Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states

Journal Article · Mon Mar 01 04:00:00 EST 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.69.033812· OSTI ID:20640901

Dell'Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio ^[1]

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1. Dipartimento di Fisica 'E. R. Caianiello', Universita di Salerno, INFM UdR di Salerno, INFN Sezione di Napoli, Gruppo Collegato di Salerno, Via S. Allende, 84081 Baronissi, SA (Italy)

We introduce a formalism of nonlinear canonical transformations for general systems of multiphoton quantum optics. For single-mode systems the transformations depend on a tunable free parameter, the homodyne local-oscillator angle; for n-mode systems they depend on n heterodyne mixing angles. The canonical formalism realizes nontrivial mixing of pairs of conjugate quadratures of the electromagnetic field in terms of homodyne variables for single-mode systems, and in terms of heterodyne variables for multimode systems. In the first instance the transformations yield nonquadratic model Hamiltonians of degenerate multiphoton processes and define a class of non-Gaussian, nonclassical multiphoton states that exhibit properties of coherence and squeezing. We show that such homodyne multiphoton squeezed states are generated by unitary operators with a nonlinear time evolution that realizes the homodyne mixing of a pair of conjugate quadratures. Tuning of the local-oscillator angle allows us to vary at will the statistical properties of such states. We discuss the relevance of the formalism for the study of degenerate (up-)down-conversion processes. In a companion paper [F. Dell'Anno, S. De Siena, and F. Illuminati, 69, 033813 (2004)], we provide the extension of the nonlinear canonical formalism to multimode systems, we introduce the associated heterodyne multiphoton squeezed states, and we discuss their possible experimental realization.

• OSTI ID: 20640901
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 69; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
CANONICAL TRANSFORMATIONS
CONVERSION
ELECTROMAGNETIC FIELDS
EVOLUTION
HAMILTONIANS
MIXING
MULTI-PHOTON PROCESSES
NONLINEAR OPTICS
NONLINEAR PROBLEMS
OSCILLATORS
QUADRATURES
TUNING
WAVELENGTHS
YIELDS