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Physics Letters A

On the spectrum of the system of interacting quantum nonlinear resonances

G. P. Berman, G. M. Zaslavsky, Andrey R. Kolovsky

Published Jan 1, 1982• 37 citations
Publisher
DOI
10.1016/0375-9601(82)90099-8

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The quantum inverse scattering method is used for the study of a nonlinear N-wave resonance interaction system. The Yang–Baxter relations are solved to get various commutation relations for the scattering data operators. The energy spectrum of the quantum Hamiltonian for the model is determined and the existence of the quantum bound states is analyzed. In the classical limit, the corresponding r matrix is found, and the well-established correspondence between the classical solitons and the quantum bound states is examined. Finally, the integrability of the same model but with both fermion fields and boson fields is discussed.
We theoretically study nonlinear optical frequency conversion with time-frequency entangled paired photons whose sum frequency is on two-photon resonance of an atomic ensemble. Assisted by a strong coupling laser, two paired photons with wide spectrum are converted into a single monochromatic photon. The on-resonance nonlinear process is made possible due to the electromagnetically induced transparency that not only eliminates the on-resonance absorption but also enhances the nonlinear interaction between the single photons and atoms. Compared to this quantum-nonlinear conversion, the classical corresponding single-photon counts from accidental two-photon coincidence has a wide spectrum and experiences large absorption. As a result, the system can be used as an efficient two-photon quantum correlator in which the classical accidental coincidences can be suppressed. We perform numerical simulations basing on a Rb atomic vapor cell with realistic operating parameters.