Optical Tomograms of Multiple-Photon-Added Gaussian States via the Intermediate State Representation Theory

Optical tomogram of a quantum state can serve as an alternative to its density matrix since it contains all the information on this state. In this paper we use the explicit expression of the intermediate state | q, f , g〉(that is, an eigenvector of the coordinate and momentum operator fQ + gP ) and...

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Bibliographic Details
Published in:Journal of experimental and theoretical physics 2018-09, Vol.127 (3), p.383-390
Main Authors: Meng, Xiang-Guo, Wang, Ji-Suo, Liang, Bao-Long, Du, Chuan-Xun
Format: Article
Language:English
Subjects:
ANNIHILATION OPERATORS
ATOMIC AND MOLECULAR PHYSICS
Atoms
Classical and Quantum Gravitation
Density
DENSITY MATRIX
DISTRIBUTION
EIGENSTATES
EIGENVECTORS
Elementary Particles
HERMITE POLYNOMIALS
INTERMEDIATE STATE
Mathematical analysis
Molecules
Optics
Particle and Nuclear Physics
PERIODICITY
Physics
Physics and Astronomy
PURE STATES
Quantum Field Theory
RADON
Radon transformation
Relativity Theory
Representations
Solid State Physics
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Summary:Optical tomogram of a quantum state can serve as an alternative to its density matrix since it contains all the information on this state. In this paper we use the explicit expression of the intermediate state | q, f , g〉(that is, an eigenvector of the coordinate and momentum operator fQ + gP ) and the Radon transform between the Wigner operator Δ(p, q) and the pure-state density operator | q, f, g 〉〈 q, f, g | to calculate the specific tomograms for multiple-photon-added coherent states (MPACSs), thermal states (MPATSs) and displaced thermal states (MPADTSs). Their analytical tomograms are actually the finite-summation representations related to single-variable Hermite polynomials. Besides, the numerical results indicate that the larger photon-addition number can lead to the multi-peak tomographic distributions for these three states, and the measurable tomograms of MPACSs and MPADTSs exhibit π-periodic features but MPATSs can’t.
ISSN:1063-7761
1090-6509
DOI:10.1134/S1063776118080113