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Title: Continuous-mode multiphoton filtering
Authors: Song, HT
Zhang, GF 
Xi, ZR
Keywords: Multiphoton states
Open quantum systems
Quantum filtering
Issue Date: 2016
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on control and optimization, 2016, v. 54, no. 3, p. 1602-1632 How to cite?
Journal: SIAM journal on control and optimization 
Abstract: 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.
ISSN: 0363-0129
EISSN: 1095-7138
DOI: 10.1137/15M1023099
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