1,156 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
On the role of electron-phonon interaction in the resistance anisotropy of two-dimensional electrons in GaAs heterostructures
A contribution of the electron-phonon interaction into the energy of a
unidirectional charge ordered state (stripe phase) of two-dimensional electrons
in GaAs heterostructures is analyzed. The dependence of the energy on the
direction of the electron density modulation is calculated. It is shown that in
electrons layers situated close to the (001) surface the interference between
the piezoelectric and the deformation potential interaction causes a
preferential orientation of the stripes along the [110] axis.Comment: 9 pages, accepted for publication in Journal of Physics: Condensed
Matte
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
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
Coulomb drag in high Landau levels
Recent experiments on Coulomb drag in the quantum Hall regime have yielded a
number of surprises. The most striking observations are that the Coulomb drag
can become negative in high Landau levels and that its temperature dependence
is non-monotonous. We develop a systematic diagrammatic theory of Coulomb drag
in strong magnetic fields explaining these puzzling experiments. The theory is
applicable both in the diffusive and the ballistic regimes; we focus on the
experimentally relevant ballistic regime (interlayer distance smaller than
the cyclotron radius ). It is shown that the drag at strong magnetic
fields is an interplay of two contributions arising from different sources of
particle-hole asymmetry, namely the curvature of the zero-field electron
dispersion and the particle-hole asymmetry associated with Landau quantization.
The former contribution is positive and governs the high-temperature increase
in the drag resistivity. On the other hand, the latter one, which is dominant
at low , has an oscillatory sign (depending on the difference in filling
factors of the two layers) and gives rise to a sharp peak in the temperature
dependence at of the order of the Landau level width.Comment: 26 pages, 13 figure
Level Statistics and Localization for Two Interacting Particles in a Random Potential
We consider two particles with a local interaction in a random potential
at a scale (the one particle localization length). A simplified
description is provided by a Gaussian matrix ensemble with a preferential
basis. We define the symmetry breaking parameter
associated to the statistical invariance under change of basis. We show that
the Wigner-Dyson rigidity of the energy levels is maintained up to an energy
. We find that when (the
inverse lifetime of the states of the preferential basis) is smaller than
(the level spacing), and when . This implies that the two-particle localization length first
increases as before eventually behaving as .Comment: 4 pages REVTEX, 4 Figures EPS, UUENCODE
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
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.
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
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
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