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arXiv:1902.10961

Control of continuous-mode single-photon states: a review

Guofeng Zhang

Published Feb 28, 2019• 0 citations
arXivHTMLPDF

Abstract

In this survey, we first introduce quantum fields and open quantum systems, then we present continuous-mode single-photon states and discuss discrete measurements of a single-photon field. After that, we introduce linear quantum systems and show how a linear quantum system responds to a single-photon input. Then we investigate how a coherent feedback network can be used to manipulate the temporal pulse shape of a single-photon state. Afterwards, we present single-photon filter and master equations. Finally, we discuss the generation of Schrödinger cat states by means of photon addition and subtraction

DOI
10.48550/arxiv.1902.10961

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In this survey, we first introduce quantum fields and open quantum systems, then we present continuous-mode single-photon states and discuss discrete measurements of a single-photon field. After that, we introduce linear quantum systems and show how a linear quantum system responds to a single-photon input. Then we investigate how a coherent feedback network can be used to manipulate the temporal pulse shape of a single-photon state. Afterwards, we present single-photon filter and master equations. Finally, we discuss the generation of Schrödinger cat states by means of photon addition and subtraction
The aim of this paper is to determine quantum master and filter equations for systems coupled to continuous-mode single photon fields. The system and field are described using a quantum stochastic unitary model, where the continuous-mode single photon state for the field is determined by a wavepacket pulse shape. The master equation is derived from this model and is given in terms of a system of coupled equations. The output field carries information about the system from the scattered photon, and is continuously monitored. The quantum filter is determined with the aid of an embedding of the system into a larger system, and is given by a system of coupled stochastic differential equations. An example is provided to illustrate the main results.
Abstract Single photons are very useful resources in quantum information science. In real applications it is often required that the photons have a well-defined spectral (or equivalently temporal) modal structure. For example, a rising exponential pulse is able to fully excite a two-level atom while a Gaussian pulse cannot. This motivates the study of continuous-mode single-photon Fock states. Such states are characterized by a spectral (or temporal) pulse shape. In this paper we investigate the statistical property of continuous-mode single-photon Fock states. Instead of the commonly used normal ordering (Wick order), the tool we proposed is the Wigner spectrum. The Wigner spectrum has two advantages: (1) it allows to study continuous-mode single-photon Fock states in the time domain and frequency domain simultaneously; (2) because it can deal with the Dirac delta function directly, it has the potential to provide more information than the normal ordering where the Dirac delta function is always discarded. We also show how various control methods in particular coherent feedback control can be used to manipulate the pulse shapes of continuous-mode single-photon Fock states.
Abstract — The aim of this paper is to determine quantum master and filter equations for systems coupled to continuous-mode single photon fields. The system and field are de-scribed using a quantum stochastic unitary model, where the continuous-mode single photon state for the field is determined by a wavepacket pulse shape. The master equation is derived from this model and is given in terms of a system of coupled equations. The output field carries information about the system from the scattered photon, and is continuously monitored. The quantum filter is determined with the aid of an embedding of the system into a larger system, and is given by a system of coupled stochastic differential equations. An example is provided to illustrate the main results. I.
The purpose of this tutorial is to give a brief introduction to linear quantum control systems. The mathematical model of linear quantum control systems is presented first, then some fundamental control-theoretic notions such as stability, controllability and observability are given, which are closely related to several important concepts in quantum information science such as decoherence-free subsystems, quantum non-demolition variables, and back-action evasion measurements. After that, quantum Gaussian states are introduced, in particular, an information-theoretic uncertainty relation is presented which often gives a better bound for mixed Gaussian states than the well-known Heisenberg uncertainty relation. The quantum Kalman filter is presented for quantum linear systems, which is the quantum analogy of the Kalman filter for classical (namely, non-quantum-mechanical) linear systems. The quantum Kalman canonical decomposition for quantum linear systems is recorded, and its application is illustrated by means of a recent experiment. As single- and multi-photon states are useful resources in quantum information technology, the response of quantum linear systems to these types of input is presented. Finally, coherent feedback control of quantum linear systems is briefly introduced, and a recent experiment is used to demonstrate the effectiveness of quantum linear systems and networks theory.