Continuous-mode single-photon states : characterization, pulse-shaping and filtering

Abstract

This thesis is devoted to studying the statistical properties and quantum filtering of continuous-mode single-photon Fock states. Four topics are under consideration: 1.Wigner spectrum of continuous-mode single-photon Fock states. 2.Coherent feedback control of continuous-mode single-photon Fock states. 3.Quantum filtering for multiple measurements of quantum systems driven by fields in continuous-mode single-photon Fock states. 4.Quantum filtering for multiple measurements of quantum systems driven by two continuous-mode single-photon Fock states. For the first topic, we propose to use Wigner spectrum to analyze continuous-mode single-photon Fock states. Normal ordering (Wick order) is commonly used in the analysis of quantum correlations. Unfortunately, it can only give partial information for correlation analysis. For example, for a continuous-mode single-photon Fock state (whose correlation function consists of two parts, one due to quantum vacuum noise and the other due to photon pulse shape), the normal ordering analysis simply ignores the contribution from the quantum vacuum noise. In this topic, we show Wigner spectrum is able to provide complete quantum correlation in time and frequency domains simultaneously. We demonstrate the effectiveness of the method by means of two examples, namely, optical cavity (a passive system) and degenerate parametric amplifier (DPA, a non-passive system). Numerical simulations show that Wigner spectra are able to reveal the clear difference between the output states of these two systems driven by the same single-photon state. For the second topic, we show how various control methods can be used to manipulate the pulse shapes of continuous-mode single-photon Fock states. More specifically, we illustrate that two control methods, direct coupling and coherent feedback control, can be used for pulse-shaping of continuous-mode single-photon Fock states. The effect of control techniques on pulse-shaping is visualized by the Wigner spectrum of the output single-photon states. It can be easily seen that the linear quantum feedback network has much more influence on the detection probability of a single-photon than the directly coupled system. In addition, for a simple quantum feedback network, the changes of the output Wigner spectrum with respect to beamsplitter parameter also have been analyzed. For the third topic, we extend the existing single-photon filtering framework by taking into account imperfect measurements. The master equations and stochastic master equations for quantum systems driven by a single-photon input state are given explicitly. More specifically, we study the case when the output light field is contaminated by a vacuum noise. We show how to design filters based on multiple measurements to achieve desired estimation performance. Two scenarios are studied: 1) homodyne plus homodyne detection, and 2) homodyne plus photon-counting detection. A numerical study of a two-level system driven by a single-photon state demonstrates the advantage of filtering design based on multiple measurement when the output filed is contaminated by quantum vacuum noise. For the fourth topic, the problem of quantum filtering with two homodyne detection measurements for a two-level system is considered. The quantum system is driven by two input light field channels, each of which contains a single photon. A quantum filter based on multiple measurements is designed; both the master equations and stochastic master equations are derived. In addition, numerical simulations for master equations with various pulse shape parameters are compared. It seems that the maximum of excitation probability can be achieved when the two photons have the same peak arrival time and the same ratio of bandwidth to the decay rate of the two-level system.