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Australian Control Conference

Exploring frequency-domain characteristics of Markovian and non-Markovian quantum dynamics

Shi-Bei Xue, Re-Bing Wu, TZYH JONG TARN, Ian R. Petersen

Published Nov 1, 2014• 1 citation
Publisher

Abstract

This paper presents a Green's function based root locus method to investigate the frequency-domain characteristics of Markovian and non-Markovian open quantum systems. A Langevin equation for the system is derived, where we show the structure of the Green's function dominates the system dynamics. In addition, by increasing the coupling between the system and its environment, variations in the modes of the Green's function are explored in the frequency domain, where both the critical transition from Markovian to non-Markovian dynamics and a critical point condition under Lorentzian noise are graphically presented using a root locus method. Related results are verified using an example of a boson-boson coupling system.

DOI
10.1109/aucc.2014.7358646

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This paper presents a Green's function based root locus method to investigate the frequency-domain characteristics of Markovian and non-Markovian open quantum systems. A Langevin equation for the system is derived, where we show the structure of the Green's function dominates the system dynamics. In addition, by increasing the coupling between the system and its environment, variations in the modes of the Green's function are explored in the frequency domain, where both the critical transition from Markovian to non-Markovian dynamics and a critical point condition under Lorentzian noise are graphically presented using a root locus method. Related results are verified using an example of a boson-boson coupling system.
This paper presents a non-Markovian coherent feedback control scheme for stabilizing a single quantum dot system. The feedback loop is closed via quantum tunneling process between the natural source and drain baths of the quantum dot. The exact feedback-controlled non-Markovian Langevin equation is derived to describe the dynamics of the quantum dot. Since the memory function in the Langevin equation is a nonlinear function of the feedback coupling strength, a method named root locus of the Green's function is presented to analyze the non-Markovian dynamics in the frequency domain. This method graphically reveals the mechanism of decoherence suppression induced by non-Markovian coherent feedback, which is verified by an example of single quantum dot systems.
We present a general theory of non-Markovian dynamics for open systems of noninteracting fermions (bosons) linearly coupled to thermal environments of noninteracting fermions (bosons). We explore the non-Markovian dynamics by connecting the exact master equations with the nonequilibirum Green's functions. Environmental backactions are fully taken into account. The non-Markovian dynamics consists of nonexponential decays and dissipationless oscillations. Nonexponential decays are induced by the discontinuity in the imaginary part of the self-energy corrections. Dissipationless oscillations arise from band gaps or the finite band structure of spectral densities. The exact analytic solutions for various non-Markovian thermal environments show that non-Markovian dynamics can be largely understood from the environmental-modified spectra of open systems.
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.
The Born-Markov approximation is widely used to study the dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to a noninteracting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has nonanalyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power-law tails. The Green's functions show a short-time ``quasi''-Markovian exponential decay before crossing over to a power-law tail governed by the nonanalyticity of the spectral function. We study a system of bosons (fermions) hopping on a one-dimensional lattice, where each site is coupled linearly to an independent bath of noninteracting bosons (fermions). We obtain exact expressions for the Green's functions of this system, which show power-law decay $\ensuremath{\sim}|t\ensuremath{-}{t}^{\ensuremath{'}}{|}^{\ensuremath{-}3/2}$. We use these to calculate the density and current profile, as well as unequal-time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long-time power-law tails $|t\ensuremath{-}{t}^{\ensuremath{'}}{|}^{\ensuremath{-}3}$ characteristic of non-Markovian dynamics. We show that the power-law decays survive in the presence of interparticle interaction in the system, but the crossover time scale is shifted to larger values with increasing interaction strength.