Superoscillations and weak measurement

Duration: 1 hour 3 mins 45 secs

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Description:	Michael Berry (H H Wills Physics Laboratory, University of Bristol) Monday 03 December 2012, 17:00-18:00

Created:

2012-12-12 13:05

Collection:

Topological Dynamics in the Physical and Biological Sciences
Rothschild Seminars

Publisher:

Isaac Newton Institute

Berry, M

Language:

eng (English)

Credits:

Producer:

Steve Greenham


Abstract:	Band-limited functions can oscillate arbitrarily faster than their fastest Fourier component over arbitrarily long intervals. Where such ‘superoscillations’occur, functions are exponentially weak. In typical monochromatic optical fields, substantial fractions of the domain (one-third in two dimensions) are superoscillatory. Superoscillations have implications for signal processing, and raise the possibility of sub-wavelength resolution microscopy without evanescent waves. In quantum mechanics, superoscillations correspond to weak measurements, suggesting ‘weak values’ of observables (e.g photon momenta) far outside the range represented in the quantum state. A weak measurement of neutrino speed could lead to a superluminal result without violating causality, but the effect is too small to explain the speed recently claimed in a recent (and now-discredited) experminent.

Abstract:

Band-limited functions can oscillate arbitrarily faster than their fastest Fourier component over arbitrarily long intervals. Where such ‘superoscillations’occur, functions are exponentially weak. In typical monochromatic optical fields, substantial fractions of the domain (one-third in two dimensions) are superoscillatory. Superoscillations have implications for signal processing, and raise the possibility of sub-wavelength resolution microscopy without evanescent waves. In quantum mechanics, superoscillations correspond to weak measurements, suggesting ‘weak values’ of observables (e.g photon momenta) far outside the range represented in the quantum state. A weak measurement of neutrino speed could lead to a superluminal result without violating causality, but the effect is too small to explain the speed recently claimed in a recent (and now-discredited) experminent.

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