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arXiv:2003.13357

Non-Markovian resonance fluorescence

Abhishek Kumar

Published Mar 30, 2020• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2003.13357

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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.
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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.
We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting continuous-time dynamics is an integro-differential equation that augments the Gorini-Kossakowski-Sudarshan-Lindblad equation with a memory integral, and is capable of describing the quantum state of systems exposed to noise with any integrable power spectral density with no further approximations. We then establish a formalism to evaluate multi-time correlations of measurement outcomes in this general setting, obviating the need for a regression theorem. As an application, we derive the emission spectrum of a driven two-level system coupled to a non-Markovian bath: the familiar Mollow triplet acquires a frequency-dependent linewidth that encodes the memory of the bath. Our work provides a rigorous yet transparent description of the quantum state of non-Markovian systems, opening the door for state estimation and state-based quantum control beyond the Markovian regime.