By Christian J. Bordé (auth.), F. T. Arecchi, F. Strumia, H. Walther (eds.)

ISBN-10: 1461337151

ISBN-13: 9781461337157

ISBN-10: 1461337178

ISBN-13: 9781461337171

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**Example text**

1. Space and time do not playa symmetric role. They should always appear together as a single four-vector whereas in the previous theory, time is the only evolution parameter. 2. Relativistic expressions of the eigenvalues of the Hamiltonian have been artificially introduced whereas they should result from a relativistic expression of the Hamiltonian that is from a relativistic equation for the density operator itself. g. I6,I7 We have therefore to introduce field operators for the molecules in the various states a as well as for the light field.

5. a a a' a a a a' a' a a a 13' Figure 5 a (3' c. J. BORDE 34 With these new diagrams we have the choice between two possibilities : I) Use second-quantization for the electromagnetic field as well as for molecules. It is then necessary to introduce a propagator for the radiation density matrix elements. 2) Use the semiclassical approximation in which the classical electromagnetic field enters at each vertex with the corresponding space-time argument. ' s ,whereas the exponential factor exp i0 oscillates rapidly ex~ept when the phase is stationary,and the greatest contribution to the velocity and.

X /~' G(X)1 2 (117) The line shape (corresponding to the squared modulus of the Fourier transform of each field zone) is now modulated by interference fringes and the fringe spacing is determined by d/v. The physics can be understood by inspection of the diagrams. The constant term corresponds to both one-photon processes occurring in the same field zone,whereas the oscillating term comes from an interference of two one-photon processes occurring in two different zones. On the diagram, we can also see that, at the first vertex in the first field zone, an optical dipole (off-diagonal matrix element or optical coherence) is created and precesses freely in the dark zone for the time duration d/v.

### Advances in Laser Spectroscopy by Christian J. Bordé (auth.), F. T. Arecchi, F. Strumia, H. Walther (eds.)

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