Quantum-optical Space-time Wave Frames: When light coordinates itself coherently

J S Briggs

ABSTRACT For free propagation from a focus, the Hermite–Gauss wave functions of optics spread in space. In quantum mechanics, the Hermite–Gauss functions are referred to as the harmonic oscillator eigenfunctions. These functions are used here to describe the interference of wave packets. It has been shown that when transformed to a frame moving with the normal to the wave front trajectories, the Hermite–Gauss functions are constant up to a phase factor which is the Gouy phase. The Gouy phase itself assumes the role of proper space or time coordinate. Along the whole of such a trajectory, the space wave function is proportional to the wave number or momentum function. An arbitrary normalizable wave packet can be expanded using the Hermite–Gauss functions as a basis. As example, it is shown that in the transformed frame, a displaced Gaussian does not spread but rather becomes a coherent state. This allows a particularly simple representation of the Young's interference pattern from two or more slits.

Wolfgang P. Schleich

S. Olivares

J S Briggs

For free propagation from a focus the Hermite-Gauss wave functions of optics spread in space. In quantum mechanics the Hermite-Gauss functions are referred to as the harmonic oscillator eigen- functions. These functions are used here to describe the interference of wave packets. It has been shown that when transformed to a frame moving with the normal to the wave front trajectories, the Hermite-Gauss functions are constant up to a phase factor which is the Gouy phase. The Gouy phase itself assumes the role of proper space or time coordinate. Along the whole of such a trajectory, the space wave function is proportional to the wave number function. An arbitrary normalisable wave packet can be expanded using the Hermite-Gauss functions as a basis. As example, it is shown that in the co-moving frame, a displaced Gaussian does not spread but rather becomes a coherent state. This allows a particularly simple representation of the Young's interference pattern from two or more slits.

Y. S. Kim, Eugene Paul Wigner

It is suggested that the light-cone coordinate system is the natural language for the Lorentz-covariant phase-space representation of quantum mechanics. The localized light wave is discussed as an illustrative example. It is shown that the unitary transformation of a localized light wave from one Lorentz frame to another can be achieved through its covariant phase-space representation.

Ruslan P. Ozerov, Anatoli A. Vorobyev