30 research outputs found
Fractional charges in conventional sequential electron tunneling
The notion of fractional charges was up until now reserved for quasiparticle
excitations emerging in strongly correlated quantum systems, such as Laughlin
states in the fractional quantum Hall effect, Luttinger quasiparticles, or
parafermions. Here, we consider topological transitions in the full counting
statistics of standard sequential electron tunneling, and find that they lead
to the same type of charge fractionalization - strikingly without requiring
exotic quantum correlations. This conclusion relies on the realization that
fundamental integer charge quantization fixes the global properties of the
transport statistics whereas fractional charges can only be well-defined
locally. We then show that the reconciliation of these two contradicting
notions results in a nontrivially quantized geometric phase defined in the
detector space. In doing so, we show that detector degrees of freedom can be
used to describe topological transitions in nonequilibrium open quantum
systems. Moreover, the quantized geometric phase reveals a profound analogy
between the fractional charge effect in sequential tunneling and fractional
Josephson effect in topological superconducting junctions, where likewise the
Majorana- or parafermions exhibit a charge which is at odds with the Cooper
pair charge as the underlying unit of the supercurrent. In order to provide
means for an experimental verification of our claims, we demonstrate the
fractional nature of transport statistics at the example of highly feasible
transport models, such as weakly tunnel-coupled quantum dots or charge islands.
We then show that the geometric phase can be accessed through the detector's
waiting time distribution. Finally, we find that topological transitions in the
transport statistics could even lead to new applications, such as the
unexpected possibility to directly measure features beyond the resolution limit
of a detector.Comment: 28 pages, 10 figures; Supplemental Material linked under ancillary
file
Charge quantization and detector resolution
Charge quantization, or the absence thereof, is a central theme in quantum
circuit theory, with dramatic consequences for the predicted circuit dynamics.
Very recently, the question of whether or not charge should actually be
described as quantized has enjoyed renewed widespread interest, with however
seemingly contradictory propositions. Here, we intend to reconcile these
different approaches, by arguing that ultimately, charge quantization is not an
intrinsic system property, but instead depends on the spatial resolution of the
charge detector. We show that the latter can be directly probed by unique
geometric signatures in the correlations of the supercurrent. We illustrate
these findings at the example Josephson junction arrays in the superinductor
regime, where the transported charge appears to be continuous. Finally, we
comment on potential consequences of charge quantization beyond superconducting
circuits.Comment: 26 pages, 3 figure
Zero-frequency noise in adiabatically driven, interacting quantum systems
We investigate current-current correlations of adiabatic charge pumping
through interacting quantum dots weakly coupled to reservoirs. To calculate the
zero-frequency noise for a time-dependently driven system, possibly in the
presence of an additional dc bias, we perform within a real-time diagrammatic
approach a perturbative expansion in the tunnel coupling to the reservoirs in
leading and next-to-leading order. We apply this formalism to study the
adiabatic correction to the zero-frequency noise, i.e., the pumping noise, in
the case of a single-level quantum dot charge pump. If no stationary bias is
applied, the adiabatic correction shows Coulomb-interaction-induced deviations
from the fluctuation-dissipation theorem. Furthermore, we show that the
adiabatic correction to the Fano factor carries information about the coupling
asymmetry and is independent of the choice of the pumping parameters. When
including a time-dependent finite bias, we find that there can be pumping noise
even if there is zero adiabatically pumped charge. The pumping noise also
indicates the respective direction of the bias-induced current and the pumping
current
Compact description of quantum phase slip junctions
Quantum circuit theory is a powerful and ever-evolving tool to predict the
dynamics of superconducting circuits. In its language, quantum phase slips
(QPSs) are famously considered to be the exact dual to the Josephson effect.
