K. V. Vasavada, G. Vemuri, and G. S. Agarwal, “Diode-laser-noise-based spectroscopy of allowed and crossover resonances,” Phys. Rev. A 52, 4159 (1995).

[CrossRef]
[PubMed]

See, for example, A. F. Molisch, W. Schupita, B. P. Oehry, B. Sumetsberger, and G. Magerl, “Modeling and efficient computation of nonlinear radiation trapping in three-level atomic vapors,” Phys. Rev. A 51, 3576 (1995).

[CrossRef]
[PubMed]

R. Walser, J. Cooper, and P. Zoller, “Saturated absorption spectroscopy using diode-laser phase noise,” Phys. Rev. A 50, 4303 (1994).

[CrossRef]
[PubMed]

R. Walser and P. Zoller, “Laser-noise-induced polarization fluctuations as a spectroscopic tool,” Phys. Rev. A 49, 5067 (1994).

[CrossRef]
[PubMed]

R. J. McLean, P. Hannaford, C. E. Fairchild, and P. L. Dyson, “Tunable diode-laser heterodyne spectroscopy of atmospheric oxygen,” Opt. Lett. 18, 1675 (1993).

[CrossRef]
[PubMed]

D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, “Diode-laser noise spectroscopy of rubidium,” Opt. Lett. 18, 1816 (1993).

[CrossRef]
[PubMed]

J. C. Camparo and P. Lambropoulos, “Monte Carlo simulation of field fluctuations in strongly driven resonant transitions,” Phys. Rev. A 47, 480 (1993).

[CrossRef]
[PubMed]

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453 (1991).

[CrossRef]
[PubMed]

See, for example, M. H. Anderson, R. D. Jones, J. Cooper, S. J. Smith, D. S. Elliot, H. Ritsch, and P. Zoller, “Variance and spectra of fluorescence-intensity fluctuations from two-level atoms in a phase-diffusing field,” Phys. Rev. A 42, 6690 (1990), and references therein.

[CrossRef]
[PubMed]

P. Minguzzi and A. Di Lieto, “Simple Padé approximations for the width of a Voigt profile,” J. Mol. Spectrosc. 109, 388 (1985).

[CrossRef]

Y. Yamamoto, S. Saito, and T. Mukai, “AM and FM quantum noise in semiconductor lasers. II. Comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47 (1983).

[CrossRef]

H. Tsuchida and T. Tako, “Relation between frequency and intensity stabilities in AlGaAs semiconductor laser,” Jpn. J. Appl. Phys. 22, 1152 (1983).

[CrossRef]

V. N. Belov, “Application of the magnetic-scanning method to the measurement of the broadening and shift constants of the rubidium D_{2} line (780.0 nm) by foreign gases,” Opt. Spectrosc. (USSR) 51, 22 (1981).

The acronyms TJS and CSP stand for transverse junction stripe and channeled substrate planar, respectively, and refer to the physical construction of the diode laser. See D. Botez, “Single-mode AlGaAs diode lasers,” J. Opt. Commun. 1, 42 (1980) for a more detailed discussion.

[CrossRef]

I. Botev, “A new conception of Bouguer–Lambert–Beer’s law,” Fresenius J. Anal. Chem. 297, 419 (1979).

[CrossRef]

N. D. Bhaskar, M. Hou, B. Suleman, and W. Happer, “Propagating, optical-pumping wave fronts,” Phys. Rev. Lett. 43, 519 (1979).

[CrossRef]

P. Zoller and P. Lambropoulos, “Non-Lorentzian laser lineshapes in intense field–atom interaction,” J. Phys. B 12, L547 (1979).

[CrossRef]

F. A. Franz and C. Volk, “Spin relaxation of rubidium atoms in sudden and quasimolecular collisions with light-noble-gas atoms,” Phys. Rev. A 14, 1711 (1976).

[CrossRef]

F. A. Franz, “Relaxation at cell walls in optical pumping experiments,” Phys. Rev. A 6, 1921 (1972).

[CrossRef]

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169 (1972).

