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Protected quantum correlations in multiple non-Markovian system-reservoir dynamics

Oliver Kaestle, Regina Finsterhoelzl, Andreas Knorr, Alexander Carmele

Published Nov 10, 2020• 1 citation
OpenAlex

Abstract

Based on tensor network realizations of path integrals reducing exponential memory scaling to polynomial efficiency, we investigate a quantum system simultaneously exposed to two structured reservoirs. For this purpose, we employ a quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian dynamical interplay between discrete photonic feedback and structured acoustic phonon modes, resulting in long-living population trapping within an initially-excited two-level system and allowing for an interfering memory-induced stable dissipative structure.

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Based on tensor network realizations of path integrals reducing exponential memory scaling to polynomial efficiency, we investigate a quantum system simultaneously exposed to two structured reservoirs. For this purpose, we employ a quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian dynamical interplay between discrete photonic feedback and structured acoustic phonon modes, resulting in long-living population trapping within an initially-excited two-level system and allowing for an interfering memory-induced stable dissipative structure.
Theoretical investigations of open quantum systems have uncovered a wide variety of unique dynamical phenomena. For instance, current research in quantum information technology aims to control and utilize time-delayed system-reservoir interactions and phonon-induced dynamical dissipative processes for the design of novel chip-integrated quantum optical devices. This thesis develops and advances multiple theoretical approaches for the accurate and efficient description of open quantum systems, where a high degree of information compression is essential to extract crucial information from the open system degrees of freedom which scale exponentially with the system size. The presented methods range from correlation expansions to second-order perturbative master equations, real-time path integral formulations, numerical realizations of high-dimensional tensor networks and, based on the most recent theoretical developments, machine learning implementations in the form of artificial neural networks. We explore all of these techniques with respect to their compression efficiency, performance and representational limits by applying them to a variety of physical setups and scenarios. Firstly, emerging non-Markovian memory effects in open quantum systems are investigated, e.g., resulting from interactions with a structured phonon environment or time-discrete coherent quantum feedback, leading to information exchange and a time-delayed dynamical interplay between system and reservoir. Examined systems range from solid state p-wave topological superconductors coupled to a structured phonon environment, where a memory-induced stabilization and recovery of topological properties is observed, to semiconductor quantum dot nanostructures exhibiting complete population inversion and unidirectional quantum transport as a result of dissipation-induced non-Markovian system-reservoir interactions, and quantum emitters simultaneously subjected to coherent quantum feedback and a decoherence-inducing structured phonon reservoir, leading to the formation of dynamical dissipative structures and population trapping. Secondly, novel machine learning techniques based on artificial neural networks are investigated, enabling simulations of symmetric open quantum spin-1/2 systems with Markovian dynamics. Combining their potential for parallelization and efficient Hilbert space truncation, they facilitate unmatched degrees of information compression and numerical performance for large systems. In this thesis, we expand the representational limits of the restricted Boltzmann machine neural network architecture by developing novel hybrid sampling strategies for a highly customizable compression of configuration space, rendering accurate and efficient simulations of asymmetric systems feasible. Finally, the applicability of the neural network is extended beyond pure spin-1/2 systems by introducing a neural bit encoding scheme for Fock number states, facilitating high performing calculations of large hybrid open quantum systems with bosonic degrees of freedom.
Quantum collision models are receiving increasing attention as they describe many nontrivial phenomena in the dynamics of open quantum systems. In a general scenario of both fundamental and practical interest, a quantum system repeatedly interacts with individual particles or modes, forming a correlated and structured reservoir; however, classical and quantum environment correlations greatly complicate the calculation and interpretation of the system dynamics. Here, we propose an exact solution to this problem based on the tensor network formalism. We find a natural Markovian embedding for the system dynamics, where the role of an auxiliary system is played by virtual indices of the network. The constructed embedding is amenable to an analytical treatment for a number of timely problems such as the system interaction with two-photon wave packets, structured photonic states, and one-dimensional spin chains. We also derive a time-convolution master equation and relate its memory kernel with the environment correlation function, thus revealing a clear physical picture of memory effects in the dynamics. The results advance tensor-network methods in the fields of quantum optics and quantum transport.
We study the population and disentanglement dynamics of two identical quantum dots placed inside the structured electromagnetic reservoir of a photonic crystal and coupled to an independent bath of thermal phonons. A formalism based on the method of generalized-Laplace transforms is developed to study the population and disentanglement dynamics. The effect of resonant dipole dipole interaction between the two quantum dots on the population dynamics in the presence of phonons and shows that the two two-level atoms can have a residual population at long times in the structured reservoir of a photonic crystal due to the formation of a photon-atom bound state. The disentanglement dynamics of the two quantum dots (assumed to be initially entangled) is studied using concurrence as a measure and is computed from the reduced two two-level system density matrix using the method of generalized-Laplace transforms. We show that partial disentanglement results from the interaction of the two quantum dots with the electromagnetic and phonon reservoirs. However, substantial entanglement is preserved in the fractionalized steady state formed if the transition frequency of two the quantum dots lies in the vicinity of the photonic band edge. We also discuss in detail the role of acoustic phonons on the population and disentanglement dynamics and the long time residual entanglement.
When a quantum system interacts with multiple reservoirs, the environmental effects are usually treated in an additive manner. We show that this assumption breaks down for non-Markovian environments that have finite memory times. Specifically, we demonstrate that quantum interferences between independent environments can qualitatively modify the dynamics of the physical system. We illustrate this effect with a two-level system coupled to two structured photonic reservoirs, discuss its origin using a nonequilibrium diagrammatic technique, and show an example when the application of this interference can result in an improved dark state preparation in a $\ensuremath{\Lambda}$ system.
We propose a general approach of protecting a two-level system against decoherence via quantum engineering of non-classical multiple superpositions of coherent states in a non-Markovian reservoir. The scheme surprisingly only uses the system-environment interaction responsible for the decoherence and projective measurements of the two-level system. We demonstrate the method on the example of an excitonic qubit in self-assembled semiconductor quantum dots coupled to the super-Ohmic reservoir of acoustic phonons.