Quantum Uncertainty in the Beam Width of Spatial Optical Modes

TL;DR

This paper explores the quantum uncertainty in the beam width of optical modes, defining a quantum operator and analyzing how quantum noise affects beam width, with implications for noise reduction strategies.

Contribution

It introduces a quantum operator for beam width, analyzes quantum noise in single and multimode states, and identifies a mode-specific quadrature uncertainty as the main noise source.

Findings

Quantum uncertainty in beam width is linked to a specific mode's amplitude quadrature.

The quantum operator for beam width is explicitly defined and analyzed.

Noise reduction can be achieved by selecting appropriate quantum states.

Abstract

We theoretically investigate the quantum uncertainty in the beam width of transverse optical modes and, for this purpose, define a corresponding quantum operator. Single mode states are studied as well as multimode states with small quantum noise. General relations are derived, and specific examples of different modes and quantum states are examined. For the multimode case, we show that the quantum uncertainty in the beam width can be completely attributed to the amplitude quadrature uncertainty of one specific mode, which is uniquely determined by the field under investigation. This discovery provides us with a strategy for the reduction of the beam width noise by an appropriate choice of the quantum state.