[CrossRef]

N. W. Ressler, R. H. Sands, and T. E. Stark, “Measurement of spin-exchange cross sections for Cs^{133}, Rb^{87}, Rb^{85}, K^{39}, and Na^{23},” Phys. Rev. 184, 102 (1969).

[CrossRef]

P. Minguzzi, F. Strumia, and P. Violino, “Temperature effects in the relaxation of optically oriented alkali vapors,” Nuovo Cimento 46B, 145 (1966).

[CrossRef]

T. J. Killian, “Thermionic phenomena caused by vapors of rubidium and potassium,” Phys. Rev. 27, 578 (1926).

[CrossRef]

K. V. Vasavada, G. Vemuri, and G. S. Agarwal, “Diode-laser-noise-based spectroscopy of allowed and crossover resonances,” Phys. Rev. A 52, 4159 (1995).

[CrossRef]
[PubMed]

See, for example, M. H. Anderson, R. D. Jones, J. Cooper, S. J. Smith, D. S. Elliot, H. Ritsch, and P. Zoller, “Variance and spectra of fluorescence-intensity fluctuations from two-level atoms in a phase-diffusing field,” Phys. Rev. A 42, 6690 (1990), and references therein.

[CrossRef]
[PubMed]

V. N. Belov, “Application of the magnetic-scanning method to the measurement of the broadening and shift constants of the rubidium D_{2} line (780.0 nm) by foreign gases,” Opt. Spectrosc. (USSR) 51, 22 (1981).

N. D. Bhaskar, M. Hou, B. Suleman, and W. Happer, “Propagating, optical-pumping wave fronts,” Phys. Rev. Lett. 43, 519 (1979).

[CrossRef]

I. Botev, “A new conception of Bouguer–Lambert–Beer’s law,” Fresenius J. Anal. Chem. 297, 419 (1979).

[CrossRef]

The acronyms TJS and CSP stand for transverse junction stripe and channeled substrate planar, respectively, and refer to the physical construction of the diode laser. See D. Botez, “Single-mode AlGaAs diode lasers,” J. Opt. Commun. 1, 42 (1980) for a more detailed discussion.

[CrossRef]

J. C. Camparo and P. Lambropoulos, “Monte Carlo simulation of field fluctuations in strongly driven resonant transitions,” Phys. Rev. A 47, 480 (1993).

[CrossRef]
[PubMed]

R. Walser, J. Cooper, and P. Zoller, “Saturated absorption spectroscopy using diode-laser phase noise,” Phys. Rev. A 50, 4303 (1994).

[CrossRef]
[PubMed]

D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, “Diode-laser noise spectroscopy of rubidium,” Opt. Lett. 18, 1816 (1993).

[CrossRef]
[PubMed]

See, for example, M. H. Anderson, R. D. Jones, J. Cooper, S. J. Smith, D. S. Elliot, H. Ritsch, and P. Zoller, “Variance and spectra of fluorescence-intensity fluctuations from two-level atoms in a phase-diffusing field,” Phys. Rev. A 42, 6690 (1990), and references therein.

[CrossRef]
[PubMed]

P. Minguzzi and A. Di Lieto, “Simple Padé approximations for the width of a Voigt profile,” J. Mol. Spectrosc. 109, 388 (1985).

[CrossRef]

See, for example, M. H. Anderson, R. D. Jones, J. Cooper, S. J. Smith, D. S. Elliot, H. Ritsch, and P. Zoller, “Variance and spectra of fluorescence-intensity fluctuations from two-level atoms in a phase-diffusing field,” Phys. Rev. A 42, 6690 (1990), and references therein.

[CrossRef]
[PubMed]

D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, “Diode-laser noise spectroscopy of rubidium,” Opt. Lett. 18, 1816 (1993).

[CrossRef]
[PubMed]

R. J. McLean, P. Hannaford, C. E. Fairchild, and P. L. Dyson, “Tunable diode-laser heterodyne spectroscopy of atmospheric oxygen,” Opt. Lett. 18, 1675 (1993).

