tomasi, S. Milosevic, P. Verkerk, A. Fioretti, M. Allegrini, Z. J. Jabbour, and J. Huennekens, “Experimental study of caesium 6PJ+6PJ→7PJ+6S energy pooling collisions and modelling of the excited atom density in the presence of optical pumping and radiation trapping,” J. Phys. B 30, 4991–5008 (1997).
[CrossRef]

Z. J. Jabbour, R. K. Namiotka, J. Huennekens, M. Allegrini, S. Milosevic, and F. de Tomasi, “Energy-pooling collisions in cesium: 6PJ+6PJ→6S+(nl=7P,  6D,  8S, 4F),” Phys. Rev. A 54, 1372–1384 (1996).
[CrossRef] [PubMed]

Jozefowski, L.

V. G. Bordo, J. Loerke, L. Jozefowski, and H.-G. Rubahn, “Two-photon laser spectroscopy of the gas boundary layer in crossed evanescent and volume waves,” Phys. Rev. A 64, 012903/1–11 (2001).
[CrossRef]

Lai, H. M.

Langmuir, I.

J. B. Taylor and I. Langmuir, “Vapour pressure of Caesium by the positive ion method,” Phys. Rev. 51, 753–760 (1937).
[CrossRef]

Le Bris, K.

Loerke, J.

V. G. Bordo, J. Loerke, L. Jozefowski, and H.-G. Rubahn, “Two-photon laser spectroscopy of the gas boundary layer in crossed evanescent and volume waves,” Phys. Rev. A 64, 012903/1–11 (2001).
[CrossRef]

Milosevic, S.

F. de Tomasi, S. Milosevic, P. Verkerk, A. Fioretti, M. Allegrini, Z. J. Jabbour, and J. Huennekens, “Experimental study of caesium 6PJ+6PJ→7PJ+6S energy pooling collisions and modelling of the excited atom density in the presence of optical pumping and radiation trapping,” J. Phys. B 30, 4991–5008 (1997).
[CrossRef]

Z. J. Jabbour, R. K. Namiotka, J. Huennekens, M. Allegrini, S. Milosevic, and F. de Tomasi, “Energy-pooling collisions in cesium: 6PJ+6PJ→6S+(nl=7P,  6D,  8S, 4F),” Phys. Rev. A 54, 1372–1384 (1996).
[CrossRef] [PubMed]

Namiotka, R. K.

Z. J. Jabbour, R. K. Namiotka, J. Huennekens, M. Allegrini, S. Milosevic, and F. de Tomasi, “Energy-pooling collisions in cesium: 6PJ+6PJ→6S+(nl=7P,  6D,  8S, 4F),” Phys. Rev. A 54, 1372–1384 (1996).
[CrossRef] [PubMed]

Oria, M.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. (Paris) II 2, 631–657 (1992).

Prock, A.

R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” J. Chem. Phys. 62, 2245–2253 (1975).
[CrossRef]

Rahmat, G.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. (Paris) II 2, 631–657 (1992).

Rubahn, H.-G.

V. G. Bordo, J. Loerke, L. Jozefowski, and H.-G. Rubahn, “Two-photon laser spectroscopy of the gas boundary layer in crossed evanescent and volume waves,” Phys. Rev. A 64, 012903/1–11 (2001).
[CrossRef]

Silbey, R.

R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” J. Chem. Phys. 62, 2245–2253 (1975).
[CrossRef]

Taylor, J. B.

J. B. Taylor and I. Langmuir, “Vapour pressure of Caesium by the positive ion method,” Phys. Rev. 51, 753–760 (1937).
[CrossRef]

Verkerk, P.

F. de Tomasi, S. Milosevic, P. Verkerk, A. Fioretti, M. Allegrini, Z. J. Jabbour, and J. Huennekens, “Experimental study of caesium 6PJ+6PJ→7PJ+6S energy pooling collisions and modelling of the excited atom density in the presence of optical pumping and radiation trapping,” J. Phys. B 30, 4991–5008 (1997).
[CrossRef]

Wu, Z.

