Laser Spectroscopy pp 283-291 | Cite as

# Coherent Transient Study of Velocity-Changing Collisions

## Abstract

The effect of velocity-changing collisions on the optical phase memory of coherently prepared molecular gas samples is examined by the method of Stark-pulse switching. Experiments are interpreted through the solution of a transport equation, which extends the earlier Fokker-P1anck description known both in NMR and in Dicke line narrowing. The magnitude of a characteristic velocity jump for binary molecular collisions and its cross section are thereby obtained.

It is well known that collisions between molecules can influence their optical lineshape through changes in molecular velocity. Theoretical discussions ^{1 – 5} of this problem usually invoke a Brownian motion diffusion model in velocity space that is based on a solution of the Fokker-Planck equation.^{6,7} A Doppler or Gaussian lineshape is predicted for low pressure and a Lorentzian profile for high pressure, the width becoming narrower with increasing presure as first recognized by Dicke.^{1} To be valid, these treatments imply characteristically small Doppler phase changes ktΔu_{rms} ≪ 1 over the period of observation t where \(
\mathop {\rm{k}}\limits^ \to
\) is the propagation vector of light and Δu_{rms} is a characteristic velocity jump, essentially the root mean square change in velocity per collision.

## Keywords

Spin Echo Density Matrix Element Velocity Jump Collision Kernel Photon Echo## Preview

Unable to display preview. Download preview PDF.

## References

- 1.R. H. Dicke, Phys. Rev. 89, 472 (1953); J. P. Wittke and R. H. Dicke, ibid 103, 620 (1956).ADSCrossRefGoogle Scholar
- 2.P. R. Berman and W. E. Lamb, Jr., Phys. Rev. A2, 2435 (1970); P. R. Berman, ibid A6, 2157 (1972) and references therein.ADSCrossRefGoogle Scholar
- 3.M. Borenstein and W. E. Lamb, Jr., Phys. Rev. A5, 1311 (1972).ADSCrossRefGoogle Scholar
- 4.S. G. Rautian and I. I. Sobelman, Soviet Physics Uspekhi 9, 701 (1967); V. A. Alekseev, T. L. Andreeva, and I. I. Sobelman, Soviet Physics JETP 35, 325 (1972).ADSCrossRefGoogle Scholar
- 5.L. Galatry, Phys. Rev. 122, 1218 (1961).ADSMATHCrossRefGoogle Scholar
- 6.S. Chandrasekhar, Reviews of Modern Physics 15, 1 (1943).MathSciNetADSMATHCrossRefGoogle Scholar
- 7.G. E. Uhlenbeck and L. S. Ornstein, Phys. Rev. 36, 823 (1930).ADSCrossRefGoogle Scholar
- 8.R. G. Brewer and R. L. Shoemaker, Phys. Rev. Letters 27, 631 (1971); ibid Phys. Rev. A6, 2001 (1972).ADSCrossRefGoogle Scholar
- 9.R. L. Shoemaker and R. G. Brewer, Phys. Rev. Letters 28, 1430 (1972); R. G. Brewer and E. L. Hahn, Phys. Rev. A8, 464 (1973).ADSCrossRefGoogle Scholar
- 10.J. Keilson and J. E. Storer, Quarterly of Applied Mathematics 10, 243 (1952).MathSciNetMATHGoogle Scholar
- 11.E. L. Hahn, Phys. Rev. 80, 580 (1950).ADSMATHCrossRefGoogle Scholar
- 12.B. Herzog and E. L. Hahn, Phys. Rev. 103, 148 (1956); J. R. Klauder and P. W. Anderson, Phys. Rev: 125, 912 (1962); W. B. Mims, Phys. Rev. 168, 370 (1968).ADSCrossRefGoogle Scholar
- 13.H. Y. Carr and E. M. Purcell, Phys. Rev. 94, 630 (1954).ADSCrossRefGoogle Scholar
- 14.A radiative interaction, such as Coherent Raman beats,
^{9}whereby the sample is driven slightly between the pulses could account for an intensity dependent dephasing and such an effect is observed. It should be noted that the two-pulse echo data of Fig. 1 yields Δu = 80 em/sec and σ = 3900Å^{2}in the absence of any intensity extrapolation.Google Scholar