Vol. 9, no.1, 2017


Vladimir A. Andreev
P.N. Lebedev Physical Institute, Russian Academy of Sciences, http://www.lebedev.ru
119991 Moscow, Russian Federation

Received 22.04.2017
Abstract. A review is given of the properties of two types of quantum states, which have great uncertainty in the coordinate and momentum. Both are obtained from the states of a harmonic oscillator by means of certain transformations. The first type is correlated states, they are obtained from coherent states with a help of the Bogolyubov transform. The variances of the coordinate and momentum of such a state depend on the Bogolyubov transform parameters and can, in general, take arbitrarily large values. Their specific values are determined by the physical processes with which the Bogolyubov transform is realized. A concrete example of such physical process is considered. Another type are stretched states. Formally, they arise when the n-partial state of a harmonic oscillator undergoes a transform associated with a scale transformation of the phase space. The dispersion of the coordinate and momentum of these states depends on the scale transformation parameter and can also take arbitrarily large values. Physically stretched states can be obtained by passing n-photon states through a quantum amplifier. The role of the scale transformation of the phase space is played by the gain of the quantum amplifier

Keywords: harmonic oscillator, correlated states, compressed states, stretched states, uncertainty relations, Planck constant

PACS 03.65.−w, 23.20.Lv

RENSIT, 2017, 9(1):8-20 DOI: 10.17725/rensit.2017.09.008

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