However, this duality renders the integration of QPS junctions into a unified
theoretical framework very difficult, and as we show, gives rise to serious
inconsistencies for different formalisms, and in some cases difficulties to
include time-dependent flux driving. We propose to resolve these issues by
reducing and compactifying the Hilbert space describing the QPS processes. Our
treatment provides for the first time a unified description of the
Aharonov-Bohm and Aharonov-Casher effects, properly defines the valid form of
inductive interactions to an environment, and allows to account for recent
insights on how to include electromotive forces. Finally, we show that the
compactification is likewise important for correctly predicting the available
computational space for qubit architectures involving QPS junctions.Comment: 25 pages, 7 figures, supplementary. Revisions in main text and
supplementar
Transport fluctuation relations in interacting quantum pumps
The understanding of out-of-equilibrium fluctuation relations in small open
quantum systems has been a focal point of research in recent years. In
particular, for systems with adiabatic time-dependent driving, it was shown
that the fluctuation relations known from stationary systems do no longer apply
due the geometric nature of the pumping current response. However, the precise
physical interpretation of the corrected pumping fluctuation relations as well
as the role of many-body interactions remained unexplored. Here, we study
quantum systems with many-body interactions subject to slow time-dependent
driving, and show that fluctuation relations of the charge current can in
general not be formulated without taking into account the total energy current
put into the system through the pumping process. Moreover, we show that this
correction due to the input energy is nonzero only when Coulomb-interactions
are present. Thus, fluctuation response relations offer an until now unrevealed
opportunity to probe many-body correlations in quantum systems. We demonstrate
our general findings at the concrete example of a single-level quantum dot
model, and propose a scheme to measure the interaction-induced discrepancies
from the stationary case.Comment: 13 pages, 2 figure
Readout of relaxation rates by nonadiabatic pumping spectroscopy
We put forward nonadiabatic charge pumping as a method for accessing the
different charge relaxation rates as well as the relaxation rates of excited
orbital states in double-quantum-dot setups, based on extremely size-limited
quantum dots and dopant systems. The rates are obtained in a well-separated
manner from plateaus, occurring when comparing the steady-state current for
reversed driving cycles. This yields a reliable readout independent of any
fitting parameters. Importantly, the nonadiabatic pumping spectroscopy
essentially exploits the same driving scheme as the operation of these devices
generally employs. We provide a detailed analysis of the working principle of
the readout scheme as well as of possible errors, thereby demonstrating its
broad applicability. The precise knowledge of relaxation rates is highly
relevant for the implementation of time-dependently operated devices, such as
electron pumps for metrology or qubits in quantum information.Comment: 14 pages, 5 figure
Circuit quantization with time-dependent magnetic fields for realistic geometries
Quantum circuit theory has become a powerful and indispensable tool to
predict the dynamics of superconducting circuits. Surprisingly however, the
question of how to properly account for a time-dependent driving via external
magnetic fields has hardly been addressed so far. Here, we derive a general
recipe to construct a low-energy Hamiltonian, taking as input only the circuit
geometry and the solution of the external magnetic fields. A gauge fixing
procedure for the scalar and vector potentials is given which assures that
time-varying magnetic fluxes make contributions only to the potential function
in the Schr\"odinger equation. Our proposed procedure is valid for continuum
geometries and thus significantly generalizes previous efforts, which were
based on discrete circuits. We study some implications of our results for the
concrete example of a parallel-plate SQUID circuit. We show that if we insist
on representing the response of this SQUID with individual, discrete
capacitances associated with each individual Josephson junction, this is only
possible if we permit the individual capacitance values to be negative,
time-dependent or even momentarily singular. Finally, we provide some
experimentally testable predictions, such as a strong enhancement of the qubit
relaxation rates arising from the effective negative capacitances, and the
emergence of a Berry phase due to time dependence of these capacitances.Comment: 17 pages, 4 figure
Control of Andreev bound state population and related charge-imbalance effect
Motivated by recent experimental research, we study the processes in an ac
driven superconducting constriction whereby one quasiparticle is promoted to
the delocalized states outside the superconducting gap. We demonstrate that
with these processes one can control the population of the Andreev bound states
in the constriction. We stress an interesting charge asymmetry of these
processes that may produce a charge imbalance of accumulated quasiparticles,
which depends on the phase
Electromotive force in driven topological quantum circuits
Time-dependent control of superconducting quantum circuits is a prerequisite
for building scalable quantum hardware. The quantum description of these
circuits is complicated due to the electromotive force (emf) induced by
time-varying magnetic fields. Here, we examine how the emf modifies the
fractional Josephson effect. We show that a time-varying flux introduces a new
term that depends on the geometry of both the circuit and the applied magnetic
field. This term can be probed via current and charge measurements in
closed-loop and open-circuit geometries. Our results refine the current
understanding of how to properly describe time-dependent control of topological
quantum circuits.Comment: 13 pages, 5 figures; added appendix C, added acknowledgments,
improved overall flow, results and figures unchange