Beam Focusing and Reduction of Quantum Uncertainty in Width at the Few-Photon Level via Multi-Spatial-Mode Squeezing.

We show for the first time that it is possible to realize laser beam focusing at the few-photon level in the four-wave-mixing process, and at the same time reduce the quantum uncertainty in width. The reduction in quantum uncertainty results directly from the strong suppression of local intensity fluctuations. This surprising effect of simultaneous focusing and reduction of width uncertainty is enabled by multi-spatial-mode (MSM) squeezing, and is not possible via any classical optical approach or single-spatial-mode squeezing. Our results open promising possibilities for quantum-enhanced imaging and metrology; as an example, the limit on the measurement of very small beam displacement can be enhanced within feasible experimental parameters because of beam focusing and the noiseless amplification in the MSM squeezing process.