Zhao, K.

J. Chem. Phys. (1)

R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” J. Chem. Phys. 62, 2245–2253 (1975).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. (Paris) II (1)

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. (Paris) II 2, 631–657 (1992).

J. Phys. B (1)

F. de Tomasi, S. Milosevic, P. Verkerk, A. Fioretti, M. Allegrini, Z. J. Jabbour, and J. Huennekens, “Experimental study of caesium 6PJ+6PJ→7PJ+6S energy pooling collisions and modelling of the excited atom density in the presence of optical pumping and radiation trapping,” J. Phys. B 30, 4991–5008 (1997).
[CrossRef]

Phys. Rev. (1)

J. B. Taylor and I. Langmuir, “Vapour pressure of Caesium by the positive ion method,” Phys. Rev. 51, 753–760 (1937).
[CrossRef]

Phys. Rev. A (2)

V. G. Bordo, J. Loerke, L. Jozefowski, and H.-G. Rubahn, “Two-photon laser spectroscopy of the gas boundary layer in crossed evanescent and volume waves,” Phys. Rev. A 64, 012903/1–11 (2001).
[CrossRef]

Z. J. Jabbour, R. K. Namiotka, J. Huennekens, M. Allegrini, S. Milosevic, and F. de Tomasi, “Energy-pooling collisions in cesium: 6PJ+6PJ→6S+(nl=7P,  6D,  8S, 4F),” Phys. Rev. A 54, 1372–1384 (1996).
[CrossRef] [PubMed]

Other (2)

L. Krause, “Sensitized fluorescence and quenching,” The Excited State in Chemical Physics, J. W. McGowan, ed. (Wiley, New York, 1975), pp. 267–316.

M. Zinkin, MFIT version 0.3 (1997), http://www.ill.fr/tas/matlab/.

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Figures (8)

Fig. 1
Fig. 1

Spectrum wavelength and lower excited levels of the Cs atom that we studied. Wavelengths are given in nanometers. The populations in the high-lying levels are attributed to excited-atoms–excited atom collisions in which two atoms pool their internal energy to produce a ground-state atom and one in a more highly excited level. Solid downward arrows represent radiative transition and broken arrows represent collisional processes.

Fig. 2
Fig. 2

Schematic of the energy level diagram of Cs.

Fig. 3
Fig. 3

Physical description of the characteristic region of the window cell: (a) glass substrate with adsorbed Cs atoms, (b) interface region where Cs atoms interact strongly with the surface, (c) region of free atoms.

Fig. 4
Fig. 4

Geometric description of the characteristic region of the window cell.

Fig. 5
Fig. 5

Experimental setup: P, polarization rotator; L, lens; M, mirror; P.P, polarizing prism; P.M, photomultiplier; D, spatial filter.

Fig. 6
Fig. 6

Atomic retrofluorescence spectra. Top, the 852.2-nm laser tuned to the maximum of the 455.5-nm retrofluorescence signal. Bottom, the laser tuned to the center of the 455.5-nm inhibition. The temperature of the vapor was 129 °C.

Fig. 7
Fig. 7

Retrofluorescence signal at 852.2 nm (left column) and 455 nm (right column) as a function of laser detuning around 852.2 nm for different temperatures. Experimental results, dotted curves and theorical results, solid curves. All observations are in the linear regime.

Fig. 8
Fig. 8

Variation of the nonradiative parameter (AJeJgf/AJeJg)×x¯f, as a function of temperature calculated directly from the integrated resonance retrofluorescence signal at 852.2 nm (●) and from the integrated pooling-effect-induced retrofluorescence signal at 455.5 nm ( * ) with a hyperfine structure.

