We experimentally investigate theoretical predictions of universal impedance fluctuations in wave chaotic systems using a microwave analog of a quantum chaotic infinite square well potential. Our approach emphases the use of the radiation impedance to remove the non-universal effects of the particular coupling from the outside world to the scatterer. Specific predictions that we test include the probability distribution functions (PDFs) of the real (related to the local density of states in disordered metals) and imaginary parts of the normalized cavity impedance, the equality of the variances of these PDFs, and the dependence of the universal PDFs on a single control parameter characterizing the level of loss. We find excellent agreement between the statistical data and theoretical predictions. There is interest in the small wavelength behavior of quantum (wave) systems whose classical (ray orbit) limit is chaotic. Despite their apparent complexity, quantum chaotic systems have remarkable universal properties. Much prior work has focused on identifying the universal statistical properties of wave chaotic systems such as quantum dots and atomic nuclei [1][2][3]. For example, the nearest neighbor energy level spacing statistics of these systems have universal distributions that fall into one of three classes, depending on the existence or absence of time-reversal symmetry and symplectic properties. Likewise the eigenfunctions of wave chaotic systems have universal statistical properties, such as one-point and two-point statistical distribution functions [4][5][6]. It has been challenging to experimentally measure the corresponding universal properties of the scattering and impedance matrices of lossy multi-port wave chaotic systems. Here, we experimentally examine universal statistical properties of the complex impedance (or scattering) matrix fluctuations of such systems.We consider wave systems in the semiclassical limit consisting of enclosures that show chaos in the ray limit, but which are also coupled to their surroundings through a finite number of leads or ports, and also include loss. Examples include quantum dots together with their leads, wave chaotic microwave or acoustical cavities together with their coupling ports, or scattering experiments on nuclei or atoms. Theoretical studies of chaotic scattering have examined the eigenphases of the scattering (S) matrix, [7] the time-delay distribution, [8,9,10] and the distribution of the scalar reflection and transmission coefficients. [10,11,12,13] Experimental work has concentrated on the energy decay and S-matrix autocorrelation functions in chaotic systems, [14,15,16,17] and most recently the distribution of scalar reflection coefficients [18]. In the related field of statistical electromagnetism [19], the statistical distribution of electromagnetic fields [20] and impedance [21] within complicated enclosed systems has been studied, but these results have not been generalized to other wave chaotic systems.Ref.[18] (and references therein) takes into acc...

Metamaterials are engineered materials composed of small electrical circuits producing novel interactions with electromagnetic waves. Recently, a new class of metamaterials has been created to mimic the behavior of media displaying electromagnetically induced transparency (EIT). Here we introduce a planar EIT metamaterial that creates a very large loss contrast between the dark and radiative resonators by employing a superconducting Nb film in the dark element and a normal-metal Au film in the radiative element. Below the critical temperature of Nb, the resistance contrast opens up a transparency window along with a large enhancement in group delay, enabling a significant slowdown of waves. We further demonstrate precise control of the EIT response through changes in the superfluid density. Such tunable metamaterials may be useful for telecommunication because of their large delay-bandwidth products.

Precise microwave measurements of sample conductivity, dielectric, and magnetic properties are routinely performed with cavity perturbation measurements. These methods require the accurate determination of quality factor and resonant frequency of microwave resonators. Seven different methods to determine the resonant frequency and quality factor from complex transmission coefficient data are discussed and compared to find which is most accurate and precise when tested using identical data. We find that the nonlinear least-squares fit to the phase vs. frequency is the most accurate and precise when the signal-to-noise ratio is greater than 65. For noisier data, the nonlinear least squares fit to a Lorentzian curve is more accurate and precise.The results are general and can be applied to the analysis of many kinds of resonant phenomena.

It has been predicted that in the semiclassical regime the level statistics of a classically chaotic system correspond to that of the Gaussian unitary ensemble (GUE) of random matrices when time reversal symmetry is broken. This Letter presents the first experimental test of this prediction. The system employed is a microwave cavity containing a thin ferrite strip adjacent to one of the walls. When a sufficiently large magnetic field is applied to the ferrite (thus breaking the time reversal symmetry) good agreement with GUE statistics is obtained. The transition from Gaussian orthogonal ensemble (GOE) (which applies in the absence of the applied field) to GUE is also investigated.PACS numbers: 05.45.+b It has been conjectured that, for chaotic systems in the semiclassical limit, the spectral statistics of the Schrodinger equation correspond to that of random matrices with the same symmetry [1]. In particular, when the system is time reversible, the statistical fIuctuations of the energy levels are conjectured to be the same as those for the "Gaussian orthogonal ensemble" (GOE) of random matrices. As a simple example of this class of systems, consider a charged particle in a scalar potential. By reversing the direction of the momentum of the particle, the classical particle will retrace its own path. The wave equation for this particle is real and the corresponding GOE consists of real random symmetric matrices. On the other hand, when a magnetic field 8 is applied, the time reversal symmetry is broken. A classical charged particle will no longer retrace its own path when the direction of its momentum is reversed. In this case, the Schrodinger equation is complex, p -ihV -qA(r), and (in the absence of special symmetries) the statistical fIuctuations of the energy levels are conjectured to be the same as those for the "Gaussian unitary ensemble" (GUE) of random Hermitian matrices. Although the predictions of GOE statistics in actual physical systems have been observed by others [2 -5], there has been no experimental verification of the GUE predictions. The purpose of the present work is to verify the GUE predictions in an experimental setting using a 2D microwave cavity with a thin magnetized ferrite strip adjacent to one of the walls. To see how a magnetized ferrite breaks the time reversal symmetry in the electromagnetic wave equation, consider the situation when a plane wave with the electric field E = E, exp(ik, x + ikYy)z perpendicular to the plane of incidence is incident from the left (x~0) on a slab of magnetized ferrite (0 ( x ( d) which is placed adjacent to a perfect conductor on the right (x = d). In the presence of a static magnetic field B = Bi perpendicular to the plane of incidence, the magnetic permeability p, of the ferrite, in the absence of losses, is @II lK 0 P l K P'lI 0 l (1) 0 0 p, , where p,~~, K, and p, , are real. At the interface between the ferrite and the empty cavity, the boundary conditions require the continuity of both E, and the tangential component of H, which, in the ferrite, i...

Evanescent wave amplification has been predicted under the ideal condition that the index of refraction, n=−1+i0 precisely, but is difficult to observe in practice because current metamaterials suffer from high losses. We present experimental results on a metamaterial that employs superconducting Nb metals and low-loss dielectric materials. Results include transmission data on a wire, split-ring resonator, and a combination medium at temperatures between 4.2 and 297K. Evidence of negative effective permittivity, permeability, and a negative effective index passband are seen in the superconducting state between 50MHz and 18GHz. We find a dielectric loss of εeff,2=2.6×10−3 in a superconducting wire array at 10.75GHz.