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Quantum Optics$
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John Garrison and Raymond Chiao

Print publication date: 2008

Print ISBN-13: 9780198508861

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780198508861.001.0001

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Quantum tomography

Quantum tomography

Chapter:
(p.529) 17 Quantum tomography
Source:
Quantum Optics
Author(s):

J. C. Garrison

R. Y. Chiao

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198508861.003.0018

This chapter begins with a review of classical tomography, which reconstructs hidden structures inside an object by successive transmissions of an X-ray beam at different angles and lateral displacements. By interpreting the Wigner distribution as an analogue of the density distribution in a physical object, the mathematical methods of classical tomography — the Radon transform, the Fourier slice theorem, and the inverse Radon transform — are adapted to perform a high resolution determination of a quantum state of light. In optical homodyne tomography, the classical transmission angle is replaced by the adjustable phase of a local oscillator, and the successive lateral displacements are replaced by a series of measurements of the quadrature operator defined by the local oscillator phase. Experimental data is presented showing various properties of the Wigner distribution for a coherent state.

Keywords:   classical tomography, Wigner distribution, Radon transform, Fourier slice theorem, inverse Radon transform, optical homodyne tomography, local oscillator, quadrature operator

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