Universität zu Köln

Javed, Mohammad Atif ORCID: 0000-0003-0868-0218 (2025). Using exceptional points and non Hermitian topology to study fractional charges and apparent event horizons in superconducting circuits. PhD thesis, Universität zu Köln.

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Abstract

Conventional superconductors are one of the most well known example of macroscopic quantum phenomena, therefore superconducting circuits have emerged as a promising platform for qubits, quantum information processing and simulating light-matter interactions. The endeavor of simulating exotic physics on superconducting circuits is also accompanied with search of new circuit elements, apart from already existing elements such as capacitors, inductors and Josephson junctions, that can help in reproducing these novel phenomena experimentally. In this thesis we discuss three different projects that are unified by presence of exceptional points and non-Hermitian topology, that touch on one or both of these aspects of superconducting circuits. In the first project we study a system with both supercurrents and lossy currents in order to unify the two distinct ways of detecting fractional charges. We find that charge quantization is here a conserved property of the detector basis of the Lindbladian, while charge fractionalization is a topological property of its complex-valued eigenspectrum. We show that already conventional superconductor-normal metal hybrid circuits exhibit a variety of topological phases, including an open quantum system version of a fractional Josephson effect, due to the presence of exceptional points in its spectrum. In the second project we study topology of a dissipative system, that can mimic some essential features of an Andreev bound state spectrum of a multi-terminal Josephson junction. We find that this system indeed has topological properties that are encoded in an open system version of Chern number. We also find the full counting statistics for this toy model and conclude that this Chern number is not measurable via any regular transport experiment. Finally in the third project we show how superconducting circuit hardware can implement a variety of classical and quantum spacetime geometries on lattices, by both using established circuit elements and introducing new ones. We demonstrate the possibility of a metric sharply changing within a single lattice point, thus entering a regime where the modulation of system parameters is (in a sense) trans-Planckian, and the Hawking temperature ill-defined. In fact, our approach suggests that stable, thermal event horizons are incompatible with strictly discrete lattice models. Contrary to regular Hawking radiation (nonzero boson occupation number), the instability manifests as an accumulation of charge and phase quantum fluctuations over short time scales- a robust signature even in the presence of an environment. Moreover, we present a loop-hole for the typical black/white hole ambiguity in lattice simulations: exceptional points in the dispersion relation allows for the creation of pure black (or white) hole horizons, at the expense of radically changing the interior wormhole dynamics.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Javed, Mohammad Atif mjaved1@smail.uni-koeln.de orcid.org/0000-0003-0868-0218 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-780930
Date:	19 May 2025
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Außeruniversitäre Forschungseinrichtungen > Forschungszentrum Jülich
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language Superconducting circuits, circuit QED, fractional charges, exceptional points, non-Hermitian physics, open quantum systems, non-Hermitian topology, Josephson junctions, weak measurement, tenfold way, analog event horizons, bosonic Bogoliubov transformations, negative inductance English
Date of oral exam:	14 March 2025
Referee:	Name Academic Title Riwar, Roman-Pascal Dr. Diehl, Sebastian Prof.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/78093