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Journal of Experimental and Theoretical Physics

Three-photon interference: Spectroscopy of linear and nonlinear media

A. V. Burlakov, S. P. Kulik, Alexander N. Penin, Maria V. Chekhova

Published Jun 1, 1998• 12 citations
Publisher

Abstract

The nonlinear interference accompanying three-photon spontaneous parametric light scattering is considered. The frequency-angle line shape of the scattering is calculated for nonlinear-crystal/ linear-dispersive-medium/nonlinear-crystal and nonlinear-crystal/nonlinear-crystal systems. The question of the possible use of nonlinear interference in spectroscopy is discussed.

DOI
10.1134/1.558576

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The interference of biphotonic light produced in the process of spontaneous parametric scattering (SPS) in two spatially separated non-centrally symmetric crystals is considered. A scheme of the nonlinear Mach—Zehnder interferometer is realised. It is shown that in this case, the frequency-angular intensity distribution in the far-field zone (the SPS spectrum) contains information not only on non-centrally symmetric crystals, where biphotonic fields are created, but also on the optical properties of the medium located between the scattering crystals. The algorithms for the determination of the dispersion law in this medium are developed.
Interference is observed between the spontaneous parametric radiation from two nonlinear crystals separated by a macroscopic air gap and excited in series by a common pump beam. The phase of the interference depends on the phase shifts at three frequencies. A simple quantum model agrees well with the experimental results and makes it possible to interpret the effect in terms of general vacuum fluctuations which give rise to the spontaneous emission of mutually coherent radiation from the two crystals.
Coherent four-photon scattering of light due to excited and autoionizing states of atomic systems is considered. We analyze the influence of one-photon resonances at the frequency of the anti-Stokes signal and at the frequency of the pump wave on the shape of the spectrum of four-photon scattering. We derive analytical expressions for the line shapes of four-photon scattering involving one-photon resonances with allowance for phase-matching conditions and variation in the populations of excited states for limiting regimes of tight focusing and strong absorption in a medium with a cubic nonlinearity. The calculated spectra of four-photon scattering include the interference of resonant and nonresonant components of the third-order nonlinear susceptibility with allowance for one-photon saturation. We develop a method for normalizing experimental spectra of four-photon scattering with one-photon resonances that takes into account distortion of spectral lines due to the influence of phase mismatch and one- photon absorption.
Two types of interference were observed using two-photon spontaneous parametric radiation from two nonlinear interaction regions. Two experimental setups analogous to the Young and Mach-Zehnder interferometers were used. An interesting feature of the two-photon Young interference is the opposite conditions for its observation by two different methods: by measuring intensity of light at a single frequency and by measuring correlation of intensities at two conjugated frequencies (method of coincidences). Two-photon Mach-Zehnder interference resembles the Ramsey method of separated fields, which is used in beam spectroscopy. A simple macroscopic quantum model agrees well with the experimental results and enables their interpretation in terms of ``biphotons'' carrying information about the pump phase.