[CrossRef]
[PubMed]

F. A. Franz and C. Volk, “Spin relaxation of rubidium atoms in sudden and quasimolecular collisions with light-noble-gas atoms,” Phys. Rev. A 14, 1711 (1976).

[CrossRef]

F. A. Franz, “Relaxation at cell walls in optical pumping experiments,” Phys. Rev. A 6, 1921 (1972).

[CrossRef]

N. D. Bhaskar, M. Hou, B. Suleman, and W. Happer, “Propagating, optical-pumping wave fronts,” Phys. Rev. Lett. 43, 519 (1979).

[CrossRef]

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169 (1972).

[CrossRef]

N. D. Bhaskar, M. Hou, B. Suleman, and W. Happer, “Propagating, optical-pumping wave fronts,” Phys. Rev. Lett. 43, 519 (1979).

[CrossRef]

See, for example, M. H. Anderson, R. D. Jones, J. Cooper, S. J. Smith, D. S. Elliot, H. Ritsch, and P. Zoller, “Variance and spectra of fluorescence-intensity fluctuations from two-level atoms in a phase-diffusing field,” Phys. Rev. A 42, 6690 (1990), and references therein.

[CrossRef]
[PubMed]

T. J. Killian, “Thermionic phenomena caused by vapors of rubidium and potassium,” Phys. Rev. 27, 578 (1926).

[CrossRef]

J. C. Camparo and P. Lambropoulos, “Monte Carlo simulation of field fluctuations in strongly driven resonant transitions,” Phys. Rev. A 47, 480 (1993).

[CrossRef]
[PubMed]

P. Zoller and P. Lambropoulos, “Non-Lorentzian laser lineshapes in intense field–atom interaction,” J. Phys. B 12, L547 (1979).

[CrossRef]

See, for example, A. F. Molisch, W. Schupita, B. P. Oehry, B. Sumetsberger, and G. Magerl, “Modeling and efficient computation of nonlinear radiation trapping in three-level atomic vapors,” Phys. Rev. A 51, 3576 (1995).

[CrossRef]
[PubMed]

P. Minguzzi and A. Di Lieto, “Simple Padé approximations for the width of a Voigt profile,” J. Mol. Spectrosc. 109, 388 (1985).

[CrossRef]

P. Minguzzi, F. Strumia, and P. Violino, “Temperature effects in the relaxation of optically oriented alkali vapors,” Nuovo Cimento 46B, 145 (1966).

[CrossRef]

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453 (1991).

[CrossRef]
[PubMed]

See, for example, A. F. Molisch, W. Schupita, B. P. Oehry, B. Sumetsberger, and G. Magerl, “Modeling and efficient computation of nonlinear radiation trapping in three-level atomic vapors,” Phys. Rev. A 51, 3576 (1995).

[CrossRef]
[PubMed]

Y. Yamamoto, S. Saito, and T. Mukai, “AM and FM quantum noise in semiconductor lasers. II. Comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47 (1983).

[CrossRef]

See, for example, A. F. Molisch, W. Schupita, B. P. Oehry, B. Sumetsberger, and G. Magerl, “Modeling and efficient computation of nonlinear radiation trapping in three-level atomic vapors,” Phys. Rev. A 51, 3576 (1995).

[CrossRef]
[PubMed]

N. W. Ressler, R. H. Sands, and T. E. Stark, “Measurement of spin-exchange cross sections for Cs^{133}, Rb^{87}, Rb^{85}, K^{39}, and Na^{23},” Phys. Rev. 184, 102 (1969).

[CrossRef]

See, for example, M. H. Anderson, R. D. Jones, J. Cooper, S. J. Smith, D. S. Elliot, H. Ritsch, and P. Zoller, “Variance and spectra of fluorescence-intensity fluctuations from two-level atoms in a phase-diffusing field,” Phys. Rev. A 42, 6690 (1990), and references therein.

