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Optics Communications

Generalised semiclassical formalism for two-photon resonant problems

J.N. Elgin, G.H.C. New, K. E. Orkney

Published Aug 1, 1976• 36 citations
Publisher
DOI
10.1016/0030-4018(76)90124-3

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The analysis of two-photon resonant third-harmonic generation is generalised to include, in particular, the effects of imperfect index matching and two-photon tuning. Furthermore, whereas previously the authors considered only the temporal properties of the generated harmonic signal, here is spectral characteristics are also considered. The authors comment on a discrepancy between the predictions of semiclassical and quantised field formalisms. In the semiclassical analysis, it is shown that for large energy input pulses the harmonic spectrum is double peaked even near exact resonance and that this structure can be interpreted in terms of transitions between sets of doublet states of the Autler-Townes (1955) type. In a quantised field formalism, however, the picture is radically altered near exact resonance where a three-peaked spectrum is predicted.
For pt.I see Chem. Phys. Lett. vol.96, p.464 (1983). The non-linear multiphoton excitation dynamics of two-level systems under the influence of two strong linearly polarised monochromatic fields is studied exactly for the first time along the semiclassical many-mode Floquet theory. The present approach relaxes the restrictions of the conventional generalised rotating-wave approximation (GRWA) and allows correct treatment of various non-linear features such as power broadening, resonance shift, asymmetry in absorption lineshape, etc. By extending the nearly degenerate perturbative method of Salwen (1955), approximate analytical expressions for transition probabilities are obtained for multiphoton resonance processes for which (n+1) photons of one field are absorbed, whereas n photons of the other field are emitted, where n is an arbitrary integer. Detailed comparison of the analytical, the GRWA and the numerically exact results is given. Also presented is a case study of the time evolution of spin 1/2 systems in multi-quantum NMR transitions driven by pulsed bichromatic radiofrequency fields.
We explore the possibility of using an optomechanical resonator to induce a conditional phase gate for single photons. The problem provides an illustration of the application to optomechanical systems of a recently developed input-output formalism for single- (or few-) photon states of the radiation field. At the two-photon level, we find significant departures from expectations based on a semiclassical treatment. We also find a tradeoff between the maximum achievable conditional phase and the fidelity of the final state, consistent with other multimode studies of conditional phases based on optical nonlinearities.1 MoreReceived 31 December 2013DOI:https://doi.org/10.1103/PhysRevA.89.052327©2014 American Physical Society