Tables (1)

Tables Icon

Table 1 Calculated Values Obtained with Hyperfine Fitting of the Characteristic Parametersa

Equations (36)

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Cs(62PJ)+Cs(62PJ)Cs(nlJ)+Cs(62S1/2),
Cs (62P3/2)+Cs (62S1/2)Cs (62P1/2)+Cs (62S1/2),
2Cs(62P3/2)Cs(72PJ)+Cs(62S1/2)2Cs(62S1/2)+hν(455.5and459.3nm).
k˜72PJ=k˜72PJ(3/2)+Γ82S1/272PJeΓ82S1/2ek˜82S1/2(3/2),
Lν,xJ(νL, Fg)
=hν2Γ72PJ62S1/2eα72PJ62S1/2l
×exp[-τ¯62S1/272PJf(ν)]n72PJ(x, νL, Fg)
×exp[-k¯62S1/272PJl(ν)x],
ddtn72PJ(x, νL, Fg)=k˜72PJ2n62P3/22(x, νL, Fg)-Γ72PJen72PJ(x, νL, Fg),
n72PJ(x, νL, Fg)=k˜72PJ2(Γ72PJe)-1n62P3/22(x, νL, Fg).
dn62P3/2(x, νL, Fg)dt
=dFx(νL)hνL-Γ62P3/2en62P3/2(x, νL, Fg),
n62P3/2(x, νL, Fg)=dFx(νL)hνLΓ62P3/2e.
dFx(νL)=-FνLFek¯FgFel(νL)exp-Feτ¯FgFef(νL)×exp-Fek¯FgFel(νL)x,
k¯FgFel(νL)=λ28 2Je+12Jg+1AJeJgn¯FggFeFgαFgFel(νL),
τ¯FgFef(νL)=λ28π 2Je+12Jg+1A¯FeFgfn¯Fgx¯fgFeFgαFeFef(νL),
A¯FeFgf=AJeJgε¯FggFeFg,
gFeFg=(2Fe+1)(2Fg+1)(2I+1){ 6j }2,
A¯JeJgf=FeFgA¯FeFgf=AJeJgFeFgε¯FggFeFg.
ϕJ(νL, Fg)LJ(νL, Fg)=Δν0+Lν,xJ(νL, Fg)dxdν,
ϕJ(νL, Fg)FνL2Γ72PJ62S1/2ek˜72PJl(Γ62P3/2e)2Γ72PJe Fe[k¯FgFel(νL)]2×exp-2Fτ¯FgFef(νL)Θ72PJ62S1/2(νL),
Θ72PJ62S1/2(νL, Fg)
= α72PJ62S1/2l(ν)exp[-τ¯62S1/272PJf(ν)]k¯62S1/272PJl(ν)+2Fek¯FgFel(νL) dν.
k¯62S1/272PJl(ν)2Fek¯FgFel(νL),
ϕJn(νL, Fg)=FegFeFgαFgFel(νL)×exp-2Feτ¯FgFef(νL).
ϕJn(νL)=FgFegFeFgαFgFel(νL)×exp-2FgFeτ¯FgFef(νL).
FegFeFgαFg=4Fei(νL)
=g34α43i(νL, ν¯43, γGi, γLi)+g44α44i(νL, ν¯43-α, γGi, γLi)+g54α45i(νL, ν¯43-b, γGi, γLi),
A¯JeJgf=AJeJg16(9ε¯Fg=4+7ε¯Fg=3).
ϕ455.5nm(νL)ϕ459.3nm(νL)=Γ72P3/262S1/2eΓ72P1/2ek˜72P3/2Θ455.5nmΓ72P1/262S1/2eΓ72P3/2ek˜72P1/2Θ459.3nm,
Θ455.5nmΘ459.3nm
=Δνα72P3/262S1/2l(ν)exp[-τ¯62S1/272P3/2f(ν)]dνΔνα72P1/262S1/2l(ν)exp[-τ¯62S1/272P1/2f(ν)]dν.
Γ72P3/2e=8.25×106 s-1,
Γ72P3/262S1/2e=2.97×106 s-1,
Γ72P1/2e=7.23×106 s-1,
Γ72P1/262S1/2e=2.12×106 s-1,

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