651 research outputs found
Multi-particle content of Majorana zero-modes in the interacting p-wave wire
In the topological phase of p-wave superconductors, zero-energy Majorana
quasi-particle excitations can be well-defined in the presence of local
density-density interactions. Here we examine this phenomenon from the
perspective of matrix representations of the commutator ,with the aim of characterising the multi-particle content of the
many-body Majorana mode. To do this we show that, for quadratic fermionic
systems, can always be decomposed into sub-blocks that act as
multi-particle generalisations of the BdG/Majorana forms that encode
single-particle excitations. In this picture, density-density like interactions
will break this exact excitation-number symmetry, coupling different sub-blocks
and lifting degeneracies so that the eigen-operators of the commutator
take the form of individual eigenstate transitions . However, the Majorana mode is special in that zero-energy
transitions are not destroyed by local interactions and it becomes possible to
define many-body Majoranas as the odd-parity zero-energy solutions of
that minimise their excitation number. This idea forms the basis
for an algorithm which is used to characterise the multi-particle excitation
content of the Majorana zero modes of the one-dimensional p-wave lattice model.
We find that the multi-particle content of the Majorana zero-mode operators is
significant even at modest interaction strengths. This has important
consequences for the stability of Majorana based qubits when they are coupled
to a heat bath. We will also discuss how these findings differ from previous
work regarding the structure of the many-body-Majorana operators and point out
that this should affect how certain experimental features are interpreted.Comment: 16 pages , 11 figure
Many-body Majorana operators and the equivalence of parity sectors
The one-dimensional p-wave topological superconductor model with
open-boundary conditions is examined in its topological phase. Using the
eigenbasis of the non-interacting system I show that, provided the interactions
are local and do not result in a closing of the gap, then even and odd parity
sectors are unitarily equivalent. Following on from this, it is possible to
define two many-body operators that connect each state in one sector with a
degenerate counterpart in the sector with opposite parity. This result applies
to all states in the system and therefore establishes, for a long enough wire,
that all even-odd eigenpairs remain essentially degenerate in the presence of
local interactions. Building on this observation I then set out a full
definition of the related many-body Majorana operators and point out that their
structure cannot be fully revealed using cross-correlation data obtained from
the ground state manifold alone. Although all results are formulated in the
context of the 1-dimensional p-wave model, I argue why they should also apply
to more realistic realisations (e.g. the multi-channel p-wave wire and
proximity coupled models) of topological superconductivity.Comment: 8 pages, 1 figur
Near-zero-energy end states in topologically trivial spin-orbit coupled superconducting nanowires with a smooth confinement
A one-dimensional spin-orbit coupled nanowire with proximity-induced pairing
from a nearby s-wave superconductor may be in a topological nontrivial state,
in which it has a zero energy Majorana bound state at each end. We find that
the topological trivial phase may have fermionic end states with an
exponentially small energy, if the confinement potential at the wire's ends is
smooth. The possible existence of such near-zero energy levels implies that the
mere observation of a zero-bias peak in the tunneling conductance is not an
exclusive signature of a topological superconducting phase even in the ideal
clean single channel limit.Comment: 4 pages, 4 figure
Extraction of energy from gravitational waves by laser interferometer detectors
In this paper we discuss the energy interaction between gravitational waves
and laser interferom- eter gravitational wave detectors. We show that the
widely held view that the laser interferometer gravitational wave detector
absorbs no energy from gravitational waves is only valid under the
approximation of a frequency-independent optomechanical coupling strength and a
pump laser without detuning with respect to the resonance of the
interferometer. For a strongly detuned interferometer, the optical-damping
dynamics dissipates gravitational wave energy through the interaction between
the test masses and the optical field. For a non-detuned interferometer, the
frequency-dependence of the optomechanical coupling strength causes a tiny
energy dissipation, which is proved to be equivalent to the Doppler friction
raised by Braginsky et.al.Comment: 20 pages, 7 figure
Topological Blocking in Quantum Quench Dynamics
We study the non-equilibrium dynamics of quenching through a quantum critical
point in topological systems, focusing on one of their defining features:
ground state degeneracies and associated topological sectors. We present the
notion of 'topological blocking', experienced by the dynamics due to a mismatch
in degeneracies between two phases and we argue that the dynamic evolution of
the quench depends strongly on the topological sector being probed. We
demonstrate this interplay between quench and topology in models stemming from
two extensively studied systems, the transverse Ising chain and the Kitaev
honeycomb model. Through non-local maps of each of these systems, we
effectively study spinless fermionic -wave paired superconductors. Confining
the systems to ring and toroidal geometries, respectively, enables us to
cleanly address degeneracies, subtle issues of fermion occupation and parity,
and mismatches between topological sectors. We show that various features of
the quench, which are related to Kibble-Zurek physics, are sensitive to the
topological sector being probed, in particular, the overlap between the
time-evolved initial ground state and an appropriate low-energy state of the
final Hamiltonian. While most of our study is confined to translationally
invariant systems, where momentum is a convenient quantum number, we briefly
consider the effect of disorder and illustrate how this can influence the
quench in a qualitatively different way depending on the topological sector
considered.Comment: 18 pages, 11 figure
Zero energy and chiral edge modes in a p-wave magnetic spin model
In this work we discuss the formation of zero energy vortex and chiral edge modes in a fermionic representation
of the Kitaev honeycomb model. We introduce the representation and show how the associated
Jordan-Wigner procedure naturally defines the so-called branch cuts that connect the topological vortex excitations.
