14,217 research outputs found
Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems
The purpose of this paper is to study and design direct and indirect
couplings for use in coherent feedback control of a class of linear quantum
stochastic systems. A general physical model for a nominal linear quantum
system coupled directly and indirectly to external systems is presented.
Fundamental properties of stability, dissipation, passivity, and gain for this
class of linear quantum models are presented and characterized using complex
Lyapunov equations and linear matrix inequalities (LMIs). Coherent
and LQG synthesis methods are extended to accommodate direct couplings using
multistep optimization. Examples are given to illustrate the results.Comment: 33 pages, 7 figures; accepted for publication in IEEE Transactions on
Automatic Control, October 201
Zero-dynamics principle for perfect quantum memory in linear networks
In this paper, we study a general linear networked system that contains a
tunable memory subsystem; that is, it is decoupled from an optical field for
state transportation during the storage process, while it couples to the field
during the writing or reading process. The input is given by a single photon
state or a coherent state in a pulsed light field. We then completely and
explicitly characterize the condition required on the pulse shape achieving the
perfect state transfer from the light field to the memory subsystem. The key
idea to obtain this result is the use of zero-dynamics principle, which in our
case means that, for perfect state transfer, the output field during the
writing process must be a vacuum. A useful interpretation of the result in
terms of the transfer function is also given. Moreover, a four-nodes network
composed of atomic ensembles is studied as an example, demonstrating how the
input field state is transferred to the memory subsystem and how the input
pulse shape to be engineered for perfect memory looks like.Comment: 31 pages, 5 figure
A Popov Stability Condition for Uncertain Linear Quantum Systems
This paper considers a Popov type approach to the problem of robust stability
for a class of uncertain linear quantum systems subject to unknown
perturbations in the system Hamiltonian. A general stability result is given
for a general class of perturbations to the system Hamiltonian. Then, the
special case of a nominal linear quantum system is considered with quadratic
perturbations to the system Hamiltonian. In this case, a robust stability
condition is given in terms of a frequency domain condition which is of the
same form as the standard Popov stability condition.Comment: A shortened version to appear in the proceedings of the 2013 American
Control Conferenc
Ground-state Stabilization of Open Quantum Systems by Dissipation
Control by dissipation, or environment engineering, constitutes an important
methodology within quantum coherent control which was proposed to improve the
robustness and scalability of quantum control systems. The system-environment
coupling, often considered to be detrimental to quantum coherence, also
provides the means to steer the system to desired states. This paper aims to
develop the theory for engineering of the dissipation, based on a ground-state
Lyapunov stability analysis of open quantum systems via a Heisenberg-picture
approach. Algebraic conditions concerning the ground-state stability and
scalability of quantum systems are obtained. In particular, Lyapunov stability
conditions expressed as operator inequalities allow a purely algebraic
treatment of the environment engineering problem, which facilitates the
integration of quantum components into a large-scale quantum system and draws
an explicit connection to the classical theory of vector Lyapunov functions and
decomposition-aggregation methods for control of complex systems. The
implications of the results in relation to dissipative quantum computing and
state engineering are also discussed in this paper.Comment: 18 pages, to appear in Automatic
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