25 research outputs found
Dephasing and leakage dynamics of noisy Majorana-based qubits: Topological versus Andreev
Topological quantum computation encodes quantum information nonlocally by nucleating non-Abelian anyons separated by distances L, typically spanning the qubit device size. This nonlocality renders topological qubits exponentially immune to dephasing from all sources of classical noise with operator support local on the scale of L. We perform detailed analytical and numerical analyses of a time-domain Ramsey-type protocol for noisy Majorana-based qubits that is designed to validate this coveted topological protection in near-term devices such as the so-called “tetron” design. By assessing dependence of dephasing times on tunable parameters, e.g., magnetic field, our proposed protocol can clearly distinguish a bona fide Majorana qubit from one constructed from semilocal Andreev bound states, which can otherwise closely mimic the true topological scenario in local probes. In addition, we analyze leakage of the qubit out of its low-energy manifold due to classical-noise-induced generation of quasiparticle excitations; leakage limits the qubit lifetime when the bulk gap collapses, and hence our protocol further reveals the onset of a topological phase transition. This experiment requires measurement of two nearby Majorana modes for both initialization and readout—achievable, for example, by tunnel coupling to a nearby quantum dot—but no further Majorana manipulations, and thus constitutes an enticing prebraiding experiment. Along the way, we address conceptual subtleties encountered when discussing dephasing and leakage in the context of Majorana qubits
Vibrational absorption sidebands in the Coulomb blockade regime of single-molecule transistors
Current-driven vibrational non-equilibrium induces vibrational sidebands in
single-molecule transistors which arise from tunneling processes accompanied by
absorption of vibrational quanta. Unlike conventional sidebands, these
absorption sidebands occur in a regime where the current is nominally Coulomb
blockaded. Here, we develop a detailed and analytical theory of absorption
sidebands, including current-voltage characteristics as well as shot noise. We
discuss the relation of our predictions to recent experiments.Comment: 7 pages, 6 figures; revised discussion of relation to experimen
Scattering theory of current-induced forces in mesoscopic systems
We develop a scattering theory of current-induced forces exerted by the
conduction electrons of a general mesoscopic conductor on slow "mechanical"
degrees of freedom. Our theory describes the current-induced forces both in and
out of equilibrium in terms of the scattering matrix of the phase-coherent
conductor. Under general nonequilibrium conditions, the resulting mechanical
Langevin dynamics is subject to both non-conservative and velocity-dependent
Lorentz-like forces, in addition to (possibly negative) friction. We illustrate
our results with a two-mode model inspired by hydrogen molecules in a break
junction which exhibits limit-cycle dynamics of the mechanical modes.Comment: 4+ pages, 1 figure; v2: minor modification
General Localization Lengths for Two Interacting Particles in a Disordered Chain
The propagation of an interacting particle pair in a disordered chain is
characterized by a set of localization lengths which we define. The
localization lengths are computed by a new decimation algorithm and provide a
more comprehensive picture of the two-particle propagation. We find that the
interaction delocalizes predominantly the center-of-mass motion of the pair and
use our approach to propose a consistent interpretation of the discrepancies
between previous numerical results.Comment: 4 pages, 2 epsi figure
Theory of the Franck-Condon blockade regime
Strong coupling of electronic and vibrational degrees of freedom entails a
low-bias suppression of the current through single-molecule devices, termed
Franck-Condon blockade. In the limit of slow vibrational relaxation, transport
in the Franck-Condon-blockade regime proceeds via avalanches of large numbers
of electrons, which are interrupted by long waiting times without electron
transfer. The avalanches consist of smaller avalanches, leading to a
self-similar hierarchy which terminates once the number of transferred
electrons per avalanche becomes of the order of unity. Experimental signatures
of self-similar avalanche transport are strongly enhanced current (shot) noise,
as expressed by giant Fano factors, and a power-law noise spectrum. We develop
a theory of the Franck-Condon-blockade regime with particular emphasis on
effects of electron cotunneling through highly excited vibrational states. As
opposed to the exponential suppression of sequential tunneling rates for
low-lying vibrational states, cotunneling rates suffer only a power-law
suppression. This leads to a regime where cotunneling dominates the current for
any gate voltage. Including cotunneling within a rate-equation approach to
transport, we find that both the Franck-Condon blockade and self-similar
avalanche transport remain intact in this regime. We predict that cotunneling
leads to absorption-induced vibrational sidebands in the Coulomb-blockaded
regime as well as intrinsic telegraph noise near the charge degeneracy point.Comment: 20 pages, 10 figures; minor changes, version published in Phys. Rev.
