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Doppler broadening arises from the random distribution of absorption (or emission) frequencies of atoms (or molecules). The distribution of frequencies occurs because the atoms have a distribution of velocities relative to the laser beam and are therefore Doppler shifted by:
w = wo ± k * v
where w is the laser frequency, wo is the transition frequency, k is the wavevector of the radiation, and v is the velocity of the atom. Removing Doppler broadening allows measurement of the natural linewidth, and shows any underlying fine structure such as isotope shifts, hyperfine splitting, and Zeeman splitting.
Counterpropagating laser beams produce a Doppler-free saturation dip (Lamb dip) in the center of a Doppler-broadened line. When the laser frequency is tuned off line center, one beam interacts with +k*v atoms, while the beam propagating in the opposite direction interacts with -k*v atoms. At the center of the Doppler line both laser beams interact with the same velocity group (k*v=0, i.e., atoms moving perpendicular to the laser beams). When the laser intensity is high enough to saturate the transition, the counterpropagating beam adds no additional excitation of the k*v=0 atoms and the overall observed signal is less than that for the case when exciting k*v atoms. This decrease in the signal appears as a narrow Lamb dip.
For atoms or molecules with convenient two-photon transitions, the Doppler width can be eliminated by using counterpropagating beams. In the atomic frame of reference, the two laser beams appear at frequencies of wo(1- k*v/c) and wo(1+ k*v/c), where wo is the frequency halfway to the two-photon level. The velocity dependence cancels out and the net result is that all atoms will absorb photons with a total energy of the two-photon transition. Due to absorption of two photons travelling in the same direction, this method will have some residual absorption of the full Doppler width.
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