Ince's limits for confluent and double-confluent Heun equations

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable $z$, while the other is given by a series of modified Bessel functions and converges for $|z|>|z_{0}|$, where $z_{0}$ denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when $z_{0}$ tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schr\"odinger equation for inverse fourth and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.Comment: Submitted to Journal of Mathmatical Physic

Coplanar stripline antenna design for optically detected magnetic resonance on semiconductor quantum dots

We report on the development and testing of a coplanar stripline antenna that is designed for integration in a magneto-photoluminescence experiment to allow coherent control of individual electron spins confined in single self-assembled semiconductor quantum dots. We discuss the design criteria for such a structure which is multi-functional in the sense that it serves not only as microwave delivery but also as electrical top gate and shadow mask for the single quantum dot spectroscopy. We present test measurements on hydrogenated amorphous silicon, demonstrating electrically detected magnetic resonance using the in-plane component of the oscillating magnetic field created by the coplanar stripline antenna necessary due to the particular geometry of the quantum dot spectroscopy. From reference measurements using a commercial electron spin resonance setup in combination with finite element calculations simulating the field distribution in the structure, we obtain an average magnetic field of ~0.2mT at the position where the quantum dots would be integrated into the device. The corresponding pi-pulse time of ~0.3us fully meets the requirements set by the high sensitivity optical spin read-out scheme developed for the quantum dot

Magnetic levitation on a type-I superconductor as a practical demonstration experiment for students

We describe and discuss an experimental set-up which allows undergraduate and graduate students to view and study magnetic levitation on a type-I superconductor. The demonstration can be repeated many times using one readily available 25 liter liquid helium dewar. We study the equilibrium position of a magnet that levitates over a lead bowl immersed in a liquid hand-held helium cryostat. We combine the measurement of the position of the magnet with simple analytical calculations. This provides a vivid visualization of magnetic levitation from the balance between pure flux expulsion and gravitation. The experiment contrasts and illustrates the case of magnetic levitation with high temperature type-II superconductors using liquid nitrogen, where levitation results from partial flux expulsion and vortex physics

The Suprafroth (Superconducting Froth)

The structure and dynamics of froths have been subjects of intense interest due to the desire to understand the behaviour of complex systems where topological intricacy prohibits exact evaluation of the ground state. The dynamics of a traditional froth involves drainage and drying in the cell boundaries, thus it is irreversible. We report a new member to the froths family: suprafroth, in which the cell boundaries are superconducting and the cell interior is normal phase. Despite very different microscopic origin, topological analysis of the structure of the suprafroth shows that statistical von Neumann and Lewis laws apply. Furthermore, for the first time in the analysis of froths there is a global measurable property, the magnetic moment, which can be directly related to the suprafroth structure. We propose that this suprafroth is a new, model system for the analysis of the complex physics of two-dimensional froths

Geoacoustic inversion by mode amplitude perturbation

Author Posting. © Acoustical Society of America, 2008. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 123 (2008): 667-678, doi:10.1121/1.2821975.This paper introduces a perturbative inversion algorithm for determining sea floor acoustic properties, which uses modal amplitudes as input data. Perturbative inverse methods have been used in the past to estimate bottom acoustic properties in sediments, but up to this point these methods have used only the modal eigenvalues as input data. As with previous perturbative inversion methods, the one developed in this paper solves the nonlinear inverse problem using a series of approximate, linear steps. Examples of the method applied to synthetic and experimental data are provided to demonstrate the method's feasibility. Finally, it is shown that modal eigenvalue and amplitude perturbation can be combined into a single inversion algorithm that uses all of the potentially available modal data.Funding for the research presented here was provided by the Office of Naval Research, and the WHOI Academic Programs Office

Enhanced thermal stability and spin-lattice relaxation rate of N@C60 inside carbon nanotubes

We studied the temperature stability of the endohedral fullerene molecule, N@C60, inside single-wall carbon nanotubes using electron spin resonance spectroscopy. We found that the nitrogen escapes at higher temperatures in the encapsulated material as compared to its pristine, crystalline form. The temperature dependent spin-lattice relaxation time, T_1, of the encapsulated molecule is significantly shorter than that of the crystalline material, which is explained by the interaction of the nitrogen spin with the conduction electrons of the nanotubes.Comment: 5 pages, 4 figures, 1 tabl

Periodic and Quasi-Periodic Compensation Strategies of Extreme Outages caused by Polarization Mode Dispersion and Amplifier Noise

Effect of birefringent disorder on the Bit Error Rate (BER) in an optical fiber telecommunication system subject to amplifier noise may lead to extreme outages, related to anomalously large values of BER. We analyze the Probability Distribution Function (PDF) of BER for various strategies of Polarization Mode Dispersion (PMD) compensation. A compensation method is proposed that is capable of more efficient extreme outages suppression, which leads to substantial improvement of the fiber system performance.Comment: 3 pages, 1 figure, Submitted to IEEE Photonics Letter

Locally Preferred Structure and Frustration in Glassforming Liquids: A Clue to Polyamorphism?

We propose that the concept of liquids characterized by a given locally preferred structure (LPS) could help in understanding the observed phenomenon of polyamorphism. ``True polyamorphism'' would involve the competition between two (or more) distinct LPS, one favored at low pressure because of its low energy and one favored at high pressure because of its small specific volume, as in tetrahedrally coordinated systems. ``Apparent polyamorphism'' could be associated with the existence of a poorly crystallized defect-ordered phase with a large unit cell and small crystallites, which may be illustrated by the metastable glacial phase of the fragile glassformer triphenylphosphite; the apparent polyamorphism might result from structural frustration, i. e., a competition between the tendency to extend the LPS and a global constraint that prevents tiling of the whole space by the LPS.Comment: 11, 6 figures, Proceedings of the Conference "Horizons in Complex Systems", Messina; in honor of the 60th birthday of H.E. Stanle

Photon Shot Noise Dephasing in the Strong-Dispersive Limit of Circuit QED

We study the photon shot noise dephasing of a superconducting transmon qubit in the strong-dispersive limit, due to the coupling of the qubit to its readout cavity. As each random arrival or departure of a photon is expected to completely dephase the qubit, we can control the rate at which the qubit experiences dephasing events by varying \textit{in situ} the cavity mode population and decay rate. This allows us to verify a pure dephasing mechanism that matches theoretical predictions, and in fact explains the increased dephasing seen in recent transmon experiments as a function of cryostat temperature. We investigate photon dynamics in this limit and observe large increases in coherence times as the cavity is decoupled from the environment. Our experiments suggest that the intrinsic coherence of small Josephson junctions, when corrected with a single Hahn echo, is greater than several hundred microseconds.Comment: 5 pages, 4 figures; includes Supporting Online Material of 6 pages with 5 figure

A general interpolation scheme for thermal fluctuations in superconductors

We present a general interpolation theory for the phenomenological effects of thermal fluctuations in superconductors. Fluctuations are described by a simple gauge invariant extension of the gaussian effective potential for the Ginzburg-Landau static model. The approach is shown to be a genuine variational method, and to be stationary for infinitesimal gauge variations around the Landau gauge. Correlation and penetration lengths are shown to depart from the mean field behaviour in a more or less wide range of temperature below the critical regime, depending on the class of material considered. The method is quite general and yields a very good interpolation of the experimental data for very different materials.Comment: some misprints have been corrected in Eq.(15),(19); more references and comments have been adde