## Generalized uncertainty relations and coherent and squeezed states

JOSA A, Vol. 17, Issue 12, pp. 2486-2495 (2000)

http://dx.doi.org/10.1364/JOSAA.17.002486

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### Abstract

Characteristic uncertainty relations and their related squeezed states are briefly reviewed and compared in accordance with the generalizations of three equivalent definitions of canonical coherent states. The standard SU(1, 1) coherent states are shown to be the unique states that minimize the Schrödinger uncertainty relation for every pair of the three generators and the Robertson relation for the three generators. The characteristic uncertainty inequalities are naturally extended to the case of several states. It is shown that these inequalities can be written in the equivalent complementary form.

© 2000 Optical Society of America

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.6570) Quantum optics : Squeezed states

**History**

Original Manuscript: March 9, 2000

Revised Manuscript: July 20, 2000

Manuscript Accepted: July 31, 2000

Published: December 1, 2000

**Citation**

D. A. Trifonov, "Generalized uncertainty relations and coherent and squeezed states," J. Opt. Soc. Am. A **17**, 2486-2495 (2000)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-12-2486

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