873 research outputs found
State-recycling and time-resolved imaging in topological photonic lattices
Photonic lattices - arrays of optical waveguides - are powerful platforms for
simulating a range of phenomena, including topological phases. While probing
dynamics is possible in these systems, by reinterpreting the propagation
direction as "time," accessing long timescales constitutes a severe
experimental challenge. Here, we overcome this limitation by placing the
photonic lattice in a cavity, which allows the optical state to evolve through
the lattice multiple times. The accompanying detection method, which exploits a
multi-pixel single-photon detector array, offers quasi-real time-resolved
measurements after each round trip. We apply the state-recycling scheme to
intriguing photonic lattices emulating Dirac fermions and Floquet topological
phases. In this new platform, we also realise a synthetic pulsed electric
field, which can be used to drive transport within photonic lattices. This work
opens a new route towards the detection of long timescale effects in engineered
photonic lattices and the realization of hybrid analogue-digital simulators.Comment: Comments are welcom
Anderson localization in generalized discrete time quantum walks
We study Anderson localization in a generalized discrete time quantum walk -
a unitary map related to a Floquet driven quantum lattice. It is controlled by
a quantum coin matrix which depends on four angles with the meaning of
potential and kinetic energy, and external and internal synthetic flux. Such
quantum coins can be engineered with microwave pulses in qubit chains. The
ordered case yields a two-band eigenvalue structure on the unit circle which
becomes completely flat in the limit of vanishing kinetic energy. Disorder in
the external magnetic field does not impact localization. Disorder in all the
remaining angles yields Anderson localization. In particular, kinetic energy
disorder leads to logarithmic divergence of the localization length at spectral
symmetry points. Strong disorder in potential and internal magnetic field
energies allows to obtain analytical expressions for spectrally independent
localization length which is highly useful for various applications.Comment: 11 pages, 14 figure
Topological Photonics
Topological photonics is a rapidly emerging field of research in which
geometrical and topological ideas are exploited to design and control the
behavior of light. Drawing inspiration from the discovery of the quantum Hall
effects and topological insulators in condensed matter, recent advances have
shown how to engineer analogous effects also for photons, leading to remarkable
phenomena such as the robust unidirectional propagation of light, which hold
great promise for applications. Thanks to the flexibility and diversity of
photonics systems, this field is also opening up new opportunities to realize
exotic topological models and to probe and exploit topological effects in new
ways. This article reviews experimental and theoretical developments in
topological photonics across a wide range of experimental platforms, including
photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon
photonics, and circuit QED. A discussion of how changing the dimensionality and
symmetries of photonics systems has allowed for the realization of different
topological phases is offered, and progress in understanding the interplay of
topology with non-Hermitian effects, such as dissipation, is reviewed. As an
exciting perspective, topological photonics can be combined with optical
nonlinearities, leading toward new collective phenomena and novel strongly
correlated states of light, such as an analog of the fractional quantum Hall
effect.Comment: 87 pages, 30 figures, published versio
Spectral Theory of Sparse Non-Hermitian Random Matrices
Sparse non-Hermitian random matrices arise in the study of disordered
physical systems with asymmetric local interactions, and have applications
ranging from neural networks to ecosystem dynamics. The spectral
characteristics of these matrices provide crucial information on system
stability and susceptibility, however, their study is greatly complicated by
the twin challenges of a lack of symmetry and a sparse interaction structure.
In this review we provide a concise and systematic introduction to the main
tools and results in this field. We show how the spectra of sparse
non-Hermitian matrices can be computed via an analogy with infinite dimensional
operators obeying certain recursion relations. With reference to three
illustrative examples --- adjacency matrices of regular oriented graphs,
adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency
matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the
use of these methods to obtain both analytic and numerical results for the
spectrum, the spectral distribution, the location of outlier eigenvalues, and
the statistical properties of eigenvectors.Comment: 60 pages, 10 figure
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Photonic Quantum Simulators
Quantum simulators are controllable quantum systems that can be used to mimic other quantum systems. They have the potential to enable the tackling of problems that are intractable on conventional computers. The photonic quantum technology available today is reaching the stage where significant advantages arise for the simulation of interesting problems in quantum chemistry, quantum biology and solid-state physics. In addition, photonic quantum systems also offer the unique benefit of being mobile over free space and in waveguide structures, which opens new perspectives to the field by enabling the natural investigation of quantum transport phenomena. Here, we review recent progress in the field of photonic quantum simulation, which should break the ground towards the realization of versatile quantum simulators.Chemistry and Chemical Biolog
Quantum walk approach to search on fractal structures
We study continuous-time quantum walks mimicking the quantum search based on
Grover's procedure. This allows us to consider structures, that is, databases,
with arbitrary topological arrangements of their entries. We show that the
topological structure of the database plays a crucial role by analyzing, both
analytically and numerically, the transition from the ground to the first
excited state of the Hamiltonian associated with different (fractal)
structures. Additionally, we use the probability of successfully finding a
specific target as another indicator of the importance of the topological
structure.Comment: 15 pages, 14 figure
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