A rigorous uncertainty relation (Cauchy Inequality) for an electromagnetic field in quantum superpositions of coherent states and in a two-photon coherent state

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• 作者：A. V. Kozlovskii
• 刊名：Optics and Spectroscopy
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：120
• 期：4
• 页码：596-604
• 全文大小：655 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Optical Spectroscopy and Ultrafast Optics
  Russian Library of Science
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1562-6911
• 卷排序：120

文摘

It is shown that the Heisenberg uncertainty relation (or soft uncertainty relation) determined by the commutation properties of operators of electromagnetic field quadratures differs significantly from the Robertson–Schrödinger uncertainty relation (or rigorous uncertainty relation) determined by the quantum correlation properties of field quadratures. In the case of field quantum states, for which mutually noncommuting field operators are quantum-statistically independent or their quantum central correlation moment is zero, the rigorous uncertainty relation makes it possible to measure simultaneously and exactly the observables corresponding to both operators or measure exactly the observable of one of the operators at a finite measurement uncertainty for the other observable. The significant difference between the rigorous and soft uncertainty relations for quantum superpositions of coherent states and the two-photon coherent state of electromagnetic field (which is a state with minimum uncertainty, according to the rigorous uncertainty relation) is analyzed.Original Russian Text © A.V. Kozlovskii, 2016, published in Optika i Spektroskopiya, 2016, Vol. 120, No. 4, pp. 626–635.