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Soviet Journal of Quantum Electronics

Quantum-statistical properties of optical parametric processes

Ladislav Mišta, Jan Peřina, Vlasta Peřinová

Published Dec 31, 1977• 0 citations
Publisher

Abstract

An analysis is made of the possibility of observing an anticorrelation effect in optical parametric processes (both degenerate and nondegenerate) with classical and quantum pumping. It is shown that the time dependence of the photon statistics in the anticorrelation regime reduces the indeterminacy (quantum noise) to a level below that in the coherent state case.

DOI
10.1070/qe1977v007n12abeh008264

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An analysis is made of the possibility of observing an anticorrelation effect in optical parametric processes (both degenerate and nondegenerate) with classical and quantum pumping. It is shown that the time dependence of the photon statistics in the anticorrelation regime reduces the indeterminacy (quantum noise) to a level below that in the coherent state case.
The photon statistics of quadratic parametric two-mode processes are derived starting from the results of the first part of this paper. A general theory is presented and particular processes are discussed. Assuming the initial field to be coherent, fluctuations of the pumping field are taken into account. The effects of antibunching and anticorrelation of photons on the photon distribution, its factorial moments, fluctuations in modes and their correlations for the amplification process are demonstrated and their dependence on levels of pumping field fluctuations is shown.
Quantum properties of parametric amplification and frequency conversion of an optical image in coupled parametric interactions are analyzed for the case of a remote object. The coupled-wave interaction consists of a traditional process of parametric amplification in the high-frequency pump field accompanied by the frequency mixing of generated and pump waves. The photon number density and signal-to-noise ratio at the interacting frequencies are studied in the image plane at the output of the nonlinear frequency converter in the fixed pump field approximation. The degree of entanglement of optical images at frequencies above and below the pump frequency is investigated.
We consider the classical and quantum-mechanical processes of three-wave interactions in different phase regimes and present numerical calculations for the quantum case, where all three modes are sizably excited from the beginning. These excitations are coherent so that various important phase regimes can be adjusted. In addition, one mode can also be prepared in a squeezed or Kerr state. The classical solutions are well known and are briefly summarized, but certain phase regimes are classically unexplored and we show here that they give interesting and surprising results. In the out-of-phase regime (where the photon numbers do not change in the first order of time) we get, with an initial Kerr state, strongly sub-Poissonian photon statistics in the signal after a short interaction time. This effect is limited by the classically described phase shifts that are present even in the parametric approximation. This nonclassical phenomenon (due to the Kerr state) helps us to understand similar nonclassical effects generated by entangled states of the pump and signal during sum-frequency generation. \textcopyright{} 1996 The American Physical Society.
Abstract It is shown that the anticorrelations in the photon numbers of the signal and the idler wave, respectively, generated in parametric three‐wave interaction under suitable conditions, violate an inequality well‐known in classical communication theory. Hence, it must be concluded that these anticorrelations reflect a typical quantum mechanical feature of light. In fact, this nonclassical behaviour is responsible for the occurrence of photon antibunching in the superposition field made up of both the signal and the idler wave, as will be pointed out in some detail.