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Split Cooper pair is a natural source for entangled electrons which is a basic ingredient for quantum information in solid state. We report an experiment on a superconductor-graphene double quantum dot (QD) system, in which we observe Cooper pair splitting (CPS) up to a CPS efficiency of ~ 10%. With bias on both QDs, we are able to detect a positive conductance correlation across the two distinctly decoupled QDs. Furthermore, with bias only on one QD, CPS and elastic co-tunneling can be distinguished by tuning the energy levels of the QDs to be asymmetric or symmetric with respect to the Fermi level in the superconductor., Comment: 5 pages, 5 figures, supplement at http://ltl.tkk.fi/~pjh/CPS/Supplementary.pdf

We have investigated shot noise and conductance of multi-terminal graphene nanoribbon devices at temperatures down to 50 mK. Away from the charge neutrality point, we find a Fano factor $F \approx 0.4$, nearly independent of the charge density. Our shot noise results are consistent with theoretical models for disordered graphene ribbons with a dimensionless scattering strength $K_0 \approx 10$ corresponding to rather strong disorder. Close to charge neutrality, an increase in $F$ up to $\sim 0.7$ is found, which indicates the presence of a dominant Coulomb gap possibly due to a single quantum dot in the transport gap., Comment: 5 pages, 5 figures

There exist two popular energy-momentum tensors for an electromagnetic wave in a dielectric medium. The Abraham expression is robust to experimental verification but more mathematically demanding, while the Minkowski expression is the foundation of a number of simplifications commonly found within the literature, including the relative refractive index transformation often used in modelling optical tweezers. These simplifications are based on neglecting the Minkowski tensor's material counterpart, a process known to be incompatible with conservation of angular momentum, and in conflict with experimental results, yet they are very successful in a wide range of circumstances. This paper combines existing constraints on their usage with recent theoretical analysis to obtain a list of conditions which much be satisfied to safely use the simplified Minkowski approach. Applying these conditions to an experiment proposed by Padgett et al., we find their prediction in agreement with that obtained using the total energy-momentum tensor., Comment: 8 pages, RevTeX 4. Removed an erroneous factor of mu/mu_0 from Eq.(1)

The optical forces in optical tweezers can be robustly modeled over a broad range of parameters using generalsed Lorenz-Mie theory. We describe the procedure, and show how the combination of experimental measurement of properties of the trap coupled with computational modeling, can allow unknown parameters of the particle - in this case, the refractive index - to be determined., Comment: 5 pages, 4 figures, presented at 17th AIP Congress, Brisbane, 2006

Project-based assessment, in the form of take-home exams, was trialed in an honours/masters level electromagnetic theory course. This assessment formed an integral part of the learning experience of the students, and students felt that this was effective method of learning., Comment: 5 pages, no figures, presented at 17th AIP Congress, Brisbane, 2006

Particles that can be trapped in optical tweezers range from tens of microns down to tens of nanometres in size. Interestingly, this size range includes large macromolecules. We show experimentally, in agreement with theoretical expectations, that optical tweezers can be used to manipulate single molecules of polyethylene oxide suspended in water. The trapped molecules accumulate without aggregating, so this provides optical control of the concentration of macromolecules in solution. Apart from possible applications such as the micromanipulation of nanoparticles, nanoassembly, microchemistry, and the study of biological macromolecules, our results also provide insight into the thermodynamics of optical tweezers., Comment: 5 pages, 3 figures, presented at 17th AIP Congress, Brisbane, 2006

The successful development and optimisation of optically-driven micromachines will be greatly enhanced by the ability to computationally model the optical forces and torques applied to such devices. In principle, this can be done by calculating the light-scattering properties of such devices. However, while fast methods exist for scattering calculations for spheres and axisymmetric particles, optically-driven micromachines will almost always be more geometrically complex. Fortunately, such micromachines will typically possess a high degree of symmetry, typically discrete rotational symmetry. Many current designs for optically-driven micromachines are also mirror-symmetric about a plane. We show how such symmetries can be used to reduce the computational time required by orders of magnitude. Similar improvements are also possible for other highly-symmetric objects such as crystals. We demonstrate the efficacy of such methods by modelling the optical trapping of a cube, and show that even simple shapes can function as optically-driven micromachines., Comment: 5 pages, 2 figures, presented at 17th AIP Congress, Brisbane, 2006

Computational methods for electromagnetic and light scattering can be used for the calculation of optical forces and torques. Since typical particles that are optically trapped or manipulated are on the order of the wavelength in size, approximate methods such as geometric optics or Rayleigh scattering are inapplicable, and solution or either the Maxwell equations or the vector Helmholtz equation must be resorted to. Traditionally, such solutions were only feasible for the simplest geometries; modern computational power enable the rapid solution of more general--but still simple--geometries such as axisymmetric, homogeneous, and isotropic scatterers. However, optically-driven micromachines necessarily require more complex geometries, and their computational modelling thus remains in the realm of challenging computational problems. We review our progress towards efficient computational modelling of optical tweezers and micromanipulation, including the trapping and manipulation of complex structures such as optical micromachines. In particular, we consider the exploitation of symmetry in the modelling of such devices., Comment: 5 pages, 4 figures

What we believe to be a new type of resonant coupling of an incident bulk wave into guided modes of a slab with a thick holographic grating is shown to occur in the presence of strong frequency detunings of the Bragg condition. This happens through the reflection of the strongly noneigen +1 diffracted order with the slab-grating boundaries, the resultant reflected waves forming a guided slab mode. Rigorous coupled-wave analysis is used for the numerical analysis of the predicted resonant effects. Possible applications include enhanced options for the design of multiplexing and demultiplexing systems, optical signal-processing devices, optical sensors, and measurement techniques., Comment: 9 pages, 6 figures

Extremely asymmetrical scattering (EAS) is an unusual type of Bragg scattering in slanted periodic gratings with the scattered wave (the +1 diffracted order) propagating parallel to the grating boundaries. Here, a unique and strong sensitivity of EAS to small stepwise variations of mean structural parameters at the grating boundaries is predicted theoretically (by means of approximate and rigorous analyses) for bulk TE electromagnetic waves and slab optical modes of arbitrary polarization in holographic (for bulk waves) and corrugation (for slab modes) gratings. The predicted effects are explained using one of the main physical reasons for EAS--the diffractional divergence of the scattered wave (similar to divergence of a laser beam). The approximate method of analysis is based on this understanding of the role of the divergence of the scattered wave, while the rigorous analysis uses the enhanced T-matrix algorithm. The effect of small and large stepwise variations of the mean permittivity at the grating boundaries is analysed. Two distinctly different and unusual patterns of EAS are predicted in the cases of wide and narrow (compared to a critical width) gratings. Comparison between the approximate and rigorous theories is carried out., Comment: 16 pages, 5 figures

Extremely asymmetrical scattering (EAS) is a new type of Bragg scattering in thick, slanted, periodic gratings. It is realised when the scattered wave propagates parallel to the front boundary of the grating. Its most important feature is the strong resonant increase in the scattered wave amplitude compared to the amplitude of the incident wave: the smaller the grating amplitude, the larger the amplitude of the scattered wave. In this paper, rigorous numerical analysis of EAS is carried out by means of the enhanced T-matrix algorithm. This includes investigation of harmonic generation inside and outside the grating, unusually strong edge effects, fast oscillations of the incident wave amplitude in the grating, etc. Comparison with the previously developed approximate theory is carried out. In particular, it is demonstrated that the applicability conditions for the two-wave approximation in the case of EAS are noticeably more restrictive than those for the conventional Bragg scattering. At the same time, it is shown that the approximate theory is usually highly accurate in terms of description of EAS in the most interesting cases of scattering with strong resonant increase of the scattered wave amplitude. Physical explanation of the predicted effects is presented., Comment: 14 pages, 7 figures; v2: corrections to metadata and bibliographical info in preprint

Grazing-angle scattering (GAS) is a type of Bragg scattering of waves in slanted non-uniform periodic gratings, when the diffracted order satisfying the Bragg condition propagates at a grazing angle with respect to the boundaries of a slab-like grating. Rigorous analysis of GAS of bulk TE electromagnetic waves is undertaken in holographic gratings by means of the enhanced T-matrix algorithm. A comparison of the rigorous and the previously developed approximate theories of GAS is carried out. A complex pattern of numerous previously unknown resonances is discovered and analysed in detail for gratings with large amplitude, for which the approximate theory fails. These resonances are associated not only with the geometry of GAS, but are also typical for wide transmitting gratings. Their dependence on grating amplitude, angles of incidence and scattering, and grating width is investigated numerically. Physical interpretation of the predicted resonances is linked to the existence and the resonant generation of special new eigenmodes of slanted gratings. Main properties of these modes and their field structure are discussed., Comment: 21 pages, 13 figures

A highly unusual pattern of strong multiple resonances for bulk electromagnetic waves is predicted and analysed numerically in thick periodic holographic gratings in a slab with the mean permittivity that is larger than that of the surrounding media. This pattern is shown to exist in the geometry of grazing-angle scattering (GAS), that is when the scattered wave (+1 diffracted order) in the slab propagates almost parallel to the slab (grating) boundaries. The predicted resonances are demonstrated to be unrelated to resonant generation of the conventional guided modes of the slab. Their physical explanation is associated with resonant generation of a completely new type of eigenmodes in a thick slab with a periodic grating. These new slab eigenmodes are generically related to the grating; they do not exist if the grating amplitude is zero. The field structure of these eigenmodes and their dependence on structural and wave parameters is analysed. The results are extended to the case of GAS of guided modes in a slab with a periodic groove array of small corrugation amplitude and small variations in the mean thickness of the slab at the array boundaries., Comment: 16 pages, 6 figures

We have measured the influence of shot noise on hysteretic Josephson junctions initially in macroscopic quantum tunnelling (MQT) regime. Escape threshold current into the resistive state decreases monotonically with increasing average current through the scattering conductor, which is another tunnel junction. Escape is predominantly determined by excitation due to the wide-band shot noise. This process is equivalent to thermal activation (TA) over the barrier at temperatures up to about four times above the critical temperature of the superconductor. The presented TA model is in excellent agreement with the experimental results.

We have investigated the dynamics of underdamped Josephson junctions. In addition to the usual crossover between macroscopic quantum tunnelling and thermally activated (TA) behaviour we observe in our samples with relatively small Josephson coupling E_J, for the first time, the transition from TA behaviour to underdamped phase diffusion. Above the crossover temperature the threshold for switching into the finite voltage state becomes extremely sharp. We propose a (T,E_J) phase-diagram with various regimes and show that for a proper description of it dissipation and level quantization in a metastable well are crucial., Comment: 4 pages, 3 figures

We concentrate on the forces and torques exerted on transparent and absorbing particles trapped in laser beams containing optical vortices. We review previous theoretical and experimental work and then present new calculations of the effect of vortex beams on absorbing particles., Comment: 32 pages, 9 figures

This paper analyses theoretically and numerically the effect of varying grating amplitude on the extremely asymmetrical scattering (EAS) of bulk and guided optical modes in non-uniform strip-like periodic Bragg arrays with stepwise and gradual variations in the grating amplitude across the array. A recently developed new approach based on allowance for the diffractional divergence of the scattered wave is used for this analysis. It is demonstrated that gradual variations in magnitude of the grating amplitude may change the pattern of EAS noticeably but not radically. On the other hand, phase variations in the grating may result in a radically new type of Bragg scattering - double-resonant EAS (DEAS). In this case, a combination of two strong simultaneous resonances (one with respect to frequency, and another with respect to the phase variation) is predicted to take place in non-uniform arrays with a step-like phase and gradual magnitude variations of the grating amplitude. The tolerances of EAS and DEAS to small gradual variations in the grating amplitude are determined. The main features of these types of scattering in non-uniform arrays are explained by the diffractional divergence of the scattered wave inside and outside the array., Comment: 13 pages, 10 figures

Radiation pressure forces in a focussed laser beam can be used to trap microscopic absorbing particles against a substrate. Calculations based on momentum transfer considerations show that stable trapping occurs before the beam waist, and that trapping is more effective with doughnut beams. Such doughnut beams can transfer angular momentum leading to rotation of the trapped particles. Energy is also transferred, which can result in heating of the particles to temperatures above the boiling point of the surrounding medium., Comment: 13 pages, 11 figures

Two strong simultaneous resonances of scattering--double-resonant extremely asymmetrical scattering (DEAS)--are predicted in two parallel, oblique, periodic Bragg arrays separated by a gap, when the scattered wave propagates parallel to the arrays. One of these resonances is with respect to frequency (which is common to all types of Bragg scattering), and another is with respect to phase variation between the arrays. The diffractional divergence of the scattered wave is shown to be the main physical reason for DEAS in the considered structure. Although the arrays are separated, they are shown to interact by means of the diffractional divergence of the scattered wave across the gap from one array into the other. It is also shown that increasing separation between the two arrays results in a broader and weaker resonance with respect to phase shift. The analysis is based on a recently developed new approach allowing for the diffractional divergence of the scattered wave inside and outside the arrays. Physical interpretations of the predicted features of DEAS in separated arrays are also presented. Applicability conditions for the developed theory are derived., Comment: 8 pages, 5 figures

We show theoretically and demonstrate experimentally that highly absorbing particles can be trapped and manipulated in a single highly focused Gaussian beam. Our studies of the effects of polarized light on such particles show that they can be set into rotation by elliptically polarized light and that both the sense and the speed of their rotation can be smoothly controlled., Comment: 3 pages, 3 figures

Light-induced rotation of absorbing microscopic particles by transfer of angular momentum from light to the material raises the possibility of optically driven micromachines. The phenomenon has been observed using elliptically polarized laser beams or beams with helical phase structure. But it is difficult to develop high power in such experiments because of overheating and unwanted axial forces, limiting the achievable rotation rates to a few hertz. This problem can in principle be overcome by using transparent particles, transferring angular momentum by a mechanism first observed by Beth in 1936, when he reported a tiny torque developed in a quartz waveplate due to the change in polarization of transmitted light. Here we show that an optical torque can be induced on microscopic birefringent particles of calcite held by optical tweezers. Depending on the polarization of the incident beam, the particles either become aligned with the plane of polarization (and thus can be rotated through specified angles) or spin with constant rotation frequency. Because these microscopic particles are transparent, they can be held in three-dimensional optical traps at very high power without heating. We have observed rotation rates in excess of 350 Hz., Comment: 4 pages, 4 figures

Optical tweezers are widely used for the manipulation of cells and their internal structures. However, the degree of manipulation possible is limited by poor control over the orientation of trapped cells. We show that it is possible to controllably align or rotate disc shaped cells - chloroplasts of Spinacia oleracea - in a plane polarised Gaussian beam trap, using optical torques resulting predominantly from circular polarisation induced in the transmitted beam by the non-spherical shape of the cells., Comment: 9 pages, 6 figures

Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised Lorenz-Mie theory (GLMT). In general, it is theoretically straightforward to find a vector spherical wavefunction representation of an arbitrary radiation field. For example, a simple formula results in the useful case of an incident plane wave. Laser beams present some difficulties. These problems are not a result of any deficiency in the basic process of spherical wavefunction expansion, but are due to the fact that laser beams, in their standard representations, are not radiation fields, but only approximations of radiation fields. This results from the standard laser beam representations being solutions to the paraxial scalar wave equation. We present an efficient method for determining the multipole representation of an arbitrary focussed beam., Comment: 13 pages, 7 figures

The T-matrix method is widely used for the calculation of scattering by particles of sizes on the order of the illuminating wavelength. Although the extended boundary condition method (EBCM) is the most commonly used technique for calculating the T-matrix, a variety of methods can be used. We consider some general principles of calculating T-matrices, and apply the point-matching method to calculate the T-matrix for particles devoid of symmetry. This method avoids the time-consuming surface integrals required by the EBCM., Comment: 10 pages. 2 figures, 1 table

Optical trapping, where microscopic particles are trapped and manipulated by light is a powerful and widespread technique, with the single-beam gradient trap (also known as optical tweezers) in use for a large number of biological and other applications. The forces and torques acting on a trapped particle result from the transfer of momentum and angular momentum from the trapping beam to the particle. Despite the apparent simplicity of a laser trap, with a single particle in a single beam, exact calculation of the optical forces and torques acting on particles is difficult. Calculations can be performed using approximate methods, but are only applicable within their ranges of validity, such as for particles much larger than, or much smaller than, the trapping wavelength, and for spherical isotropic particles. This leaves unfortunate gaps, since wavelength-scale particles are of great practical interest because they are readily and strongly trapped and are used to probe interesting microscopic and macroscopic phenomena, and non-spherical or anisotropic particles, biological, crystalline, or other, due to their frequent occurance in nature, and the possibility of rotating such objects or controlling or sensing their orientation. The systematic application of electromagnetic scattering theory can provide a general theory of laser trapping, and render results missing from existing theory. We present here calculations of force and torque on a trapped particle obtained from this theory and discuss the possible applications, including the optical measurement of the force and torque., Comment: 10 pages, 5 figures

In recent years there has been an explosive development of interest in the measurement of forces at the microscopic level, such as within living cells, as well as the properties of fluids and suspensions on this scale, using optically trapped particles as probes. The next step would be to measure torques and associated rotational motion. This would allow measurement on very small scales since no translational motion is needed. It could also provide an absolute measurement of the forces holding a stationary non-rotating particle in place. The laser-induced torque acting on an optically trapped microscopic birefringent particle can be used for these measurements. Here we present a new method for simple, robust, accurate, simultaneous measurement of the rotation speed of a laser trapped birefringent particle, and the optical torque acting on it, by measuring the change in angular momentum of the light from passing through the particle. This method does not depend on the size or shape of the particle or the laser beam geometry, nor does it depend on the properties of the surrounding medium. This could allow accurate measurement of viscosity on a microscopic scale., Comment: 9 pages, 2 figures

Optical trapping is a widely used technique, with many important applications in biology and metrology. Complete modelling of trapping requires calculation of optical forces, primarily a scattering problem, and non-optical forces. The T-matrix method is used to calculate forces acting on spheroidal and cylindrical particles., Comment: 4 pages, 4 figures

The calculation of expected spectral line strengths and profiles is a powerful tool for the analysis of the solar atmosphere, and other stellar atmospheres. We present here a recipe in seven easy steps for the development of such spectral synthesis software., Comment: 4 pages, 1 figure, 1 table