Zitterbewegung of optical pulses in nonlinear frequency conversion

TL;DR

This paper demonstrates that pulse walk-off in nonlinear frequency conversion causes jittering similar to Zitterbewegung in relativistic particles, proposing a new optical analogy to simulate the Dirac equation.

Contribution

It introduces an analytical model linking pulse walk-off to Zitterbewegung and suggests nonlinear optics as a platform to simulate relativistic quantum phenomena.

Findings

Analytical expression for pulse center of mass trajectory derived.

Numerical examples of Zitterbewegung in sum frequency generation provided.

Proposes nonlinear optics as a quantum simulation platform for the Dirac equation.

Abstract

Pulse walk-off in the process of sum frequency generation in a nonlinear $\chi^{(2)}$ crystal is shown to be responsible for pulse jittering which is reminiscent to the Zitterbewegung (trembling motion) of a relativistic freely moving Dirac particle. An analytical expression for the pulse center of mass trajectory is derived in the no-pump-depletion limit, and numerical examples of Zitterbewegung are presented for sum frequency generation in periodically-poled lithium niobate. The proposed quantum-optical analogy indicates that frequency conversion in nonlinear optics could provide an experimentally accessible simulator of the Dirac equation.