Probability distribution of Majorana end-state energies in disordered wires
One-dimensional topological superconductors harbor Majorana bound states at
their ends. For superconducting wires of finite length L, these Majorana states
combine into fermionic excitations with an energy that is
exponentially small in L. Weak disorder leaves the energy splitting
exponentially small, but affects its typical value and causes large
sample-to-sample fluctuations. We show that the probability distribution of
is log normal in the limit of large L, whereas the distribution of
the lowest-lying bulk energy level has an algebraic tail at small
. Our findings have implications for the speed at which a
topological quantum computer can be operated.Comment: 4 pages, 2 figure
Thermopower of Single-Molecule Devices
We investigate the thermopower of single molecules weakly coupled to metallic
leads. We model the molecule in terms of the relevant electronic orbitals
coupled to phonons corresponding to both internal vibrations and to
oscillations of the molecule as a whole. The thermopower is computed by means
of rate equations including both sequential-tunneling and cotunneling
processes. Under certain conditions, the thermopower allows one to access the
electronic and phononic excitation spectrum of the molecule in a
linear-response measurement. In particular, we find that the phonon features
are more pronounced for weak lead-molecule coupling. This way of measuring the
excitation spectrum is less invasive than the more conventional current-voltage
characteristic, which, by contrast, probes the system far from equilibrium.Comment: 13 pages, 7 figures included; minor changes, version published in PR
Flexural phonons in free-standing graphene
Rotation and reflection symmetries impose that out-of-plane (flexural)
phonons of free-standing graphene membranes have a quadratic dispersion at long
wavelength and can be excited by charge carriers in pairs only. As a result, we
find that flexural phonons dominate the phonon contribution to the resistivity
below a crossover temperature T_x where we obtain an anomalous
temperature dependence . The logarithmic factor
arises from renormalizations of the flexural phonon dispersion due to coupling
between bending and stretching degrees of freedom of the membrane.Comment: 4 pages, 2 figure
Interaction-Induced Magnetization of the Two-Dimensional Electron Gas
We consider the contribution of electron-electron interactions to the orbital
magnetization of a two-dimensional electron gas, focusing on the ballistic
limit in the regime of negligible Landau-level spacing. This regime can be
described by combining diagrammatic perturbation theory with semiclassical
techniques. At sufficiently low temperatures, the interaction-induced
magnetization overwhelms the Landau and Pauli contributions. Curiously, the
interaction-induced magnetization is third-order in the (renormalized) Coulomb
interaction. We give a simple interpretation of this effect in terms of
classical paths using a renormalization argument: a polygon must have at least
three sides in order to enclose area. To leading order in the renormalized
interaction, the renormalization argument gives exactly the same result as the
full treatment.Comment: 11 pages including 4 ps figures; uses revtex and epsf.st
Interaction-induced delocalization of two particles in a random potential: Scaling properties
The localization length for coherent propagation of two interacting
particles in a random potential is studied using a novel and efficient
numerical method. We find that the enhancement of over the one-particle
localization length satisfies the scaling relation
, where is the interaction strength and
the level spacing of a wire of length . The scaling
function is linear over the investigated parameter range. This implies that
increases faster with than previously predicted. We also study a
novel mapping of the problem to a banded-random-matrix model.Comment: 5 pages and two figures in a uuencoded, compressed tar file; uses
revtex and psfig.sty (included); substantial revision of a previous version
of the paper including newly discovered scaling behavio