[CrossRef]
[PubMed]

Y. Yamamoto, S. Saito, and T. Mukai, “AM and FM quantum noise in semiconductor lasers. II. Comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47 (1983).

[CrossRef]

N. W. Ressler, R. H. Sands, and T. E. Stark, “Measurement of spin-exchange cross sections for Cs^{133}, Rb^{87}, Rb^{85}, K^{39}, and Na^{23},” Phys. Rev. 184, 102 (1969).

[CrossRef]

See, for example, A. F. Molisch, W. Schupita, B. P. Oehry, B. Sumetsberger, and G. Magerl, “Modeling and efficient computation of nonlinear radiation trapping in three-level atomic vapors,” Phys. Rev. A 51, 3576 (1995).

[CrossRef]
[PubMed]

See, for example, M. H. Anderson, R. D. Jones, J. Cooper, S. J. Smith, D. S. Elliot, H. Ritsch, and P. Zoller, “Variance and spectra of fluorescence-intensity fluctuations from two-level atoms in a phase-diffusing field,” Phys. Rev. A 42, 6690 (1990), and references therein.

[CrossRef]
[PubMed]

N. W. Ressler, R. H. Sands, and T. E. Stark, “Measurement of spin-exchange cross sections for Cs^{133}, Rb^{87}, Rb^{85}, K^{39}, and Na^{23},” Phys. Rev. 184, 102 (1969).

[CrossRef]

P. Minguzzi, F. Strumia, and P. Violino, “Temperature effects in the relaxation of optically oriented alkali vapors,” Nuovo Cimento 46B, 145 (1966).

[CrossRef]

N. D. Bhaskar, M. Hou, B. Suleman, and W. Happer, “Propagating, optical-pumping wave fronts,” Phys. Rev. Lett. 43, 519 (1979).

[CrossRef]

See, for example, A. F. Molisch, W. Schupita, B. P. Oehry, B. Sumetsberger, and G. Magerl, “Modeling and efficient computation of nonlinear radiation trapping in three-level atomic vapors,” Phys. Rev. A 51, 3576 (1995).

[CrossRef]
[PubMed]

H. Tsuchida and T. Tako, “Relation between frequency and intensity stabilities in AlGaAs semiconductor laser,” Jpn. J. Appl. Phys. 22, 1152 (1983).

[CrossRef]

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453 (1991).

[CrossRef]
[PubMed]

H. Tsuchida and T. Tako, “Relation between frequency and intensity stabilities in AlGaAs semiconductor laser,” Jpn. J. Appl. Phys. 22, 1152 (1983).

[CrossRef]

K. V. Vasavada, G. Vemuri, and G. S. Agarwal, “Diode-laser-noise-based spectroscopy of allowed and crossover resonances,” Phys. Rev. A 52, 4159 (1995).

[CrossRef]
[PubMed]

K. V. Vasavada, G. Vemuri, and G. S. Agarwal, “Diode-laser-noise-based spectroscopy of allowed and crossover resonances,” Phys. Rev. A 52, 4159 (1995).

[CrossRef]
[PubMed]

P. Minguzzi, F. Strumia, and P. Violino, “Temperature effects in the relaxation of optically oriented alkali vapors,” Nuovo Cimento 46B, 145 (1966).

[CrossRef]

F. A. Franz and C. Volk, “Spin relaxation of rubidium atoms in sudden and quasimolecular collisions with light-noble-gas atoms,” Phys. Rev. A 14, 1711 (1976).

[CrossRef]

R. Walser, J. Cooper, and P. Zoller, “Saturated absorption spectroscopy using diode-laser phase noise,” Phys. Rev. A 50, 4303 (1994).

[CrossRef]
[PubMed]

R. Walser and P. Zoller, “Laser-noise-induced polarization fluctuations as a spectroscopic tool,” Phys. Rev. A 49, 5067 (1994).

[CrossRef]
[PubMed]

D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, “Diode-laser noise spectroscopy of rubidium,” Opt. Lett. 18, 1816 (1993).

[CrossRef]
[PubMed]

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453 (1991).

