arXiv subjects

M. R. James

Publications and source records attributed to M. R. James.

30 records · Page 2Linked to original sources

arXiv2009

Homodyne locking of a squeezer

We report on the successful implementation of a new approach to locking the frequencies of an OPO-based squeezed-vacuum source and its driving laser. The technique allows the simultaneous measurement of the phase-shifts induced by a cavity, which may be used for the purposes of frequency-locking, as well as the simultaneous measurement of the sub-quantum-noise-limited (sub-QNL) phase quadrature output of the OPO. The homodyne locking technique is cheap, easy to implement and has the distinct advantage that subsequent homodyne measurements are automatically phase-locked. The homodyne locking technique is also unique in that it is a sub-QNL frequency discriminator.

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arXiv2009

Squeezing Components in Linear Quantum Feedback Networks

The aim of this paper is to extend linear quantum dynamical network theory to include static Bogoliubov components (such as squeezers). Within this integrated quantum network theory we provide general methods for cascade or series connections, as well as feedback interconnections using linear fractional transformations. In addition, we define input-output maps and transfer functions for representing components and describing convergence. We also discuss the underlying group structure in this theory arising from series interconnection. Several examples illustrate the theory.

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arXiv2009

Coherent quantum LQG control

Based on a recently developed notion of physical realizability for quantum linear stochastic systems, we formulate a quantum LQG optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum. Such a control scheme is often referred to in the quantum control literature as "coherent feedback control.'' It distinguishes the present work from previous works on the quantum LQG problem where measurement is performed on the plant and the measurement signals are used as input to a fully classical controller with no quantum degrees of freedom. The difference in our formulation is the presence of additional non-linear and linear constraints on the coefficients of the sought after controller, rendering the problem as a type of constrained controller design problem. Due to the presence of these constraints our problem is inherently computationally hard and this also distinguishes it in an important way from the standard LQG problem. We propose a numerical procedure for solving this problem based on an alternating projections algorithm and, as initial demonstration of the feasibility of this approach, we provide fully quantum controller design examples in which numerical solutions to the problem were successfully obtained. For comparison, we also consider the case of classical linear controllers that use direct or indirect measurements, and show that there exists a fully quantum linear controller which offers an improvement in performance over the classical ones.

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arXiv2009

The Series Product and Its Application to Quantum Feedforward and Feedback Networks

The purpose of this paper is to present simple and general algebraic methods for describing series connections in quantum networks. These methods build on and generalize existing methods for series (or cascade) connections by allowing for more general interfaces, and by introducing an efficient algebraic tool, the series product. We also introduce another product, which we call the concatenation product, that is useful for assembling and representing systems without necessarily having connections. We show how the concatenation and series products can be used to describe feedforward and feedback networks. A selection of examples from the quantum control literature are analyzed to illustrate the utility of our network modeling methodology.

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arXiv2008

Quantum Feedback Networks: Hamiltonian Formulation

A quantum network is an open system consisting of several component Markovian input-output subsystems interconnected by boson field channels carrying quantum stochastic signals. Generalizing the work of Chebotarev and Gregoratti, we formulate the model description by prescribing a candidate Hamiltonian for the network including details the component systems, the field channels, their interconnections, interactions and any time delays arising from the geometry of the network. (We show that the candidate is a symmetric operator and proceed modulo the proof of self-adjointness.) The model is non-Markovian for finite time delays, but in the limit where these delays vanish we recover a Markov model and thereby deduce the rules for introducing feedback into arbitrary quantum networks. The type of feedback considered includes that mediated by the use of beam splitters. We are therefore able to give a system-theoretic approach to introducing connections between quantum mechanical state-based input-output systems, and give a unifying treatment using non-commutative fractional linear, or Mobius, transformations.

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arXiv2008

Guaranteed Cost LQG Control of Uncertain Linear Quantum Stochastic Systems

In this paper, we formulate and solve a guaranteed cost control problem for a class of uncertain linear stochastic quantum systems. For these quantum systems, a connection with an associated classical (non-quantum) system is first established. Using this connection, the desired guaranteed cost results are established. The theory presented is illustrated using an example from quantum optics.

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arXiv2007

H-Infinity Control of Linear Quantum Stochastic Systems

The purpose of this paper is to formulate and solve a H-infinity controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H-infinity control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller.

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arXiv2007

Effects of Measurement back-action in the stabilization of a Bose-Einstein condensate through feedback

We apply quantum filtering and control to a particle in a harmonic trap under continuous position measurement, and show that a simple static feedback law can be used to cool the system. The final steady state is Gaussian and dependent on the feedback strength and coupling between the system and probe. In the limit of weak coupling this final state becomes the ground state. An earlier model by Haine et. al. (PRA 69, 2004) without measurement back-action showed dark states: states that did not display error signals, thus remaining unaffected by the control. This paper shows that for a realistic measurement process this is not true, which indicates that a Bose-Einstein condensate may be driven towards the ground state from any arbitrary initial state.

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arXiv2006

Stability, Gain, and Robustness in Quantum Feedback Networks

This paper concerns the problem of stability for quantum feedback networks. We demonstrate in the context of quantum optics how stability of quantum feedback networks can be guaranteed using only simple gain inequalities for network components and algebraic relationships determined by the network. Quantum feedback networks are shown to be stable if the loop gain is less than one-this is an extension of the famous small gain theorem of classical control theory. We illustrate the simplicity and power of the small gain approach with applications to important problems of robust stability and robust stabilization.

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arXiv2005

A Quantum Langevin Formulation of Risk-Sensitive Optimal Control

In this paper we formulate a risk-sensitive optimal control problem for continuously monitored open quantum systems modelled by quantum Langevin equations. The optimal controller is expressed in terms of a modified conditional state, which we call a risk-sensitive state, that represents measurement knowledge tempered by the control purpose. One of the two components of the optimal controller is dynamic, a filter that computes the risk-sensitive state. The second component is an optimal control feedback function that is found by solving the dynamic programming equation. The optimal controller can be implemented using classical electronics. The ideas are illustrated using an example of feedback control of a two-level atom.

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arXiv2004

Pathwise Solution of a Class of Stochastic Master Equations

In this paper we consider an alternative formulation of a class of stochastic wave and master equations with scalar noise that are used in quantum optics for modelling open systems and continuously monitored systems. The reformulation is obtained by applying J.M.C. Clark's pathwise reformulation technique from the theory of classical nonlinear filtering. The pathwise versions of the stochastic wave and master equations are defined for all driving paths and depend continuously on them. In the case of white noise equations, we derive analogs of Clark's robust approximations. The results in this paper may be useful for implementing filters for the continuous monitoring and measurement feedback control of quantum systems, and for developing new types of numerical methods for unravelling master equations. The main ideas are illustrated by an example.

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arXiv2003

Risk-Sensitive Optimal Control of Quantum Systems

The importance of feedback control is being increasingly appreciated in quantum physics and applications. This paper describes the use of optimal control methods in the design of quantum feedback control systems, and in particular the paper formulates and solves a risk-sensitive optimal control problem. The resulting risk-sensitive optimal control is given in terms of a new unnormalized conditional state, whose dynamics include the cost function used to specify the performance objective. The risk-sensitive conditional dynamic equation describes the evolution of our {\em knowledge} of the quantum system tempered by our {\em purpose} for the controlled quantum system. Robustness properties of risk-sensitive controllers are discussed, and an example is provided.

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