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Conference on Lasers and Electro-Optics

Quantum enhancement of optical beam position accuracy by self-focusing

Mankei Tsang

Published May 4, 2008• 0 citations
Publisher

Abstract

The standard and Heisenberg quantum limits on the position accuracy of an optical beam are rigorously derived. A simple scheme of beating the standard quantum limit by self-focusing is proposed.
DOI
10.1109/qels.2008.4553259

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There are heuristic arguments proposing that the accuracy of monitoring position of a free mass mmm is limited by the standard quantum limit (SQL): ${\ensuremath{\sigma}}^{2}(X(t))\ensuremath{\ge}{\ensuremath{\sigma}}^{2}(X(0))+({t}^{2}/{m}^{2}){\ensuremath{\sigma}}^{2}(P(0))\ensuremath{\ge}\ensuremath{\hbar}t/m$, where ${\ensuremath{\sigma}}^{2}(X(t))$ and ${\ensuremath{\sigma}}^{2}(P(t))$ denote variances of the Heisenberg representation position and momentum operators. Yuen [Phys. Rev. Lett. 51, 719 (1983)] discovered that there are contractive states for which this result is incorrect. Here I prove universally valid rigorous quantum limits (RQL), viz. rigorous upper and lower bounds on ${\ensuremath{\sigma}}^{2}(X(t))$ in terms of ${\ensuremath{\sigma}}^{2}(X(0))$ and ${\ensuremath{\sigma}}^{2}(P(0))$, given by Eq. (12) for a free mass and by Eq. (36) for an oscillator. I also obtain the maximally contractive and maximally expanding states which saturate the RQL, and use the contractive states to set up an Ozawa-type measurement theory with accuracies respecting the RQL but beating the standard quantum limit. The contractive states for oscillators improve on the Schr\"odinger coherent states of constant variance and may be useful for gravitational wave detection and optical communication.
Quantum enhancement of optical pulse timing accuracy is investigated in the Heisenberg picture. Effects of optical loss, group-velocity dispersion, and Kerr nonlinearity on the position and momentum of an optical pulse are studied via Heisenberg equations of motion. Using the developed formalism, the impact of decoherence by optical loss on the use of adiabatic soliton control for beating the timing standard quantum limit [M. Tsang, Phys. Rev. Lett. 97, 023902 (2006)] is analyzed theoretically and numerically. The analysis shows that an appreciable enhancement can be achieved using current technology, despite an increase in timing jitter mainly due to the Gordon-Haus effect. The decoherence effect of optical loss on the transmission of quantum-enhanced timing information is also studied, in order to identify situations in which the enhancement is able to survive.