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Physical Review Letters

Second-harmonic generation from collision complexes

Ahmet Eli, David A. Depatie

Published Feb 22, 1988• 17 citations
Publisher

Abstract

We show that binary collisions among atoms can couple the fundamental mode to its second harmonic by generating polariton modes which carry phase information between random scattering events and produce a constructively interfering component of the harmonic field.
DOI
10.1103/physrevlett.60.688

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We present a comprehensive and self-consistent theory of the relative phase between fundamental and harmonic modes in the nonlinear process of second-harmonic generation. We introduce an adequate polar decomposition of the field amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties of the fields. We find the probability distribution for the relative phase and, by using a numerical diagonalization of the interaction Hamiltonian, we study its time evolution. This evolution shows quite different asymptotic behaviours for long times depending on the total number of quanta.
The second harmonic generation (SHG) process is investigated theoretically using the quantum mechanics method of coherent control. Based on the extremum conditions for the SHG intensity at the center frequency, a Fresnel-inspired binary phase shaping scheme is proposed for tailoring the fundamental pulse. The SHG spectrum can be compressed into a narrowband signal with lower background by modulating the relative phases between the frequency components within the fundamental pulse, inducing constructive interference at the center frequency and destructive interference elsewhere. Multipeak second harmonic signals can also be obtained by properly modulating various interference pathways. These results have potential applications in high resolution nonlinear spectroscopy, microscopy, and information coding.
This paper presents an analysis of the Rabi oscillations of two-level atoms in the scattering-state representation. A collision complex obtained from a pair of identical two-level atoms is coupled to a field mode and it is found that there can be three distinct Rabi frequencies. These reduce to a single Rabi frequency for a photon distribution that is sharply peaked around an average number n\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\gg}1. One then finds that, in addition to the three frequency components in the off-diagonal element of the atomic density matrix, there are two components that are symmetrically displaced around the mode frequency at intervals of twice the Rabi frequency. They represent the collisionally induced cooperative motion of the atoms. When various observable quantities are averaged over the orientation of the complex, one obtains results that apply to many-atom systems in the binary collision approximation. Collisional effects do not enter the above results as lifetimes due to the fact that scattering states have precisely defined energies and correspond to entire particle histories. The collision potential opens up new radiative coupling channels, which collectively represent spectral line broadening. The collision potential and the radiative coupling combine to produce static and quasistatic dipole moments for the complex. At the threshold for atomic population inversion, the density matrix for the complex, as well as for an atom, becomes a constant multiple of the identity matrix, demonstrating that the threshold of stimulated emission is also a critical point for collisional effects, within the approximations of this paper.