Imaging spontaneous currents in superconducting arrays of pi-junctions

Superconductors separated by a thin tunneling barrier exhibit the Josephson effect that allows charge transport at zero voltage, typically with no phase shift between the superconductors in the lowest energy state. Recently, Josephson junctions with ground state phase shifts of pi proposed by theory three decades ago have been demonstrated. In superconducting loops, pi-junctions cause spontaneous circulation of persistent currents in zero magnetic field, analogous to spin-1/2 systems. Here we image the spontaneous zero-field currents in superconducting networks of temperature-controlled pi-junctions with weakly ferromagnetic barriers using a scanning SQUID microscope. We find an onset of spontaneous supercurrents at the 0-pi transition temperature of the junctions Tpi = 3 K. We image the currents in non-uniformly frustrated arrays consisting of cells with even and odd numbers of pi-junctions. Such arrays are attractive model systems for studying the exotic phases of the 2D XY-model and achieving scalable adiabatic quantum computers.Comment: Pre-referee version. Accepted to Nature Physic

Observation of second-harmonic generation induced by pure spin currents

Extensive efforts are currently being devoted to developing a new electronic technology, called spintronics, where the spin of electrons is explored to carry information. [1,2] Several techniques have been developed to generate pure spin currents in many materials and structures. [3-10] However, there is still no method available that can be used to directly detect pure spin currents, which carry no net charge current and no net magnetization. Currently, studies of pure spin currents rely on measuring the induced spin accumulation with optical techniques [5, 11-13] or spin-valve configurations. [14-17] However, the spin accumulation does not directly reflect the spatial distribution or temporal dynamics of the pure spin current, and therefore cannot monitor the pure spin current in a real-time and real-space fashion. This imposes severe constraints on research in this field. Here we demonstrate a second-order nonlinear optical effect of the pure spin current. We show that such a nonlinear optical effect, which has never been explored before, can be used for the non-invasive, non-destructive, and real-time imaging of pure spin currents. Since this detection scheme does not rely on optical resonances, it can be generally applied in a wide range of materials with different electronic bandstructures. Furthermore, the control of nonlinear optical properties of materials with pure spin currents may have potential applications in photonics integrated with spintronics.Comment: 19 pages, 3 figures, supplementary discussion adde

Ballistic Spin Resonance

The phenomenon of spin resonance has had far reaching influence since its discovery nearly 70 years ago. Electron spin resonance (ESR) driven by high frequency magnetic fields has informed our understanding of quantum mechanics, and finds application in fields as diverse as medicine and quantum information. Spin resonance induced by high frequency electric fields, known as electric dipole spin resonance (EDSR), has also been demonstrated recently. EDSR is mediated by spin-orbit interaction (SOI), which couples the spin degree of freedom and the momentum vector. Here, we report the observation of a novel spin resonance due to SOI that does not require external driving fields. Ballistic spin resonance (BSR) is driven by an internal spin-orbit field that acts upon electrons bouncing at gigaHertz frequencies in narrow channels of ultra-clean two-dimensional electron gas (2DEG). BSR is manifested in electrical measurements of pure spin currents as a strong suppression of spin relaxation length when the motion of electrons is in resonance with spin precession. These findings point the way to gate-tunable coherent spin rotations in ballistic nanostructures without external a.c. fields.Comment: 24 pages, including supplementary material

Entanglement entropy of black holes

The entanglement entropy is a fundamental quantity which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff which regulates the short-distance correlations. The geometrical nature of the entanglement entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in 4 and 6 dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as 't Hooft's brick wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields which non-minimally couple to gravity is emphasized. The holographic description of the entanglement entropy of the black hole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.Comment: 89 pages; an invited review to be published in Living Reviews in Relativit

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

Testing CPT- and Lorentz-odd electrodynamics with waveguides

We study CPT- and Lorentz-odd electrodynamics described by the Standard Model Extension. Its radiation is confined to the geometry of hollow conductor waveguide, open along $z$. In a special class of reference frames, with vanishing both 0-th and $z$ components of the background field, $(k_{\rm AF})^\mu$, we realize a number of {\em huge and macroscopically detectable} effects on the confined waves spectra, compared to standard results. Particularly, if $(k_{\rm AF})^\mu$ points along $x$ (or $y$) direction only transverse electric modes, with $E_z=0$, should be observed propagating throughout the guide, while all the transverse magnetic, $B_z=0$, are absent. Such a strong mode suppression makes waveguides quite suitable to probe these symmetry violations using a simple and easily reproducible apparatus.Comment: 11pages, double-spacing, tex forma