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arXiv:1703.08965 · Optical and Quantum Electronics

Theory of non-Markovian dynamics in resonance fluorescence spectrum

Abhishek Kumar

Published Aug 1, 2018• 1 citation
arXivHTMLPDF
DOI
10.1007/s11082-018-1582-1

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Robust quantum coherence is an important prerequisite for any system that may be used to perform quantum information processing tasks. For systems that can be probed optically, the fluorescence spectrum may provide indirect evidence of coherence times when supplemented with an appropriate model of the decay process. A common approach is to assume a Markovian system, resulting in exponential decay of correlation functions and Lorentzian features in the associated spectrum. For physical systems with strongly history-dependent (non-Markovian) dynamics, there is currently limited systematic theoretical approach to establish the associated spectrum. In this thesis, we present a detailed theoretical method to obtain the fluorescence spectrum for a general system undergoing non-Markovian dynamics. This procedure can be used to systematically account for features in fluorescence spectra due to genuine non-Markovian dynamics. We apply this method to study the non-Markovian behaviour in the side peak of the Mollow-triplet and absorption spectrum of coherent population trapping systems.

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The dissipative dynamics of a confined single exciton coupled to a reservoir is investigated beyond the Born‐Markov approximation. Specifically, the resonance fluorescence main features are studied as the coupling strength is varied with respect to the driving laser intensity. To the lowest order, the effective Hamiltonian is treated stochastically, from which an analytical solution of the fluorescence spectrum shows the basic features of a non‐Markovian noise induced dynamics. Finally, we discuss some aspects of higher‐order effects in the non‐Markovian system‐bath dynamics.
We derive a general formula for the non-Markovian fluorescence spectrum of a multi-level system interacting with a bosonic environment. To this end, we apply linear-response theory to describe the dynamics of a detector monitoring the emission spectrum of a general multi-level system. The resultant emission lineshape function is directly related to the two-time correlation of system observables, which we derive using Nakajima-Zwanzig Generalized Master Equation without assuming a Markov approximation.
Robust quantum coherence is an important prerequisite for any system that may be used to perform quantum information processing tasks. For systems that can be probed optically, the fluorescence spectrum may provide indirect evidence of coherence times when supplemented with an appropriate model of the decay process. A common approach is to assume a Markovian system, resulting in exponential decay of correlation functions and Lorentzian features in the associated spectrum. For physical systems with strongly history-dependent (non-Markovian) dynamics, there is currently limited systematic theoretical approach to establish the associated spectrum. In this thesis, we present a detailed theoretical method to obtain the fluorescence spectrum for a general system undergoing non-Markovian dynamics. This procedure can be used to systematically account for features in fluorescence spectra due to genuine non-Markovian dynamics. We apply this method to study the non-Markovian behaviour in the side peak of the Mollow-triplet and absorption spectrum of coherent population trapping systems.