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中国科学通报：英文版

GENERATION OF NONCLASSICAL STATES OF LIGHT FIELD BY ORTHO-SYMMETRIZATION

彭石安

Published Jan 1, 1990• 0 citations
OpenAlex

Abstract

In recent years, nonclassical effects of light field havealways been a very conspicuous subject. In this field an effective approach is to construct as many as possible the nonclassical states of light field that are allowed in the frame of quantum mechanics and then to study their properties, so as to find out the relations of different nonclassical effects or states of light field and to discover new nonclassical effects or states of light field.

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In recent years, nonclassical effects of light field havealways been a very conspicuous subject. In this field an effective approach is to construct as many as possible the nonclassical states of light field that are allowed in the frame of quantum mechanics and then to study their properties, so as to find out the relations of different nonclassical effects or states of light field and to discover new nonclassical effects or states of light field.
COHERENT AND " N O N C L A S S I C A L " STATES 3 4 BRIEF HISTORY OF NONCLASSICAL STATES COHERENT AND " N O N C L A S S I C A L " STATES 5 6 BRIEF HISTORY OF NONCLASSICAL STATES CHILDHOOD OF SQUEEZED STATES 7 8 BRIEF HISTORY OF NONCLASSICAL STATES COHERENT STATES OF NONSTATIONARY OSCILLATORS 9 NON-GAUSSIAN OSCILLATOR STATES 11 12 BRIEF HISTORY OF NONCLASSICAL STATES COHERENT PHASE STATES 13 in the last decade of the 20th century (see the paragraph on photon-added states \nin section 3). Lerner [120] noticed that the commutation relations (32) do not \ndetermine the operators C, S uniquely. Earlier, the same observation was made \nby Wigner [121] with respect to the triple {n, a, a*} (see the next section). In the \ngeneral case, besides the "polar decomposition" (31), which is equivalent to the \nrelations E-\\n) = (1-Sn0)\\n - 1), E+\\n) = |n + 1), (35) one can define operator U = C + iS via the relation U\\n) = f(n)\\n -1), \nwhere function f(n) may be arbitrary enough, being restricted by the requirement /(0) =0 and certain other constraints which ensure that the spectra of the \n"cosine" and "sine" operators belong to the interval (—1,1). The properties of \nLerner's construction were studied in [122].
“The word ‘classical’ means only one thing in science: it's wrong!” We have previously emphasized the fact that all states of light are quantum mechanical and are thus nonclassical, deriving some quantum features from the discreteness of the photons. Of course, in practice, the nonclassical features of light are difficult to observe. (We shall use “quantum mechanical” and “nonclassical” more or less interchangeably here.) Already we have discussed what must certainly be the most nonclassical of all nonclassical states of light – the single-photon state. Yet, as we shall see, it is possible to have nonclassical states involving a very large number of photons. But we need a criterion for nonclassicality. Recall that in Chapter 5 we discussed such a criterion in terms of the quasi-probability distribution known as the P function, P (α). States for which P (α) is positive everywhere or no more singular than a delta function, are classical whereas those for which P (α) is negative or more singular than a delta function are nonclassical. We have shown, in fact, that P (α) for a coherent state is a delta function, and Hillery has shown that all other pure states of the field will have functions P (α) that are negative in some regions of phase space and are more singular than a delta. It is evident that the variety of possible nonclassical states of the field is quite large.