1,782 research outputs found
Statistics of resonance states in a weakly open chaotic cavity
In this letter, we demonstrate that a non-Hermitian Random Matrix description
can account for both spectral and spatial statistics of resonance states in a
weakly open chaotic wave system with continuously distributed losses. More
specifically, the statistics of resonance states in an open 2D chaotic
microwave cavity are investigated by solving the Maxwell equations with lossy
boundaries subject to Ohmic dissipation. We successfully compare the statistics
of its complex-valued resonance states and associated widths with analytical
predictions based on a non-Hermitian effective Hamiltonian model defined by a
finite number of fictitious open channels
Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
We show that topologically protected defect states can exist in open (leaky
or lossy) systems even when these systems are topologically trivial in the
closed limit. The states appear from within the continuum, thus in absence of a
band gap, and are generated via exceptional points (a spectral transition that
occurs in open wave and quantum systems with a generalized time-reversal
symmetry), or via a degeneracy induced by charge-conjugation-symmetry (which is
related to the pole transition of Majorana zero modes). We demonstrate these
findings for a leaking passive coupled-resonator optical waveguide with
asymmmetric internal scattering, where the required symmetries (non-hermitian
versions of time-reversal symmetry, chirality and charge-conjugation) emerge
dynamically.Comment: 4++ page
Degeneracy doubling and sublattice polarization in strain-induced pseudo-Landau levels
The degeneracy and spatial support of pseudo-Landau levels (pLLs) in strained
honeycomb lattices systematically depends on the geometry -- for instance, in
hexagonal and rectangular flakes the 0th pLL displays a twofold increased
degeneracy, while the characteristic sublattice polarization of the 0th pLL is
only fully realized in a zigzag-terminated triangle. These features are
dictated by algebraic constraints in the atomistic theory, and signify a
departure from the standard picture in which all qualitative differences
between pLLs and Landau levels induced by a magnetic field trace back to the
valley-antisymmetry of the pseudomagnetic field.Comment: 5 pages, 2 figure
Avoided level crossing statistics in open chaotic billiards
We investigate a two-level model with a large number of open decay channels
in order to describe avoided level crossing statistics in open chaotic
billiards. This model allows us to describe the fundamental changes of the
probability distribution of the avoided level crossings compared with the
closed case. Explicit expressions are derived for systems with preserved and
broken Time Reversal Symmetry (TRS). We find that the decay process induces a
modification at small spacings of the probability distribution of the avoided
level crossings due to an attraction of the resonances. The theoretical
predictions are in complete agreement with the recent experimental results of
Dietz \textit{et al.} (Phys. Rev. E {\bf 73} (2006) 035201)
Statistics of eigenfunctions in open chaotic systems: a perturbative approach
We investigate the statistical properties of the complexness parameter which
characterizes uniquely complexness (biorthogonality) of resonance eigenstates
of open chaotic systems. Specifying to the regime of isolated resonances, we
apply the random matrix theory to the effective Hamiltonian formalism and
derive analytically the probability distribution of the complexness parameter
for two statistical ensembles describing the systems invariant under time
reversal. For those with rigid spectra, we consider a Hamiltonian characterized
by a picket-fence spectrum without spectral fluctuations. Then, in the more
realistic case of a Hamiltonian described by the Gaussian Orthogonal Ensemble,
we reveal and discuss the r\^ole of spectral fluctuations
Observation of supersymmetric pseudo-Landau levels in strained microwave graphene
Using an array of coupled microwave resonators arranged in a deformed honeycomb lattice, we experimentally observe the formation of pseudo-Landau levels in the whole crossover from vanishing to large pseudomagnetic field strengths. This result is achieved by utilising an adaptable setup in a geometry that is compatible with the pseudo-Landau levels at all field strengths. The adopted approach enables us to observe the fully formed flat-band pseudo-Landau levels spectrally as sharp peaks in the photonic density of states and image the associated wavefunctions spatially, where we provide clear evidence for a characteristic nodal structure reflecting the previously elusive supersymmetry in the underlying low-energy theory. In particular, we resolve the full sublattice polarisation of the anomalous 0th pseudo-Landau level, which reveals a deep connection to zigzag edge states in the unstrained case
Partial chiral symmetry-breaking as a route to spectrally isolated topological defect states in two-dimensional artificial materials
Bipartite quantum systems from the chiral universality classes admit topologically protected zero modes at point defects. However, in two-dimensional systems these states can be difficult to separate from compacton-like localized states that arise from flat bands, formed if the two sublattices support a different number of sites within a unit cell. Here we identify a natural reduction of chiral symmetry, obtained by coupling sites on the majority sublattice, which gives rise to spectrally isolated point-defect states, topologically characterized as zero modes supported by the complementary minority sublattice. We observe these states in a microwave realization of a dimerized Lieb lattice with next-nearest neighbour coupling, and also demonstrate topological mode selection via sublattice-staggered absorption
Selective enhancement of topologically induced interface states
International audienceThe recent realization of topological phases in insulators and superconductors has raised the prospects to advance robust quantum technologies. The desire to demonstrate the underlying topological features with a high level of control has given incentive to explore optical platforms for analogous realizations. Here we show that the functionality of optical systems can be enhanced by combining topological protection with non-hermitian symmetries that do not have an electronic counterpart. This is achieved by combining parity-time symmetric losses with a unique feature of topologically induced interface states, namely, that they break a sublattice symmetry. This property isolates the state from the losses and enhances its visibility both in the frequency and in the time domain
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