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Exact analysis of quantum filter for systems driven by two counter-propagating single-photon states

Zhiyuan Dong, Guofeng Zhang, Nina H. Amini

Published Jul 1, 2017• 0 citations
Publisher

Abstract

In this paper, quantum filtering for a two-level atom, which is illuminated by two counter-propagating single-photon pulses, has been considered. The scenario is equivalent to that the two-level atom is driven by two input light field channels, each of which contains a single-photon. Based on two homodyne detection measurements, filtering equations in the Schrödinger picture have been derived explicitly.

DOI
10.1016/j.ifacol.2017.08.1950

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In this paper, quantum filtering for a two-level atom, which is illuminated by two counter-propagating single-photon pulses, has been considered. The scenario is equivalent to that the two-level atom is driven by two input light field channels, each of which contains a single-photon. Based on two homodyne detection measurements, filtering equations in the Schrödinger picture have been derived explicitly.
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The purpose of this paper is to derive filters for an arbitrary open quantum system driven by a light wavepacket prepared in a continuous-mode multi-photon state. A continuous-mode multi-photon state is a state of a travelling light wavepacket that contains a definite number of photons and is characterised 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 photodetection. 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 multi-photon 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 \cite{gough:2013} for the study of the single-photon filtering problem. However, the multi-photon 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, multi-photon filters can reveal interesting strong nonlinear optical phenomena absent in both the single-photon state case and the continuous-mode Fock state case.
The problem of photon-photon interaction controlled by a two-level system is studied in this paper. Specifically, we have proposed two scenarios: Case 1, how a two-level system changes the pulse shapes of two initially uncorrelated input photons in a single input channel; and Case 2, how a two-level system entangles two counter-propagating photons, one in each input channel. The steady-state output field states for both cases are derived explicitly. For Case 1, the Wigner spectrum is used to exhibit the interesting properties of the output field state. For Case 2, the nonlinear property of the interaction between the two-level system and the two input photons has been revealed by the probabilities of observing photons in the output channels. In addition, two-photon interference, similar to Hong-Ou-Mandel effect, occurs when the two input photons are chosen with the same pulse shape.