297 research outputs found
Encircling an Exceptional Point
We calculate analytically the geometric phases that the eigenvectors of a
parametric dissipative two-state system described by a complex symmetric
Hamiltonian pick up when an exceptional point (EP) is encircled. An EP is a
parameter setting where the two eigenvalues and the corresponding eigenvectors
of the Hamiltonian coalesce. We show that it can be encircled on a path along
which the eigenvectors remain approximately real and discuss a microwave cavity
experiment, where such an encircling of an EP was realized. Since the
wavefunctions remain approximately real, they could be reconstructed from the
nodal lines of the recorded spatial intensity distributions of the electric
fields inside the resonator. We measured the geometric phases that occur when
an EP is encircled four times and thus confirmed that for our system an EP is a
branch point of fourth order.Comment: RevTex 4.0, four eps-figures (low resolution
First experimental evidence for quantum echoes in scattering systems
A self-pulsing effect termed quantum echoes has been observed in experiments
with an open superconducting and a normal conducting microwave billiard whose
geometry provides soft chaos, i.e. a mixed phase space portrait with a large
stable island. For such systems a periodic response to an incoming pulse has
been predicted. Its period has been associated to the degree of development of
a horseshoe describing the topology of the classical dynamics. The experiments
confirm this picture and reveal the topological information.Comment: RevTex 4.0, 5 eps-figure
R-matrix theory of driven electromagnetic cavities
Resonances of cylindrical symmetric microwave cavities are analyzed in
R-matrix theory which transforms the input channel conditions to the output
channels. Single and interfering double resonances are studied and compared
with experimental results, obtained with superconducting microwave cavities.
Because of the equivalence of the two-dimensional Helmholtz and the stationary
Schroedinger equations, the results present insight into the resonance
structure of regular and chaotic quantum billiards.Comment: Revtex 4.
Observation of a Chiral State in a Microwave Cavity
A microwave experiment has been realized to measure the phase difference of
the oscillating electric field at two points inside the cavity. The technique
has been applied to a dissipative resonator which exhibits a singularity --
called exceptional point -- in its eigenvalue and eigenvector spectrum. At the
singularity, two modes coalesce with a phase difference of We
conclude that the state excited at the singularity has a definitiv chirality.Comment: RevTex 4, 5 figure
Phase shift experiments identifying Kramers doublets in a chaotic superconducting microwave billiard of threefold symmetry
The spectral properties of a two-dimensional microwave billiard showing
threefold symmetry have been studied with a new experimental technique. This
method is based on the behavior of the eigenmodes under variation of a phase
shift between two input channels, which strongly depends on the symmetries of
the eigenfunctions. Thereby a complete set of 108 Kramers doublets has been
identified by a simple and purely experimental method. This set clearly shows
Gaussian unitary ensemble statistics, although the system is time-reversal
invariant.Comment: RevTex 4, 5 figure
First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
We report on first experimental signatures for chaos-assisted tunneling in a
two-dimensional annular billiard. Measurements of microwave spectra from a
superconducting cavity with high frequency resolution are combined with
electromagnetic field distributions experimentally determined from a normal
conducting twin cavity with high spatial resolution to resolve eigenmodes with
properly identified quantum numbers. Distributions of so-called quasi-doublet
splittings serve as basic observables for the tunneling between whispering
gallery type modes localized to congruent, but distinct tori which are coupled
weakly to irregular eigenstates associated with the chaotic region in phase
space.Comment: 5 pages RevTex, 5 low-resolution figures (high-resolution figures:
http://linac.ikp.physik.tu-darmstadt.de/heiko/chaospub.html, to be published
in Phys. Rev. Let
Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference
Bayesian inference is applied to the level fluctuations of two coupled
microwave billiards in order to extract the coupling strength. The coupled
resonators provide a model of a chaotic quantum system containing two coupled
symmetry classes of levels. The number variance is used to quantify the level
fluctuations as a function of the coupling and to construct the conditional
probability distribution of the data. The prior distribution of the coupling
parameter is obtained from an invariance argument on the entropy of the
posterior distribution.Comment: Example from chaotic dynamics. 8 pages, 7 figures. Submitted to PR
GEO 600 and the GEO-HF upgrade program: successes and challenges
The German-British laser-interferometric gravitational wave detector GEO 600
is in its 14th year of operation since its first lock in 2001. After GEO 600
participated in science runs with other first-generation detectors, a program
known as GEO-HF began in 2009. The goal was to improve the detector sensitivity
at high frequencies, around 1 kHz and above, with technologically advanced yet
minimally invasive upgrades. Simultaneously, the detector would record science
quality data in between commissioning activities. As of early 2014, all of the
planned upgrades have been carried out and sensitivity improvements of up to a
factor of four at the high-frequency end of the observation band have been
achieved. Besides science data collection, an experimental program is ongoing
with the goal to further improve the sensitivity and evaluate future detector
technologies. We summarize the results of the GEO-HF program to date and
discuss its successes and challenges
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