Related papers: Filtering and Control in Quantum Optics
A precise time-dependent control of a quantum system relies on an accurate account of the quantum interference among the system, the control and the environment. A diagrammatic technique has been recently developed to precisely calculate…
This is a pre-publication version of a forthcoming book on quantum atom optics. It is written as a senior undergraduate to junior graduate level textbook, assuming knowledge of basic quantum mechanics, and covers the basic principles of…
We start with a discussion of the use of mathematics to model the real world then justify the role of Hilbert space formalism for such modelling in the general context of quantum logic. Following this, the incompleteness of the…
We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove…
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes,…
We numerically study a particle in a box with moving walls. In the case where the walls are oscillating sinusoidally with small amplitude, we show that states up to the fourth state can be populated with more than 80 percent population,…
Using results from quantum filtering theory and methods from classical control theory, we derive an optimal control strategy for an open two-level system (a qubit in interaction with the electromagnetic field) controlled by a laser. The aim…
We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems…
Robust control of quantum systems is an increasingly relevant field of study amidst the second quantum revolution, but there remains a gap between taming quantum physics and robust control in its modern analytical form that culminated in…
In this thesis we consider primarily the dynamics of quantum systems subjected to continuous observation. In the Schr\"{o}dinger picture the evolution of a continuously monitored quantum system, referred to as a `quantum trajectory', may be…
This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter…
The aim of this paper is to provide a short introduction to modern issues in the control of infinite dimensional closed quantum systems, driven by the bilinear Schr\"odinger equation. The first part is a quick presentation of some of the…
This thesis consists of four parts. In the first part it is shown that optimal universal cloning of photons can be realized with the help of stimulated emission. Possible schemes based on three-level systems and on parametric…
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…
We present new results on the quantum control of systems with infinitely large Hilbert spaces. A control-theoretic analysis of the control of trapped ion quantum states via optical pulses is performed. We demonstrate how resonant…
The work is dedicated to the challenge: control and manipulation of the quantum state of a remote physical object. The goal is approached via the entanglement channel between the object and a local physical system - actuator - subjected to…
We study the dynamics of the two-level atomic systems (qubits) under a double-layer environment that is consisted of a network of single-mode cavities coupled to a common reservoir. A general exact master equation for the dynamics can be…
The main aim of the paper is to present the analytical solution of the Belavkin quantum filtering equation for damped harmonic oscillator being initially in the squeezed coherent state for diffusion observation with complex white noise. The…
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…
A stochastic model for a continuous photon counting and heterodyne measurement of a coherent source is proposed. A nonlinear filtering equation for the posterior state of a single-mode field in a cavity is derived by using the methods of…