Entanglement Generation in Non-Markovian
Waveguide Quantum Electrodynamics
vorgelegt von
M. Sc.
Kisa Henriette Barkemeyer
an der Fakultät II - Mathematik und Naturwissenschaften
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften
—Dr. rer. nat.—
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. Janik Wolters
Gutachter: Prof. Dr. Andreas Knorr
Gutachter: Prof. Dr. Scott Parkins
Tag der wissenschaftlichen Aussprache: 06. April 2022
Berlin 2022
[N]ature isn’t classical, dammit, and if you want to make a simulation of nature, you’d
better make it quantum mechanical, and by golly it’s a wonderful problem, because it
doesn’t look so easy.
— Richard Feynman
Abstract
Large-scale quantum networks in which quantum information is transferred between flying and
stationary qubits play a central role in quantum information processing and communication. A
promising platform for their implementation is waveguide quantum electrodynamics (WQED).
In such setups, non-negligible delay times offer the possibility to control the system dynamics.
From a theorist’s point of view, however, they present a difficulty since they require a description
beyond the Markov approximation. In this thesis, we explore characteristic features of WQED
systems with feedback focussing on the generation of entanglement in different realms.
The first part of the thesis is concerned with multiphoton pulses in WQED systems with feedback,
the inclusion of which is essential to account for the transmission of quantum information. For
the simulation of the dynamics, we employ two different methods complementing each other.
The first is based on the matrix product state (MPS) framework and allows for the inclusion
of multiple photons due to the efficient handling of the entanglement in the system. In the
fundamental setup of a two-level emitter coupled to a semi-infinite waveguide, a bound state
exists in the continuum of propagating modes. Our simulations show that in the highly non-
Markovian regime of long delay times, the excitation of the bound state by multiphoton pulses via
stimulated emission can be significantly more efficient than its excitation via the spontaneous
decay of an initially excited emitter. The second method is a Heisenberg-operator approach,
where the arising hierarchy of multi-time correlations is unraveled by introducing a Hilbert space
unity. The method allows for the straightforward inclusion of arbitrary pulse shapes and makes
the microscopic dynamics accessible so that additional dissipation channels can be included.
This way, we are able to examine the complex interplay of the pulse shape and the feedback
delay time, as well as the influence of a phenomenological pure dephasing rendering the bound
state unattainable. Proceeding toward more complex multi-emitter networks, we study the
entanglement of two macroscopically separated emitters coupled to an infinite waveguide with
MPS. Investigating different excitation schemes, we find that, by addressing the bound state in
the system, it is possible to generate stable and controllable long-range entanglement.
The second part of the thesis deals with photon pairs entangled in different degrees of free-
dom and possibilities to control their entanglement. The energy-time entanglement of a pair
of photons emitted from a ladder-type three-level system can be detected in a Franson-type
interferometer via an interference in the second-order coherence function. The visibility of this
interference depends crucially on the decay rates of the emitter. Simulating the time evolution
within the MPS framework, we show that the implementation of an additional feedback channel
allows controlling the decay process. As a consequence, the visibility can be increased for a wide
range of parameters. Furthermore, the polarization entanglement of a pair of photons emitted
from a biexciton cascade in a semiconductor quantum dot exhibiting an excitonic spin precession
is investigated. We model the precession as a coherent process and, after the verification of
the model using experimental data, find that it affects the entanglement in the same way as a
finite fine-structure splitting. Thus, the precession is detrimental in a time-integrated measure-
ment setup, while, for a time-resolved measurement, a high degree of entanglement is attainable
nevertheless.
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