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Physical Review

Electrodynamic Displacement of Atomic Energy Levels

Robert Karplus, Abraham Klein, Julian Schwinger

Published Nov 1, 1951• 63 citations
Publisher
DOI
10.1103/physrev.84.597

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We demonstrate our experiment of controlling spatial displacements of the probe beam induced by the cross-Kerr effect in a three-level V-type atomic system. By increasing the atomic density or the intensity of strong control laser beams, spatial displacements are enhanced. We further study the difference of effects from the atomic density and the laser intensity. In addition, the spatial displacement efficiencies of the probe beam in different energy level atomic systems are compared. Such studies of controlling spatial displacements can have potential applications in soliton deflection, spatial optical switch and generating spatially correlated (entangled) laser beams in multi-level EIT systems.
We extend previous work on macroscopic canonical quantization leading to a multipolar Hamiltonian appropriate for application to quantum optics and cavity QED situations involving classical optical devices. In particular, we show that the electric displacement is the negative of the conjugate momentum field and that the Coulomb and polarization energies are equal to the sum of intra-atomic Coulomb and polarization energies and interatomic contact energies. The quantum Hamiltonian is now in a form in which the theory is manifestly gauge invariant.