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Physical Review A

Optical mesons

P. D. Drummond, Hao He

Published Aug 1, 1997• 34 citations
Publisher

Abstract

An ``optical meson''(two-photon quantum soliton) is proven to exist in a parametric waveguide. This could provide an ideal quantum soliton environment, because of more realistic formation lengths and much larger binding energies than ${\ensuremath{\chi}}^{(3)}$ quantum solitons. We estimate the binding energy, radius, and interaction length in comparison to the ${\ensuremath{\chi}}^{(3)}$ case in optical fibers.

DOI
10.1103/physreva.56.r1107

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An ``optical meson''(two-photon quantum soliton) is proven to exist in a parametric waveguide. This could provide an ideal quantum soliton environment, because of more realistic formation lengths and much larger binding energies than \ensuremathχ(3){\ensuremath{\chi}}^{(3)}\ensuremathχ(3) quantum solitons. We estimate the binding energy, radius, and interaction length in comparison to the \ensuremathχ(3){\ensuremath{\chi}}^{(3)}\ensuremathχ(3) case in optical fibers.
We consider the quantum theory of three fields interacting via parametric and repulsive quartic couplings. This can be applied to treat photonic ${\ensuremath{\chi}}^{(2)}$ and ${\ensuremath{\chi}}^{(3)}$ interactions, and interactions in atomic Bose-Einstein condensates or quantum Fermi gases, describing coherent molecule formation together with s-wave scattering. The simplest two-particle quantum solitons or bound-state solutions of the idealized Hamiltonian, without a momentum cutoff, are obtained exactly. They have a pointlike structure in two and three dimensions---even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with a momentum cutoff. The parametric quantum solitons have much more realistic length scales and binding energies than ${\ensuremath{\chi}}^{(3)}$ quantum solitons, and the resulting effects could potentially be experimentally tested in highly nonlinear optical parametric media or interacting matter-wave systems. N-particle quantum solitons and the ground state energy are analyzed using a variational approach. Applications to atomic/molecular Bose-Einstein condensates (BEC's) are given, where we predict the possibility of forming coupled BEC solitons in three space dimensions, and analyze ``superchemistry'' dynamics.
We consider the quantum field theory of two bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium, this corresponds to the process of second-harmonic generation (via ${\ensuremath{\chi}}^{(2)}$ nonlinearity) modified by the ${\ensuremath{\chi}}^{(3)}$ nonlinearity. The quantum solitons or energy eigenstates (bound-state solutions) are obtained exactly in the simplest case of two-particle binding, in one, two, and three space dimensions. We also investigate three-particle binding in one space dimension. The results indicate that the exact quantum solitons of this field theory have a singular, pointlike structure in two and three dimensions---even though the corresponding classical theory is nonsingular. To estimate the physically accessible radii and binding energies of the bound states, we impose a momentum cutoff on the nonlinear couplings. In the case of nonlinear optical interactions, the resulting radii and binding energies of these photonic particlelike excitations in highly nonlinear parametric media appear to be close to physically observable values.