5,049 research outputs found
Mixed quantum-classical linear systems synthesis and quantum feedback control designs
This thesis makes some theoretical contributions towards mixed quantum feedback network synthesis, quantum optical realization of classical linear stochastic systems and quantum feedback control designs. A mixed quantum-classical feedback network is an interconnected system consisting of a quantum system and a classical system connected by interfaces that convert quantum signals to classical signal (using homodyne detectors), and vice versa (using electro-optic modulators). In the area of mixed quantum-classical feedback networks, we present a network synthesis theory, which provides a natural framework for analysis and design for mixed linear systems. Physical realizability conditions are derived for linear stochastic differential equations to ensure that mixed systems can correspond to physical systems. The mixed network synthesis theory developed based on physical realizability conditions shows that how a classical of mixed quantum-classical systems described by linear stochastic differential equations can be built as a interconnection of linear quantum systems and linear classical systems using quantum optical devices as well as electrical and electric devices. However, an important practical problem for the implementation of mixed quantum-classical systems is the relatively slow speed of classical parts implemented with standard electrical and electronic devices, since a mixed system will not work correctly unless the electronic processing of classical devices is fast enough. Therefore, another interesting work is to show how classical linear stochastic systems build using electrical and electric devices can be physically implemented using quantum optical components. A complete procedure is proposed for a stable quantum linear stochastic system realizing a given stable classical linear stochastic system. The thesis explains how it may be possible to realize certain measurement feedback loops fully at the quantum level. In the area of quantum feedback control design, two numerical procedures based on extended linear matrix inequality (LMI) approach are proposed to design a coherent quantum controller in this thesis. The extended synthesis linear matrix inequalities are, in addition to new analysis tools, less conservative in comparison to the conventional counterparts since the optimization variables related to the system parameters in extended LMIs are independent of the symmetric Lyapunov matrix. These features may be useful in the optimal design of quantum optical networks. Time delays are frequently encountered in linear quantum feedback control systems such as long transmission lines between quantum plants and linear controllers, which may have an effect on the performance of closed-loop plant controller systems. Therefore, this thesis investigates the problem of linear quantum measurement-based feedback control systems subject to feedback-loop time delay described by linear stochastic differential equations. Several numerical procedures are proposed to design classical controllers that make quantum measurement-based feedback control systems with time delay stable and also guarantee that their desired control performance specifications are satisfied
The SLH framework for modeling quantum input-output networks
Many emerging quantum technologies demand precise engineering and control
over networks consisting of quantum mechanical degrees of freedom connected by
propagating electromagnetic fields, or quantum input-output networks. Here we
review recent progress in theory and experiment related to such quantum
input-output networks, with a focus on the SLH framework, a powerful modeling
framework for networked quantum systems that is naturally endowed with
properties such as modularity and hierarchy. We begin by explaining the
physical approximations required to represent any individual node of a network,
eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum
fields by an operator triple . Then we explain how these nodes can be
composed into a network with arbitrary connectivity, including coherent
feedback channels, using algebraic rules, and how to derive the dynamics of
network components and output fields. The second part of the review discusses
several extensions to the basic SLH framework that expand its modeling
capabilities, and the prospects for modeling integrated implementations of
quantum input-output networks. In addition to summarizing major results and
recent literature, we discuss the potential applications and limitations of the
SLH framework and quantum input-output networks, with the intention of
providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving
correction
Bayesian feedback versus Markovian feedback in a two-level atom
We compare two different approaches to the control of the dynamics of a
continuously monitored open quantum system. The first is Markovian feedback as
introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. {\bf 70},
548 (1993)]. The second is feedback based on an estimate of the system state,
developed recently by Doherty {\em et al.} [Phys. Rev. A {\bf 62}, 012105
(2000)]. Here we choose to call it, for brevity, {\em Bayesian feedback}. For
systems with nonlinear dynamics, we expect these two methods of feedback
control to give markedly different results. The simplest possible nonlinear
system is a driven and damped two-level atom, so we choose this as our model
system. The monitoring is taken to be homodyne detection of the atomic
fluorescence, and the control is by modulating the driving. The aim of the
feedback in both cases is to stabilize the internal state of the atom as close
as possible to an arbitrarily chosen pure state, in the presence of inefficient
detection and other forms of decoherence. Our results (obtain without recourse
to stochastic simulations) prove that Bayesian feedback is never inferior, and
is usually superior, to Markovian feedback. However it would be far more
difficult to implement than Markovian feedback and it loses its superiority
when obvious simplifying approximations are made. It is thus not clear which
form of feedback would be better in the face of inevitable experimental
imperfections.Comment: 10 pages, including 3 figure
Effects of time delay in feedback control of linear quantum systems
We investigate feedback control of linear quantum systems subject to
feedback-loop time delays. In particular, we examine the relation between the
potentially achievable control performance and the time delays, and provide
theoretical guidelines for the future experimental setup in two physical
systems, which are typical in this research field. The evaluation criterion for
the analysis is given by the optimal control performance formula, the
derivation of which is from the classical control theoretic results about the
input-output delay systems.Comment: 6 pages, 4 figure
Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control
In this paper we investigate parametrization-free solutions of the problem of
quantum pure state preparation and subspace stabilization by means of
Hamiltonian control, continuous measurement and quantum feedback, in the
presence of a Markovian environment. In particular, we show that whenever
suitable dissipative effects are induced either by the unmonitored environment
or by non Hermitian measurements, there is no need for feedback control to
accomplish the task. Constructive necessary and sufficient conditions on the
form of the open-loop controller can be provided in this case. When open-loop
control is not sufficient, filtering-based feedback control laws steering the
evolution towards a target pure state are provided, which generalize those
available in the literature
- …