[CrossRef]
[PubMed]

Y. Yamamoto, S. Saito, and T. Mukai, “AM and FM quantum noise in semiconductor lasers. II. Comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47 (1983).

[CrossRef]

R. Walser, J. Cooper, and P. Zoller, “Saturated absorption spectroscopy using diode-laser phase noise,” Phys. Rev. A 50, 4303 (1994).

[CrossRef]
[PubMed]

R. Walser and P. Zoller, “Laser-noise-induced polarization fluctuations as a spectroscopic tool,” Phys. Rev. A 49, 5067 (1994).

[CrossRef]
[PubMed]

See, for example, M. H. Anderson, R. D. Jones, J. Cooper, S. J. Smith, D. S. Elliot, H. Ritsch, and P. Zoller, “Variance and spectra of fluorescence-intensity fluctuations from two-level atoms in a phase-diffusing field,” Phys. Rev. A 42, 6690 (1990), and references therein.

[CrossRef]
[PubMed]

P. Zoller and P. Lambropoulos, “Non-Lorentzian laser lineshapes in intense field–atom interaction,” J. Phys. B 12, L547 (1979).

[CrossRef]

I. Botev, “A new conception of Bouguer–Lambert–Beer’s law,” Fresenius J. Anal. Chem. 297, 419 (1979).

[CrossRef]

Y. Yamamoto, S. Saito, and T. Mukai, “AM and FM quantum noise in semiconductor lasers. II. Comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47 (1983).

[CrossRef]

P. Minguzzi and A. Di Lieto, “Simple Padé approximations for the width of a Voigt profile,” J. Mol. Spectrosc. 109, 388 (1985).

[CrossRef]

The acronyms TJS and CSP stand for transverse junction stripe and channeled substrate planar, respectively, and refer to the physical construction of the diode laser. See D. Botez, “Single-mode AlGaAs diode lasers,” J. Opt. Commun. 1, 42 (1980) for a more detailed discussion.

[CrossRef]

P. Zoller and P. Lambropoulos, “Non-Lorentzian laser lineshapes in intense field–atom interaction,” J. Phys. B 12, L547 (1979).

[CrossRef]

H. Tsuchida and T. Tako, “Relation between frequency and intensity stabilities in AlGaAs semiconductor laser,” Jpn. J. Appl. Phys. 22, 1152 (1983).

[CrossRef]

P. Minguzzi, F. Strumia, and P. Violino, “Temperature effects in the relaxation of optically oriented alkali vapors,” Nuovo Cimento 46B, 145 (1966).

[CrossRef]

R. J. McLean, P. Hannaford, C. E. Fairchild, and P. L. Dyson, “Tunable diode-laser heterodyne spectroscopy of atmospheric oxygen,” Opt. Lett. 18, 1675 (1993).

[CrossRef]
[PubMed]

D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, “Diode-laser noise spectroscopy of rubidium,” Opt. Lett. 18, 1816 (1993).

[CrossRef]
[PubMed]

V. N. Belov, “Application of the magnetic-scanning method to the measurement of the broadening and shift constants of the rubidium D_{2} line (780.0 nm) by foreign gases,” Opt. Spectrosc. (USSR) 51, 22 (1981).

N. W. Ressler, R. H. Sands, and T. E. Stark, “Measurement of spin-exchange cross sections for Cs^{133}, Rb^{87}, Rb^{85}, K^{39}, and Na^{23},” Phys. Rev. 184, 102 (1969).

[CrossRef]

T. J. Killian, “Thermionic phenomena caused by vapors of rubidium and potassium,” Phys. Rev. 27, 578 (1926).

[CrossRef]

R. Walser and P. Zoller, “Laser-noise-induced polarization fluctuations as a spectroscopic tool,” Phys. Rev. A 49, 5067 (1994).

[CrossRef]
[PubMed]

F. A. Franz and C. Volk, “Spin relaxation of rubidium atoms in sudden and quasimolecular collisions with light-noble-gas atoms,” Phys. Rev. A 14, 1711 (1976).

