% IMPORTANT: The following is UTF-8 encoded. This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.
@PHDTHESIS{Ulrich:684349,
author = {Ulrich, Jascha},
othercontributors = {Hassler, Fabian and Schoeller, Herbert},
title = {{L}arge impedances and {M}ajorana bound states in
superconducting circuits},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
reportid = {RWTH-2017-01921},
pages = {1 Online-Ressource (xiv, 173 Seiten) : Diagramme},
year = {2017},
note = {Auch veröffentlicht auf dem Publikationsserver der RWTH
Aachen University; Dissertation, RWTH Aachen University,
2017},
abstract = {Superconducting circuits offer the opportunity to study
quantum mechanics on mesoscopic scales unimpeded by
dissipation. This fact and the nonlinearity of the Josephson
inductance make it possible to use superconducting circuits
as artificial atoms whose long-lived states can be
selectively addressed and studied. A pronounced nonlinearity
of the energy spectrum, however, requires quantum
fluctuations of the flux across the Josephson junction which
are large on the scale of the superconducting flux quantum
$\Phi_Q = h/2e$. This implies charge fluctuations below the
single Cooper-pair limit via flux-charge duality. The
localization of charge leads to a strong susceptibility to
interactions with charges in the environment which has
motivated the search for schemes to decouple charges from
their environment. This thesis is concerned with theoretical
challenges arising from two complementary approaches to this
problem: the realization of large impedances and the
fractionalization of electrons by means of Majorana bound
states.In recent years, the decoupling of charges from the
environment through reactive large impedances, so-called
"superinductances" $L$, has attracted much interest. These
inductances feature small parasitic capacitance $C$ such
that the characteristic impedance $\sqrt{L/C}$ is much
larger than the superconducting resistance quantum $R_Q =
h/4e^2$. Superinductances have various applications ranging
from qubit designs such as the $0$-$\pi$ qubit or the
fluxonium to impedance matching, Bloch oscillations and the
stabilization of phase slips in superconducting nanowires.
Although there exists a well-established formalism for the
quantization of superconducting circuits in terms of node
fluxes, this formalism is ill-suited for the description of
fast flux transport with localized charges in
large-impedance environments. In particular, the nonlinear
capacitive behavior of phase slip junctions cannot be
modeled in a straightforward way using node fluxes. In view
of the ever growing interest in superinductances, in the
first part of the thesis, we present a recipe for
quantization of planar circuits in terms of loop charges. As
we will show, the loop charge approach is dual to the usual
node flux formalism and well-adapted to a large impedance
setting.In the second part of the thesis, we turn to a
complementary approach of charge decoupling by means of
Majorana bound states (MBS). MBS solve the decoupling
problem by encoding a fermionic mode nonlocally into two
bound states with large spatial separation such that a local
coupling to the stored charge is no longer possible. It has
been shown that despite the apparent nonlocality of the
fermionic mode, transport through the mode remains local
unless the MBS are coupled by a global perturbation like a
finite charging energy. Here we show that, even in absence
of charging energy, decoupling the superconductor from the
ground plane achieves subtle coupling of the MBS that leads
to nonlocal transport.Finally, in the last part of the
thesis, we turn to two mesoscopic applications related to
supersymmetric quantum mechanics. The simultaneous presence
of a fermionic mode due to the MBS and a bosonic mode due to
the Cooper-pair condensate makes systems involving MBS
appealing candidates for the realization of supersymmetric
quantum mechanics. For a Majorana Cooper-pair box, we
discuss an unusual "bosonic" supersymmetry and its
experimental signatures. Since MBS remain challenging to
realize experimentally, we show that a similar supersymmetry
can even be realized in a setup using standard
superconducting circuitry without MBS.},
cin = {137230 / 130000},
ddc = {530},
cid = {$I:(DE-82)137230_20140620$ / $I:(DE-82)130000_20140620$},
typ = {PUB:(DE-HGF)11},
urn = {urn:nbn:de:hbz:82-rwth-2017-019212},
doi = {10.18154/RWTH-2017-01921},
url = {https://publications.rwth-aachen.de/record/684349},
}
guest ::