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Asian Control Conference (ASCC)

A root locus approach to constructing Markovian coupled oscillators to capture the dynamics of a non-Markovian quantum system

Shi-Bei Xue, Ian R. Petersen

Published May 1, 2015• 2 citations
Publisher

Abstract

This paper shows that a principal oscillator in a pair of Markovian coupled oscillators can be designed to capture the dynamics of a non-Markovian quantum system disturbed by Lorentzian noise. By using a Green's function based root locus approach, conditions for designing the Markovian coupled oscillators are obtained, with which the scaled system amplitude for the principal oscillator can capture that of the non-Markovian system.

DOI
10.1109/ascc.2015.7244447

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This paper shows that a principal oscillator in a pair of Markovian coupled oscillators can be designed to capture the dynamics of a non-Markovian quantum system disturbed by Lorentzian noise. By using a Green's function based root locus approach, conditions for designing the Markovian coupled oscillators are obtained, with which the scaled system amplitude for the principal oscillator can capture that of the non-Markovian system.
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In this paper we present a Markovian representation approach to constructing quantum filters for a class of non-Markovian quantum systems disturbed by Lorentzian noise. An ancillary system is introduced to convert white noise into Lorentzian noise which is injected into a principal system via a direct interaction. The resulting dynamics of the principal system are non-Markovian, which are driven by the Lorentzian noise. By probing the principal system, a quantum filter for the augmented system can be derived from standard theory, where the conditional state of the principal system can be obtained by tracing out the ancillary system.
In this paper, we propose a feedback tracking control scheme to reject Lorentzian noise in a linear non-Markovian quantum system. This non-Markovian quantum system is modelled as an augmented linear Markovian quantum system where a principal system represents the plant and an ancillary system represents the internal mode of the non-Markovian environment for generating Lorentzian noise. Based on this augmented system model, a whitening quantum filter can be constructed for continuously monitoring the dynamical variables of the principal system. To reject Lorentzian noise, a linear quadratic Gaussian (LQG) controller, using the estimate of the whitening filter and the dynamical variables of a reference system, can be designed to drive the principal system to track the reference system.
Abstract In this paper we present a non-Markovian coherent feedback scheme for decoherence suppression in single quantum dot systems. The feedback loop is closed via a quantum tunnelling junction between the natural source and drain baths of the quantum dot. The exact feedback-controlled non-Markovian Langevin equation is derived for describing the dynamics of the quantum dot. To deal with the nonlinear memory function in the Langevin equation, we analyse the Green’s function-based root locus, from which we show that the decoherence of the quantum dot can be suppressed via increasing the feedback coupling strength. The effectiveness of decoherence suppression induced by non-Markovian coherent feedback is demonstrated by a single quantum dot example bathed with Lorentzian noises.
In this paper, a quantum filter for estimating the states of a non-Markovian qubit system is presented in an augmented Markovian system framework including both the qubit system of interest and multi-ancillary systems for representing the internal modes of the non-Markovian environment. The colored noise generated by the multi-ancillary systems disturbs the qubit system via a direct interaction. The resulting non-Markovian dynamics of the qubit is determined by a memory kernel function arising from the dynamics of the ancillary system. In principle, colored noise with arbitrary power spectrum can be generated by a combination of Lorentzian noises. Hence, the quantum filter can be constructed for the qubit disturbed by arbitrary colored noise and the conditional state of the qubit system can be obtained by tracing out the multi-ancillary systems.
This brief presents an augmented Markovian system framework that can be applied to model non-Markovian quantum systems. In this augmented system model, ancillary systems are designed to play the role of internal modes of the non-Markovian environment converting white noise to colored noise. To capture the non-classical mutual influence between a quantum system and non-Markovian environments, direct interactions between a principal system and the ancillary system are introduced. Consequently, we showed that the augmented Markovian formulation can be used to theoretically model the environment for observed non-Markovian behavior in a recent experiment on quantum dots.