[CrossRef]

F. A. Franz, “Relaxation at cell walls in optical pumping experiments,” Phys. Rev. A 6, 1921 (1972).

[CrossRef]

J. C. Camparo and P. Lambropoulos, “Monte Carlo simulation of field fluctuations in strongly driven resonant transitions,” Phys. Rev. A 47, 480 (1993).

[CrossRef]
[PubMed]

See, for example, A. F. Molisch, W. Schupita, B. P. Oehry, B. Sumetsberger, and G. Magerl, “Modeling and efficient computation of nonlinear radiation trapping in three-level atomic vapors,” Phys. Rev. A 51, 3576 (1995).

[CrossRef]
[PubMed]

K. V. Vasavada, G. Vemuri, and G. S. Agarwal, “Diode-laser-noise-based spectroscopy of allowed and crossover resonances,” Phys. Rev. A 52, 4159 (1995).

[CrossRef]
[PubMed]

R. Walser, J. Cooper, and P. Zoller, “Saturated absorption spectroscopy using diode-laser phase noise,” Phys. Rev. A 50, 4303 (1994).

[CrossRef]
[PubMed]

See, for example, M. H. Anderson, R. D. Jones, J. Cooper, S. J. Smith, D. S. Elliot, H. Ritsch, and P. Zoller, “Variance and spectra of fluorescence-intensity fluctuations from two-level atoms in a phase-diffusing field,” Phys. Rev. A 42, 6690 (1990), and references therein.

[CrossRef]
[PubMed]

N. D. Bhaskar, M. Hou, B. Suleman, and W. Happer, “Propagating, optical-pumping wave fronts,” Phys. Rev. Lett. 43, 519 (1979).

[CrossRef]

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453 (1991).

[CrossRef]
[PubMed]

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169 (1972).

[CrossRef]

J. C. Camparo, “The diode laser in atomic physics,” Contemp. Phys. 26, 443 (1985); C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1 (1991).

[CrossRef]

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, London, 1971), Chap. IV.

L. Krause, “Sensitized fluorescence and quenching,” in The Excited State in Chemical Physics, J. W. McGowan, ed. (Wiley, New York, 1975), Vol. XXVIII, Chap. 4.

See J. C. Camparo and S. B. Delcamp, “Optical pumping with laser-induced-fluorescence,” Opt. Commun. 120, 257 (1995), and the discussion regarding C. H. Volk, J. C. Camparo, and R. P. Frueholz, “Investigations of laser pumped gas cell atomic frequency standard,” in Proceedings of the 13th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting (U.S. Naval Observatory, Washington, D.C., 1981), pp. 631–640.

[CrossRef]

P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, Berlin, 1991), Chap. 1.

Note that (1/v)(∂E/∂t)≈(δt_{p}/L)(E/τ_{c}), where L is the length of the medium, δt_{p} is the propagation time of a wave front through the medium, and τ_{c} is the correlation time of the field’s stochastic variations. For a medium with a length of a few centimeters, δt_{p}~10^{−10} s, whereas for the lasers of interest in our study τ_{c}~10^{−8} s. Thus the temporal variation of the electric field will be roughly 2 orders of magnitude smaller than the spatial variation for an optically thick medium where (∂E/∂z)≈E/L.

It should be noted that in addition to Eq. (1) there is a propagation equation for the phase of the field: ∂Φ/∂z+ (1/v)(∂Φ/∂t)=−[(2πk)/n^{2}]χ^{′}(z, E). Inasmuch as the laser’s phase noise yields fluctuations in both χ^{′} and χ^{″}, the optical field’s phase fluctuations grow in a complicated fashion as the field propagates through the medium. The greater degree of phase noise further enhances the fluctuations of χ^{″}, which in turn results in larger variations of the laser’s transmitted intensity. However, because χ^{′} is proportional to the real part of the atomic coherence, which is generally small unless the laser has frequency excursions of the order of the optical homogeneous linewidth, it seems reasonable to ignore this additional source of laser phase noise in the PM-to-AM conversion process associated with the present experimental conditions: laser linewidth, ≅60 MHz and atomic homogeneous linewidth, ≅200 MHz. It is worth noting, though, that there will be experimental conditions in which this additional phase noise could be an important aspect of the PM-to-AM conversion process.

