A Scanned Perturbation Technique For Imaging Electromagnetic Standing Wave Patterns of Microwave Cavities

We have developed a method to measure the electric field standing wave distributions in a microwave resonator using a scanned perturbation technique. Fast and reliable solutions to the Helmholtz equation (and to the Schrodinger equation for two dimensional systems) with arbitrarily-shaped boundaries are obtained. We use a pin perturbation to image primarily the microwave electric field amplitude, and we demonstrate the ability to image broken time-reversal symmetry standing wave patterns produced with a magnetized ferrite in the cavity. The whole cavity, including areas very close to the walls, can be imaged using this technique with high spatial resolution over a broad range of frequencies.Comment: To be published in Review of Scientific Instruments,September, 199

Activation Energy of Metastable Amorphous Ge2Sb2Te5 from Room Temperature to Melt

Resistivity of metastable amorphous Ge2Sb2Te5 (GST) measured at device level show an exponential decline with temperature matching with the steady-state thin-film resistivity measured at 858 K (melting temperature). This suggests that the free carrier activation mechanisms form a continuum in a large temperature scale (300 K - 858 K) and the metastable amorphous phase can be treated as a super-cooled liquid. The effective activation energy calculated using the resistivity versus temperature data follow a parabolic behavior, with a room temperature value of 333 meV, peaking to ~377 meV at ~465 K and reaching zero at ~930 K, using a reference activation energy of 111 meV (3kBT/2) at melt. Amorphous GST is expected to behave as a p-type semiconductor at Tmelt ~ 858 K and transitions from the semiconducting-liquid phase to the metallic-liquid phase at ~ 930 K at equilibrium. The simultaneous Seebeck (S) and resistivity versus temperature measurements of amorphous-fcc mixed-phase GST thin-films show linear S-T trends that meet S = 0 at 0 K, consistent with degenerate semiconductors, and the dS/dT and room temperature activation energy show a linear correlation. The single-crystal fcc is calculated to have dS/dT = 0.153 {\mu}V/K for an activation energy of zero and a Fermi level 0.16 eV below the valance band edge.Comment: 5 pages, 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

Influence of diffraction on the spectrum and wavefunctions of an open system

In this paper, we demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge of the system are found to have a strong influence on the transmission spectrum of the system, especially in the regime where there are no stable classical orbits. On resonance, the wavefunctions are influenced by both classical and diffractive orbits. Off resonance, the wavefunctions are determined by the constructive interference of multiple transient, nonperiodic orbits. Experimental, numerical, and semiclassical results are presented.Comment: 27 pages, 29 figures, and 3 tables. Submitted to Physical Review E. A copy with higher resolution figures is available at http://monsoon.harvard.edu/~hersch/papers.htm

Single-Atom Gating of Quantum State Superpositions

The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric interpretation: this state space--or Hilbert space--is spanned by mutually orthogonal state vectors corresponding to the quantized degrees of freedom of the real-space system. Measurement of superpositions is akin to accessing the direction of a vector in Hilbert space, determining an angle of rotation equivalent to quantum phase. Here we show that an individual atom inside a designed quantum corral can control this angle, producing arbitrary coherent superpositions of spatial quantum states. Using scanning tunnelling microscopy and nanostructures assembled atom-by-atom we demonstrate how single spins and quantum mirages can be harnessed to image the superposition of two electronic states. We also present a straightforward method to determine the atom path enacting phase rotations between any desired state vectors. A single atom thus becomes a real space handle for an abstract Hilbert space, providing a simple technique for coherent quantum state manipulation at the spatial limit of condensed matter.Comment: Published online 6 April 2008 in Nature Physics; 17 page manuscript (including 4 figures) + 3 page supplement (including 2 figures); supplementary movies available at http://mota.stanford.ed

Measurement of Wave Chaotic Eigenfunctions in the Time-Reversal Symmetry-Breaking Crossover Regime

We present experimental results on eigenfunctions of a wave chaotic system in the continuous crossover regime between time-reversal symmetric and time-reversal symmetry-broken states. The statistical properties of the eigenfunctions of a two-dimensional microwave resonator are analyzed as a function of an experimentally determined time-reversal symmetry-breaking parameter. We test four theories of onepoint eigenfunction statistics and introduce a new theory relating the one-point and two-point statistical properties in the crossover regime. We also find a universal correlation between the one-point and twopoint statistical parameters for the crossover eigenfunctions. PACS numbers: 05.45. Mt, 03.65.Sq, 11.30.Er, 84.40.Az Many complex quantum systems whose underlying classical behavior is chaotic can be described by treating their Hamiltonian matrix elements as random numbers which fluctuate around zero with a Gaussian distribution. There are universal statistical properties of the eigenvalues and eigenfunctions of these random matrices which depend only on the symmetries of the Hamiltonian. For instance, random matrix theory has been shown to be consistent with the statistical properties of nuclei [1], molecules [2], and two-dimensional quantum dots When time-reversal symmetry is present, wave chaotic systems have statistical properties described by a Gaussian orthogonal ensemble (GOE) of random matrices Here we address the evolution of eigenfunctions of semiclassical wave chaotic systems from the TRS to the TRSB limits. A considerable theoretical literature has developed proposing detailed descriptions of eigenvector statistics in the crossover regime, although little experimental data are available to test these theories. These theories treat only the evolution of the one-point statistical property of eigenfunction distribution, P͑jCj 2 ͒, which quantifies the degree of probability density, jCj 2 , fluctuations in the eigenfunctions The experimental arrangement used to create and measure the wave chaotic eigenfunctions has been described previously We have found that the nonreciprocal property of the ferrite, hence the degree of TRSB, is a function of frequency of the eigenmode in a relatively narrow range of frequency 2482 0031-9007͞00͞85(12)͞2482(4)$15.0

Thickness dependence of the amorphous-cubic and cubic-hexagonal phase transition temperatures of GeSbTe thin films on silicon nitride

The crystallization temperature of GeSbTe thin films with thicknesses between 11 and 87 nm on silicon nitride was studied through resistance versus temperature measurements. The amorphous-cubic phase transition occurs at similar to 150 degrees C for all films thicknesses, whereas the cubic-hexagonal phase transition temperature increases with film thickness, from similar to 200 degrees C for the 20 nm film to similar to 250 degrees C for the 87 nm film. The cubic-hexagonal transition occurs gradually for the 11 nm film. Implications for phase-change memory devices are discussed. (C) 2011 Elsevier B.V. All rights reserved