Sampling of photon statistics and density matrix using homodyne detection

U. Leonhardt, M. Munroe, T. Kiss, Th Richter, M. G. Raymer

Research output: Contribution to journalArticle

165 Citations (Scopus)


The photon statistics and, moreover, the density matrix (quantum state) of a single light mode can be sampled using homodyne detection. That is, the density matrix is computed by averaging a set of sampling functions with respect to the measured quadrature values. We develop a practical procedure for evaluating these functions. The algorithm is simple, stable, has small computer-memory requirements, and is last enough for real-time data processing. (Interestingly, our method involves unnormalizable solutions of the stationary Schrödinger equation. We develop the annihilation-and-creation formalism for these solutions and derive their semiclassical approximations.) We quantify the bin width required to determine the density matrix up to a maximal quantum number. Finally, we show how the statistical errors of the reconstructed density matrix can be determined from the measured data.

Original languageEnglish
Pages (from-to)144-160
Number of pages17
JournalOptics Communications
Issue number1-3
Publication statusPublished - Jun 1 1996

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Physical and Theoretical Chemistry
  • Electrical and Electronic Engineering

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