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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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Coherent states

Coherent states

(p.148) 5 Coherent states
Quantum Optics

J. C. Garrison

R. Y. Chiao

Oxford University Press

The elementary quantum theory of quasi-classical states for mechanical harmonic oscillators is applied to the radiation oscillators describing light, and thus used to define quasi-classical states of light. These states are called “coherent”, because the expectation value of any normally ordered product of creation and annihilation operators factorizes for them. A theoretical discussion of possible sources for coherent states is followed by experimental evidence for their existence. The mathematical properties of coherent states, e.g., nonorthogonality and overcompleteness, are explained in order to use them to represent states and operators. These representations provide a suitable replacement for the classical phase space description of light, which is forbidden by the uncertainty principle. The quantum phase space approach leads to the definition of the Wigner distribution, the Q-function, the P-function, and Gaussian mixed states.

Keywords:   quasiclassical, nonorthogonality, overcompleteness, phase space, Wigner distribution, Q-function, P-function, Gaussian state

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