53 research outputs found
Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard
This article presents experimental results on properties of waves propagating
in an unbounded and a bounded photonic crystal consisting of metallic cylinders
which are arranged in a triangular lattice. First, we present transmission
measurements of plane waves traversing a photonic crystal. The experiments are
performed in the vicinity of a Dirac point, i.e., an isolated conical
singularity of the photonic band structure. There, the transmission shows a
pseudodiffusive 1/L dependence, with being the thickness of the crystal, a
phenomenon also observed in graphene. Second, eigenmode intensity distributions
measured in a microwave analog of a relativistic Dirac billiard, a rectangular
microwave billiard that contains a photonic crystal, are discussed. Close to
the Dirac point states have been detected which are localized at the straight
edge of the photonic crystal corresponding to a zigzag edge in graphene
Application of a trace formula to the spectra of flat three-dimensional dielectric resonators
The length spectra of flat three-dimensional dielectric resonators of
circular shape were determined from a microwave experiment. They were compared
to a semiclassical trace formula obtained within a two-dimensional model based
on the effective index of refraction approximation and a good agreement was
found. It was necessary to take into account the dispersion of the effective
index of refraction for the two-dimensional approximation. Furthermore, small
deviations between the experimental length spectrum and the trace formula
prediction were attributed to the systematic error of the effective index of
refraction approximation. In summary, the methods developed in this article
enable the application of the trace formula for two-dimensional dielectric
resonators also to realistic, flat three-dimensional dielectric microcavities
and -lasers, allowing for the interpretation of their spectra in terms of
classical periodic orbits.Comment: 13 pages, 12 figures, 1 tabl
Spectral properties of Bunimovich mushroom billiards
Properties of a quantum mushroom billiard in the form of a superconducting
microwave resonator have been investigated. They reveal unexpected nonuniversal
features such as, e.g., a supershell effect in the level density and a dip in
the nearest-neighbor spacing distribution. Theoretical predictions for the
quantum properties of mixed systems rely on the sharp separability of phase
space - an unusual property met by mushroom billiards. We however find
deviations which are ascribed to the presence of dynamic tunneling.Comment: 4 pages, 7 .eps-figure
Experimental Observation of Localized Modes in a Dielectric Square Resonator
We investigated the frequency spectra and field distributions of a dielectric
square resonator in a microwave experiment. Since such systems cannot be
treated analytically, the experimental studies of their properties are
indispensable. The momentum representation of the measured field distributions
shows that all resonant modes are localized on specific classical tori of the
square billiard. Based on these observations a semiclassical model was
developed. It shows excellent agreement with all but a single class of measured
field distributions that will be treated separately.Comment: 6 pages, 5 figures, 1 tabl
Scattering Experiments with Microwave Billiards at an Exceptional Point under Broken Time Reversal Invariance
Scattering experiments with microwave cavities were performed and the effects
of broken time-reversal invariance (TRI), induced by means of a magnetized
ferrite placed inside the cavity, on an isolated doublet of nearly degenerate
resonances were investigated. All elements of the effective Hamiltonian of this
two-level system were extracted. As a function of two experimental parameters,
the doublet and also the associated eigenvectors could be tuned to coalesce at
a so-called exceptional point (EP). The behavior of the eigenvalues and
eigenvectors when encircling the EP in parameter space was studied, including
the geometric amplitude that builds up in the case of broken TRI. A
one-dimensional subspace of parameters was found where the differences of the
eigenvalues are either real or purely imaginary. There, the Hamiltonians were
found PT-invariant under the combined operation of parity (P) and time reversal
(T) in a generalized sense. The EP is the point of transition between both
regions. There a spontaneous breaking of PT occurs
Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
We report on the experimental study of an exceptional point (EP) in a
dissipative microwave billiard with induced time-reversal invariance (T)
violation. The associated two-state Hamiltonian is non-Hermitian and
non-symmetric. It is determined experimentally on a narrow grid in a parameter
plane around the EP. At the EP the size of T violation is given by the relative
phase of the eigenvector components. The eigenvectors are adiabatically
transported around the EP, whereupon they gather geometric phases and in
addition geometric amplitudes different from unity
Lifshitz and Excited State Quantum Phase Transitions in Microwave Dirac Billiards
We present experimental results for the density of states (DOS) of a
superconducting microwave Dirac billiard which serves as an idealized model for
the electronic properties of graphene. The DOS exhibits two sharp peaks which
evolve into van Hove singularities with increasing system size. They divide the
band structure into regions governed by the \emph{relativistic} Dirac equation
and by the \emph{non-relativistic} Schr\"odinger equation, respectively. We
demonstrate that in the thermodynamic limit a topological transition appears as
a neck-disrupting Lifshitz transition in the number susceptibility and as an
excited state transition in the electronic excitations. Furthermore, we recover
the finite-size scaling typical for excited state quantum phase transitions
involving logarithmic divergences and identify a quasi-order parameter
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