Fock expansion of multimode pure Gaussian states

Journal Article · Tue Dec 15 00:00:00 EST 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4937550· OSTI ID:22479566

Cariolaro, Gianfranco; Pierobon, Gianfranco ^[1]

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1. Università di Padova, Padova (Italy)

The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, as shown for two-mode and three-mode Gaussian states.

• OSTI ID: 22479566
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 12; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
PHASE SPACE
PHOTONS
POLYNOMIALS
QUANTUM ENTANGLEMENT
VACUUM STATES