Generalized Momentum Distributions

J. W. Clark, MANFRED L. RISTIG

Jonathan P. Dowling, G. S. Agarwal, Wolfgang P. Schleich

The general theory of quantum angular momentum is used to derive the unique Wigner distribution function for arbitrary angular-momentum states. We give the explicit distribution for atomic angular-momentum Dicke states, coherent states, and squeezed states that correspond to a collection of N two-level atoms. These Wigner functions W(\ensuremath{\theta},cphi) are represented as a pseudoprobability distribution in spherical phase space with spherical coordinates \ensuremath{\theta} and cphi on the surface of a sphere of radius \ensuremath{\Elzxh} \ensuremath{\surd}j(j+1) where j is the total angular-momentum eigenvalue.

Paul E. Sokol, Richard N. Silver, J. W. Clark

Benjamin Withers, H. R. Glyde

L. Mandeļ

It is shown that the distribution of the momentum transfer to an atom in resonance fluorescence may be easily derived from the angular distribution of spontaneously emitted photons. Some general properties of the momentum distribution are found, and explicit forms of the distribution are derived for several special cases. It is shown that the distribution tends to become Gaussian after a large number n of spontaneous photon emissions, with variance proportional to n, but it is already close to the asymptotic form when n=3. When the appropriate averaging is performed to allow for the velocity spread of the atoms, the derived distributions account for the results of atomic beam deflection measurements, but much of the information about the original distributions is thereby lost. In a standing wave field both stimulated and spontaneous emissions contribute to the atomic momentum, in such a way that the variance of the momentum spread is again proportional to the number n of photon emissions.

J. W. Clark, MANFRED L. RISTIG