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Physical Review Letters

Two-photon bound state in self-focusing media

R. Y. Chiao, Ivan Deutsch, J. C. Garrison

Published Sep 9, 1991• 35 citations
Publisher

Abstract

We derive a two-photon bound-state solution to the problem of quantum propagation of light in Kerr-effect nonlinear media which classically would exhibit self-focusing and self-trapping. We propose an experiment to see this two-photon bound state.
DOI
10.1103/physrevlett.67.1399

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Propagation of light beams in a Fabry-Perot resonator filled with a self-focusing Kerr material is described by the nonlinear Schrodinger equation. If the degrees of freedom are restricted to one transverse dimension through the use of a line focus at the input face, the system possesses classical soliton solutions analogous to those for travelling-wave self-trapped beams. When the classical field theory is quantized, one obtains an effective nonrelativistic many-body field theory in which pairs of photons interact through attractive delta function potentials. The existence of bound states between photons is the microscopic phenomenon that prevents beams from spreading by diffraction. The fundamental bound state consists of two photons, which we call the "diphoton." We consider production of these quasi-particles in a single longitudinal mode Fabry-Perot resonator filled with an alkali vapor. The injected light is strongly attenuated to excite few photons in the cavity and is detuned slightly above the atomic resonance, giving rise to the self-focusing nonlinearity. Detection of the diphoton can be achieved by rejecting the unbound component by using a spatial filter and detecting the remaining signal in coincidence counting. The diphoton signature is a characteristic Lorentzian-squared two-point correlation profile.1
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We consider two-photon bound states which may be excited in a planar waveguide filled with a self-focusing Kerr material. These bound states are the quantum analogs of the classical light bullets which form under the combined effects of self-focusing, diffraction, self-phase-modulation, and anomalous group-velocity dispersion. A variational approach is used to establish a threshold condition on the strength of the nonlinearity for the existence of the bound state, and a gedanken experiment is proposed to outline the principles for creation and detection of this quasiparticle.