Using this notion of the branch cuts we show how to, in the non-Abelian phase of the model, describe
the Majorana zero mode structure associated with vortex excitations. Furthermore we show how, by intersecting
the edges between Abelian and non-Abelian domains, the branch cuts dictate the character of the chiral
edge modes. In particular we will see in what situations the exact zero energy Majorana edge modes exist. On
a cylinder, and for the particular instances where the Abelian phase of the model is the full vacuum, we have
been able to exactly solve for the systems edge energy eigensolutions and derive a recursive formula that
exactly describes the edge mode structure. Penetration depth is also calculated and shown to be dependent on
the momentum of the edge mode. These solutions also describe the overall character of the fully open non-
Abelian domain and are excellent approximations at moderate distances from the corners
Exact results for the star lattice chiral spin liquid
We examine the star lattice Kitaev model whose ground state is a a chiral
spin liquid. We fermionize the model such that the fermionic vacua are toric
code states on an effective Kagome lattice. This implies that the Abelian phase
of the system is inherited from the fermionic vacua and that time reversal
symmetry is spontaneously broken at the level of the vacuum. In terms of these
fermions we derive the Bloch-matrix Hamiltonians for the vortex free sector and
its time reversed counterpart and illuminate the relationships between the
sectors. The phase diagram for the model is shown to be a sphere in the space
of coupling parameters around the triangles of the lattices. The abelian phase
lies inside the sphere and the critical boundary between topologically distinct
Abelian and non-Abelian phases lies on the surface. Outside the sphere the
system is generically gapped except in the planes where the coupling parameters
are zero. These cases correspond to bipartite lattice structures and the
dispersion relations are similar to that of the original Kitaev honeycomb
model. In a further analysis we demonstrate the three-fold non-Abelian
groundstate degeneracy on a torus by explicit calculation.Comment: 7 pages, 8 figure
Model of Thermal Wavefront Distortion in Interferometric Gravitational-Wave Detectors I: Thermal Focusing
We develop a steady-state analytical and numerical model of the optical
response of power-recycled Fabry-Perot Michelson laser gravitational-wave
detectors to thermal focusing in optical substrates. We assume that the thermal
distortions are small enough that we can represent the unperturbed intracavity
field anywhere in the detector as a linear combination of basis functions
related to the eigenmodes of one of the Fabry-Perot arm cavities, and we take
great care to preserve numerically the nearly ideal longitudinal phase
resonance conditions that would otherwise be provided by an external
servo-locking control system. We have included the effects of nonlinear thermal
focusing due to power absorption in both the substrates and coatings of the
mirrors and beamsplitter, the effects of a finite mismatch between the
curvatures of the laser wavefront and the mirror surface, and the diffraction
by the mirror aperture at each instance of reflection and transmission. We
demonstrate a detailed numerical example of this model using the MATLAB program
Melody for the initial LIGO detector in the Hermite-Gauss basis, and compare
the resulting computations of intracavity fields in two special cases with
those of a fast Fourier transform field propagation model. Additional
systematic perturbations (e.g., mirror tilt, thermoelastic surface
deformations, and other optical imperfections) can be included easily by
incorporating the appropriate operators into the transfer matrices describing
reflection and transmission for the mirrors and beamsplitter.Comment: 24 pages, 22 figures. Submitted to JOSA
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