J. C. Camparo and R. P. Frueholz, “A nonempirical model of the gas-cell atomic frequency standard,” J. Appl. Phys. 59, 301 (1986); “Fundamental stability limits for the diode-laser-pumped rubidium atomic frequency standard,” J. Appl. Phys. 59, 3313 (1986).

[CrossRef]

See, for example, T. G. Vold, F. J. Raab, B. Heckel, and E. N. Fortson, “Search for a permanent electric dipole moment on the ^{129}Xe atom,” Phys. Rev. Lett. 52, 2229 (1984); S. Appelt, G. Wackerle, M. Mehring, “A magnetic resonance study of non-adiabatic evolution of spin quantum numbers,” Z. Phys. D 34, 75 (1995).

[CrossRef]

D. Tupa, L. W. Anderson, D. L. Huber, and J. E. Lawler, “Effect of radiation trapping on the polarization of an optically pumped alkali-metal vapor,” Phys. Rev. A 33, 1045 (1986); D. Tupa and L. W. Anderson, “Effect of radiation trapping on the polarization of an optically pumped alkali-metal vapor in a weak magnetic field,” Phys. Rev. A 36, 2142 (1987).

[CrossRef]
[PubMed]

Because of the presence of the buffer gas, the atoms are essentially frozen in place. Thus individual atoms experience local values of the electric field amplitude rather than averaging the electric field amplitude over the resonance cell volume. See J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914 (1983); R. P. Frueholz and J. C. Camparo, “Microwave field strength measurement in a rubidium clock cavity via adiabatic rapid passage,” J. Appl. Phys. 57, 704 (1985).

[CrossRef]

The Allan standard deviation, or Allan variance, is a statistic that is typically employed to describe precise frequency standards; it has the attractive property that it converges for certain nonstationary noise processes. Essentially, a fluctuating parameter is averaged over some time τ, and differences between neighboring averages are computed. The Allan variance is the variance associated with these differences. In the present work we take advantage of the ease with which the Allan variance may be computed and its well-known relationship to the noise process’s spectral density.

J. Rutman, “Characterization of phase and frequency instabilities in precision frequency sources: fifteen years of progress,” Proc. IEEE 66, 1048 (1978); J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGuningal, J. A. Mullen, Jr., W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans Instrum. Meas. IM-20, 105 (1971).

[CrossRef]

W. Cheney and D. Kincaid, Numerical Mathematics and Computing (Brooks Cole, Monterey, Calif., 1985); W. H. Press and S. A. Teukolsky, “Adaptive stepsize Runge–Kutta integration,” Comput. Phys. 6, 188 (1992).

[CrossRef]

R. H. Pennington, Introductory Computer Methods and Numerical Analysis (Macmillan, London, 1970).

Note that with 10 Torr of N_{2} the time between velocity-changing collisions is ~10^{−7} s, based on a gas kinetic cross section for velocity-changing collisions, whereas the propagation time of a wave front through a 3-cm medium is ~10^{−10} s. Thus, on the time scale of a wave front’s propagation through the medium, each atom has a specific, essentially constant, velocity.

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[CrossRef]

G. Miletti, J. Q. Deng, F. L. Walls, J. P. Lowe, and R. E. Drullinger, “Recent progress in laser-pumped rubidium gas-cell frequency standard,” in Proceedings of the 1996 IEEE International Frequency Control Symposium (IEEE Press, Piscataway, N.J., 1996), pp. 1066–1072.

J. C. Camparo and W. F. Buell, “Laser PM to AM conversion in atomic vapors and short term clock stability,” in Proceedings of the 1997 IEEE International Frequency Control Symposium (IEEE Press, Piscataway, N.J., 1997), pp. 253–258.