39 research outputs found
Kitaev spin models from topological nanowire networks
We show that networks of topological nanowires can realize the physics of
exactly solvable Kitaev spin models with two-body interactions. This connection
arises from the description of the low-energy theory of both systems in terms
of a tight-binding model of Majorana modes. In Kitaev spin models the Majorana
description provides a convenient representation to solve the model, whereas in
an array of topological nanowires it arises, because the physical Majorana
modes localized at wire ends permit tunnelling between wire ends and across
different Josephson junctions. We explicitly show that an array of junctions of
three wires -- a setup relevant to topological quantum computing with nanowires
-- can realize the Yao-Kivelson model, a variant of Kitaev spin models on a
decorated honeycomb lattice. Translating the results from the latter, we show
that the network can be constructed to give rise to collective states
characterized by Chern numbers \nu = 0, +/-1 and +/-2, and that defects in an
array can be associated with vortex-like quasi-particle excitations. Finally,
we analyze the stability of the collective states as well as that of the
network as a quantum information processor. We show that decoherence inducing
instabilities, be them due to disorder or phase fluctuations, can be understood
in terms of proliferation of the vortex-like quasi-particles.Comment: 15 pages, 9 figure
Enhancing the effect of quantum many-body scars on dynamics by minimising the effective dimension
Quantum many-body scarring is believed to be the mechanism behind long-lived
coherent oscillations in interacting Rydberg atom chains. These persistent
oscillations are due to the large overlap of the many-body scars with certain
initial states. We show that the "effective dimension" is a useful measure for
identifying non-thermalising initial states in many-body scarred systems. By
minimising the effective dimension we find physically reasonable initial states
of the Rydberg chain that lead to more pronounced and longer lived
oscillations, accentuating the effect of the many-body scars on the dynamics.Comment: 6 pages (including references and appendix
Extreme many-body scarring in a quantum spin chain via weak dynamical constraints
It has recently been established that quantum many-body scarring can prevent
the thermalisation of some isolated quantum systems, starting from certain
initial states. One of the first models to show this was the so-called PXP
Hamiltonian, which was used to theoretically model an experiment on a chain of
strongly interacting Rydberg atoms. A defining feature of the PXP Hamiltonian
is a set of dynamical constraints that make certain states inaccessible to the
dynamics. In this paper we construct a class of spin chain models that are
parameterised by a discrete variable that controls the "strength" of a
dynamical constraint. We show that by increasing the constraint becomes
weaker, in the sense that fewer states are excluded from the dynamics. The PXP
Hamiltonian is special case for . By weakening the constraint to
, however, we find a more extreme version of quantum scarring than
in the PXP Hamiltonian, with the number of scar states growing exponentially in
the system size.Comment: 6 + 3 page
Enhanced zero-bias Majorana peak in disordered multi-subband quantum wires
A recent experiment [Mourik et al., Science 336, 1003 (2012)] on InSb quantum
wires provides possible evidence for the realization of a topological
superconducting phase and the formation of Majorana bound states. Motivated by
this experiment, we consider the signature of Majorana bound states in the
differential tunneling conductance of multi-subband wires. We show that the
weight of the Majorana-induced zero-bias peak is strongly enhanced by mixing of
subbands, when disorder is added to the end of the quantum wire. We also
consider how the topological phase transition is reflected in the gap structure
of the current-voltage characteristic.Comment: 4+ pages, 5 figures, minor changes in the text and Fig. 5, references
added; published versio
Low-energy subgap states in multichannel p-wave superconducting wires
One-dimensional p-wave superconductors are known to harbor Majorana bound
states at their ends. Superconducting wires with a finite width W may have
fermionic subgap states in addition to possible Majorana end states. While
they do not necessarily inhibit the use of Majorana end states for topological
computation, these subgap states can obscure the identification of a
topological phase through a density-of-states measurement. We present two
simple models to describe low-energy fermionic subgap states. If the wire's
width W is much smaller than the superconductor coherence length ξ, the
relevant subgap states are localized near the ends of the wire and cluster
near zero energy, whereas the lowest-energy subgap states are delocalized if
W≳ξ. Notably, the energy of the lowest-lying fermionic subgap state (if
present at all) has a maximum for W∼ξ
Impossible measurements revisited
It is by now well-recognised that the na\"ive application of the projection
postulate on composite quantum systems can induce signalling between their
constituent components, indicative of a breakdown of causality in a
relativistic spacetime context. Here we introduce a necessary and sufficient
condition for an ideal measurement of an observable to be non-signalling. As
well as being particularly simple, it generalises previous no-signalling
conditions in that it allows for degeneracies and can be applied to all bounded
self-adjoint operators. The condition is used to establish that arbitrary sums
of local observables will not signal, in accordance with our expectations from
relativistic quantum field theory. On the other hand, it is shown that the
measurement of the tensor product of commuting local observables, for example
bipartite operators of the form , can in fact signal, contrary to
the widely-held belief that such measurements are always locally realisable.
The implications for the notion of measurement in relativistic quantum field
theory are addressed; it appears that the most straightforward application of
the standard quantum formalism generically leads to violations of causality. We
conclude that either the class of observables that can be measured should be
restricted and/or that the na\"ive translation of the measurement framework of
quantum theory, in particular the projection postulate, to quantum field theory
should be re-evaluated