Continuous-mode multiphoton filtering

H. T. Song, Guofeng Zhang, Z. R. Xi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

31 Citations (Scopus)


The purpose of this paper is to derive filters for an arbitrary open quantum system driven by a light wave packet prepared in a continuous-mode multiphoton state. A continuous-mode multiphoton state is a state of a traveling light wave packet that contains a definite number of photons and is characterized by a temporal (or, equivalently, spectral) profile. After the interaction with the system, the outgoing light can be monitored by means of homodyne detection or photo-detection. Filters for both measurement schemes are derived in this paper. Unlike the vacuum or the coherent state case, the annihilation operator of the light field acting on a multiphoton state changes the state by annihilating a photon, and this makes the traditional filtering techniques inapplicable. To circumvent this difficulty, we adopt a non-Markovian embedding technique proposed in [J. E. Gough, M. R. James, and H. I. Nurdin, Quantum Inf. Process., 12 (2013), pp. 1469-1499] for the study of the single-photon filtering problem. However, the multiphoton nature of the problem addressed in this paper makes the study much more mathematically involved. Moreover, as demonstrated by an example -a two-level system driven by a continuous-mode two-photon state -multiphoton filters can reveal interesting strong nonlinear optical phenomena absent in both the single-photon state case and the continuous-mode Fock state case.
Original languageEnglish
Pages (from-to)1602-1632
Number of pages31
JournalSIAM Journal on Control and Optimization
Issue number3
Publication statusPublished - 1 Jan 2016


  • Multiphoton states
  • Open quantum systems
  • Quantum filtering

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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