One-Photon State Generation in a Kicked Cavity with Nonlinear Kerr Medium
We discuss a cavity with the nonlinear oscillator (corresponding to a Kerr medium) periodically kicked by a series of ultra-short laser pulses. This system is governed by the following Hamiltonian1 (in the interaction picture):where χ denotes nonlinearity of the Kerr medium and c is a strength of the field-medium coupling. In addition, we assume that the field is initially in the vacuum state ∣0〉. Assuming that the field coupling is weak, i.e. ∈ ≪ χ, we apply the standard perturbation method of rediagonalization of the Hamiltonian’. In consequence, we obtain the analytical formulas for the probabilities corresponding to the vacuum ∣0〉, one-photon ∣1〉 and two-photon ∣2〉 Fock states. Thus, for the time t just after k-th laser pulse, we havewhere
KeywordsLaser Pulse Numerical Experiment Number State Nonlinear Oscillator Unitary Evolution
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© Springer Science+Business Media New York 1996