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Quantum Electronics and Laser Science Conference

Precision atomic position measurement using optical fields; building Heisenberg's microscope

George R. Welch, K. D. Stokes, Jennifer Margaret Gardner, M. Marable, C. Schnurr, John E. Thomas

Published May 12, 1991• 0 citations
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The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant $\ensuremath{\Elzxh}/2$ as demonstrated by Heisenberg's thought experiment using a \ensuremath{\gamma}-ray microscope. Here it is shown that this common assumption is not universally true: a universally valid trade-off relation between the noise and the disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck's constant when the intervention is dependent. A model of measuring interaction with dependent intervention shows that Heisenberg's lower bound for the noise-disturbance product is violated even by a nearly nondisturbing precise position measurement. An experimental implementation is also proposed to realize the above model in the context of optical quadrature measurement with currently available linear optical devices.
The principle of uncertainty is one of the essential principles of quantum mechanics as it outlines that there is a reflective limit to the measurement of microscopic particle motion. However it is impossible to measure at once and accurately both the position and momentum data of any microscopic particle no matter what means are used to do so. This paper starts by discussing the notion and mathematical derivation of the uncertainty principle as put forth by Heisenberg explaining the physical relevance of the principle. It introduces the natural uncertainty the principle introduces to the dynamics of particles in the microscopic world, and the significant part it plays in the theory of quantum mechanics. The article overviews the explanations of the principle on phenomena including atomic stability and scanning tunneling microscopes, and the interference of measurement actions on the states of particles and the shortcomings of measurement precision. According to the wave-particle duality of quantum mechanics, this article gives a required theoretical basis of microscopic phenomena. Likewise, the use of the research theory on the uncertainty principle by distinguished scholars in the physics fraternity helps the readers in achieving the knowledge in related subjects more easily.
Optical atomic clocks are our most precise tools to measure time and frequency [1]–[3]. They enable precision frequency comparisons between atoms in separate locations to probe the space-time variation of fundamental constants [4] and the properties of dark matter [5], [6], to perform geodesy [4], [7], [8] and to evaluate systematic clock shifts. Measurements on independent systems are limited by the standard quantum limit (SQL); measurements on entangled systems, in contrast, can surpass the SQL to reach the ultimate precision allowed by quantum theory - the so-called Heisenberg limit. While local entangling operations have been used to demonstrate this enhancement at microscopic distances [9]–[14], frequency comparisons between remote atomic clocks require rapid high-fidelity entanglement between separate systems that have no intrinsic interactions.