13 research outputs found
Higher index focus-focus singularities in the Jayne-Cummings-Gaudin model : symplectic invariants and monodromy
We study the symplectic geometry of the Jaynes-Cummings-Gaudin model with
spins. We show that there are focus-focus singularities of maximal
Williamson type . We construct the linearized normal flows in the
vicinity of such a point and show that soliton type solutions extend them
globally on the critical torus. This allows us to compute the leading term in
the Taylor expansion of the symplectic invariants and the monodromy associated
to this singularity.Comment: 39 page
Voltage-Current curves for small Josephson junction arrays
We compute the current voltage characteristic of a chain of identical
Josephson circuits characterized by a large ratio of Josephson to charging
energy that are envisioned as the implementation of topologically protected
qubits. We show that in the limit of small coupling to the environment it
exhibits a non-monotonous behavior with a maximum voltage followed by a
parametrically large region where . We argue that its
experimental measurement provides a direct probe of the amplitude of the
quantum transitions in constituting Josephson circuits and thus allows their
full characterization.Comment: 12 pages, 4 figure
Density response and collective modes of semi-holographic non-Fermi liquids
Semi-holographic models of non-Fermi liquids have been shown to have
generically stable generalised quasi-particles on the Fermi surface. Although
these excitations are broad and exhibit particle-hole asymmetry, they were
argued to be stable from interactions at the Fermi surface. In this work, we
use this observation to compute the density response and collective behaviour
in these systems.
Compared to the Fermi liquid case, we find that the boundaries of the
particle-hole continuum are blurred by incoherent contributions. However, there
is a region inside this continuum, that we call inner core, within which
salient features of the Fermi liquid case are preserved. A particularly
striking prediction of our work is that these systems support a plasmonic
collective excitation which is well-defined at large momenta, has an
approximately linear dispersion relation and is located in the low-energy tail
of the particle-hole continuum.
Furthermore, the dynamic screening potential shows deep attractive regions as
a function of the distance at higher frequencies which might lead to long-lived
pair formation depending on the behaviour of the pair susceptibility. We also
find that Friedel oscillations are present in these systems but are highly
suppressed.Comment: 45 pages; 24 figures; published versio
Riemann meets Goldstone: magnon scattering off quantum Hall skyrmion crystals probes interplay of symmetry breaking and topology
We introduce a model to study magnon scattering in skyrmion crystals,
sandwiched between ferromagnets which act as the source of magnons. Skyrmions
are topological objects while skyrmion crystals break internal and
translational symmetries, thus our setup allows us to study the interplay of
topology and symmetry breaking. Starting from a basis of holomorphic theta
functions, we construct an analytical ansatz for such a junction with finite
spatially modulating topological charge density in the central region and
vanishing in the leads. We then construct a suitably defined energy functional
for the junction and derive the resulting equations of motion, which resemble a
Bogoliubov-de Gennes-like equation. Using analytical techniques, field theory,
heuristic models and microscopic recursive transfer-matrix numerics, we
calculate the spectra and magnon transmission properties of the skyrmion
crystal. We find that magnon transmission can be understood via a combination
of low-energy Goldstone modes and effective emergent Landau levels at higher
energies. The former manifests in discrete low-energy peaks in the transmission
spectrum which reflect the nature of the Goldstone modes arising from symmetry
breaking. The latter, which reflect the topology, lead to band-like
transmission features, from the structure of which further details of the
excitation spectrum of the skyrmion crystal can be inferred. Such
characteristic transmission features are absent in competing phases of the
quantum Hall phase diagram, and hence provide direct signatures of skyrmion
crystal phases and their spectra. Our results directly apply to quantum Hall
heterojunction experiments in monolayer graphene with the central region doped
slightly away from unit filling, a junction and
are also relevant to junctions formed by metallic magnets or in junctions with
artificial gauge fields.Comment: 20+6 pages, 9+2 figures, comments welcom
Berry phase in superconducting multiterminal quantum dots
We report on the study of the non-trivial Berry phase in superconducting
multiterminal quantum dots biased at commensurate voltages. Starting with the
time-periodic Bogoliubov-de Gennes equations, we obtain a tight binding model
in the Floquet space, and we solve these equations in the semiclassical limit.
We observe that the parameter space defined by the contact transparencies and
quartet phase splits into two components with a non-trivial Berry phase. We use
the Bohr-Sommerfeld quantization to calculate the Berry phase. We find that if
the quantum dot level sits at zero energy, then the Berry phase takes the
values or . We demonstrate that this non-trivial
Berry phase can be observed by tunneling spectroscopy in the Floquet spectra.
Consequently, the Floquet-Wannier-Stark ladder spectra of superconducting
multiterminal quantum dots are shifted by half-a-period if . Our
numerical calculations based on Keldysh Green's functions show that this Berry
phase spectral shift can be observed from the quantum dot tunneling density of
states.Comment: 15 pages, 7 figures. Supplemental Material as ancillary file (3
pages, 5 figures), manuscript in final for
Robust preparation and manipulation of protected qubits using time--varying Hamiltonians
We show that it is possible to initialize and manipulate in a deterministic
manner protected qubits using time varying Hamiltonians. Taking advantage of
the symmetries of the system, we predict the effect of the noise during the
initialization and manipulation. These predictions are in good agreement with
numerical simulations. Our study shows that the topological protection remains
efficient under realistic experimental conditions.Comment: To be published in Phys. Rev. Let
Superconducting Nanocircuits for Topologically Protected Qubits
For successful realization of a quantum computer, its building blocks
(qubits) should be simultaneously scalable and sufficiently protected from
environmental noise. Recently, a novel approach to the protection of
superconducting qubits has been proposed. The idea is to prevent errors at the
"hardware" level, by building a fault-free (topologically protected) logical
qubit from "faulty" physical qubits with properly engineered interactions
between them. It has been predicted that the decoupling of a protected logical
qubit from local noises would grow exponentially with the number of physical
qubits. Here we report on the proof-of-concept experiments with a prototype
device which consists of twelve physical qubits made of nanoscale Josephson
junctions. We observed that due to properly tuned quantum fluctuations, this
qubit is protected against magnetic flux variations well beyond linear order,
in agreement with theoretical predictions. These results demonstrate the
feasibility of topologically protected superconducting qubits.Comment: 25 pages, 5 figure
Effets coherents dans les systemes desordonnes : oscillations de magnetoresistance dans des reseaux de metaux normaux; influence d'une non-linearite du milieu
SIGLECNRS T 59523 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc
Effets coherents dans les systemes desordonnes : oscillations de magnetoresistance dans des reseaux de metaux normaux; influence d'une non-linearite du milieu
SIGLECNRS T 59523 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc