Cross-Kerr effective Hamiltonian for a non-resonant four-level atom

Details Cross-Kerr effective Hamiltonian for a non-resonant four-level atom Cross-Kerr effective Hamiltonian for a non-resonant four-level atom

2007-11-12

arxiv.org/abs/0711.1808v2

Physics

Quantum Physics

7 pages, 4 figures, submitted to Phys. Rev. A, Replacement: added Acknowledgments section

Scientific paper

We derive a cross-Kerr type effective Hamiltonian for the four-level atom interacting with three electromagnetic fields in the N-configuration. When the atom has relaxed into the ground state a cross-Kerr nonlinearity arises between two weak probe fields. As a development on earlier work we show in general that the atom will also display a linear and self-Kerr response. However, if certain resonance conditions are satisfied then the linear and self-Kerr interactions will vanish. The electrical susceptibilities of the probe transitions are also explored and it is shown that a large, pure cross-Kerr nonlinearity can be generated with vanishing absorption of both probe fields.

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