Evidence for a Second Order Phase Transition in Glasses at Very Low Temperatures -- A Macroscopic Quantum State of Tunneling Systems

Dielectric measurements at very low temperature indicate that in a glass with the eutectic composition BaO-Al$_2$O$_3$-SiO$_2$ a phase transition occurs at 5.84 mK. Below that temperature small magnetic fields of the order of 10 $\mu$T cause noticeable changes of the dielectric constant although the glass is insensitive to fields up to 20 T above 10 mK. The experimental findings may be interpreted as the signature of the formation of a new phase in which many tunneling systems perform a coherent motion resulting in a macroscopic wave function.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Magnetic Field Dependent Tunneling in Glasses

We report on experiments giving evidence for quantum effects of electromagnetic flux in barium alumosilicate glass. In contrast to expectation, below 100 mK the dielectric response becomes sensitive to magnetic fields. The experimental findings include both, the complete lifting of the dielectric saturation by weak magnetic fields and oscillations of the dielectric response in the low temperature resonant regime. As origin of these effects we suggest that the magnetic induction field violates the time reversal invariance leading to a flux periodicity in the energy levels of tunneling systems. At low temperatures, this effect is strongly enhanced by the interaction between tunneling systems and thus becomes measurable.Comment: 4 pages, 4 figure

An experimental study of reactive turbulent mixing

An experimental study of two coaxial gas streams, which react very rapidly, was performed to investigate the mixing characteristics of turbulent flow fields. The center stream consisted of a CO-N2 mixture and the outer annular stream consisted of air vitiated by H2 combustion. The streams were at equal velocity (50 m/sec) and temperature (1280 K). Turbulence measurements were obtained using hot film anemometry. A sampling probe was used to obtain time averaged gas compositions. Six different turbulence generators were placed in the annular passage to alter the flow field mixing characteristics. The turbulence generators affected the bulk mixing of the streams and the extent of CO conversion to different degrees. The effects can be related to the average eddy size (integral scale) and the bulk mixing. Higher extents of conversion of CO to CO2 were found be increasing the bulk mixing and decreasing the average eddy size

Parity Effects in Stacked Nanoscopic Quantum Rings

The ground state and the dielectric response of stacked quantum rings are investigated in the presence of an applied magnetic field along the ring axis. For odd number $N$ of rings and an electric field perpendicular to the axis, a linear Stark effect occurs at distinct values of the magnetic field. At those fields energy levels cross in the absence of electric field. For even values of $N$ a quadratic Stark effect is expected in all cases, but the induced electric polarization is discontinuous at those special magnetic fields. Experimental consequences for related nanostructures are discussed.Comment: typos corrected, to appear Phys. Rev. B (Rapid Communication) 15 Au

Correlated Persistent Tunneling Currents in Glasses

Low temperature properties of glasses are derived within a generalized tunneling model, considering the motion of charged particles on a closed path in a double-well potential. The presence of a magnetic induction field B violates the time reversal invariance due to the Aharonov-Bohm phase, and leads to flux periodic energy levels. At low temperature, this effect is shown to be strongly enhanced by dipole-dipole and elastic interactions between tunneling systems and becomes measurable. Thus, the recently observed strong sensitivity of the electric permittivity to weak magnetic fields can be explained. In addition, superimposed oscillations as a function of the magnetic field are predicted.Comment: 4 page

Magnetic field effect on the dielectric constant of glasses: Evidence of disorder within tunneling barriers

The magnetic field dependence of the low frequency dielectric constant $e_r$(H) of a structural glass a - SiO2 + xCyHz was studied from 400 mK to 50 mK and for H up to 3T. Measurement of both the real and the imaginary parts of $e_r$ is used to eliminate the difficult question of keeping constant the temperature of the sample while increasing H: a non-zero $e_r$(H) dependence is reported in the same range as that one very recently reported on multicomponent glasses. In addition to the recently proposed explanation based on interactions, the reported $e_r$(H) is interpreted quantitatively as a consequence of the disorder lying within the nanometric barriers of the elementary tunneling systems of the glass.Comment: latex Bcorrige1.tex, 5 files, 4 figures, 7 pages [SPEC-S02/009

Effect of Nuclear Quadrupole Interaction on the Relaxation in Amorphous Solids

Recently it has been experimentally demonstrated that certain glasses display an unexpected magnetic field dependence of the dielectric constant. In particular, the echo technique experiments have shown that the echo amplitude depends on the magnetic field. The analysis of these experiments results in the conclusion that the effect seems to be related to the nuclear degrees of freedom of tunneling systems. The interactions of a nuclear quadrupole electrical moment with the crystal field and of a nuclear magnetic moment with magnetic field transform the two-level tunneling systems inherent in amorphous dielectrics into many-level tunneling systems. The fact that these features show up at temperatures $T<100mK$, where the properties of amorphous materials are governed by the long-range $R^{-3}$ interaction between tunneling systems, suggests that this interaction is responsible for the magnetic field dependent relaxation. We have developed a theory of many-body relaxation in an ensemble of interacting many-level tunneling systems and show that the relaxation rate is controlled by the magnetic field. The results obtained correlate with the available experimental data. Our approach strongly supports the idea that the nuclear quadrupole interaction is just the key for understanding the unusual behavior of glasses in a magnetic field.Comment: 18 pages, 9 figure

A Classroom Demonstration of Levitation and Suspension of a Superconductor over a Magnetic Track

The suspension and levitation of superconductors by permanent magnets is one of the most fascinating consequences of superconductivity, and a wonderful instrument for generating interest in low temperature physics and electrodynamics. We present a novel classroom demonstration of the levitation/suspension of a superconductor over a magnetic track that maximizes levitation/suspension time, separation distance between the magnetic track and superconductor and also insulator aesthetics. The demonstration as described is both inexpensive and easy to construct.Comment: 5 page

Comparative study of the effects of electron irradiation and natural disorder in single crystals of SrFe2_{2}(As1−x_{1-x}Px_x)2_2 (x=x=0.35) superconductor

London penetration depth, $\lambda(T)$, was measured in single crystals of SrFe$_2$(As$_{1-x}$P$_x$)$_2$ ($x=$0.35) iron - based superconductor. The influence of disorder on the transition temperature, $T_c$, and on $\lambda(T)$ was investigated. The effects of scattering controlled by the annealing of as-grown crystals was compared with the effects of artificial disorder introduced by 2.5~MeV electron irradiation. The low temperature behavior of $\lambda(T)$ can be described by a power-law function, $\Delta \lambda (T)=AT^n$, with the exponent $n$ close to one in pristine annealed samples, as expected for superconducting gap with line nodes. Upon $1.2 \times 10^{19}$ \ecm irradiation, the exponent $n$ increases rapidly exceeding a dirty limit value of $n=$ 2 implying that the nodes in the superconducting gap are accidental and can be lifted by the disorder. The variation of the exponent $n$ with $T_c$ is much stronger in the irradiated crystals compared to the crystals in which disorder was controlled by the annealing of the growth defects. We discuss the results in terms of different influence of different types of disorder on intra- and inter- band scattering