arXiv subjects

N. R. Heckenberg

Publications and source records attributed to N. R. Heckenberg.

At least 19 recordsLinked to original sources

arXiv2009

Observation of shock waves in a large Bose-Einstein condensate

We observe the formation of shock waves in a Bose-Einstein condensate containing a large number of sodium atoms. The shock wave is initiated with a repulsive, blue-detuned light barrier, intersecting the BEC, after which two shock fronts appear. We observe breaking of these waves when the size of these waves approaches the healing length of the condensate. At this time, the wave front splits into two parts and clear fringes appear. The experiment is modeled using an effective 1D Gross-Pitaevskii-like equation and gives excellent quantitative agreement with the experiment, even though matter waves with wavelengths two orders of magnitude smaller than the healing length are present. In these experiments, no significant heating or particle loss is observed.

cond-mat.quant-gas↗

arXiv2009

Constraining Validity of the Minkowski Energy-Momentum Tensor

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.

physics.class-ph↗

arXiv2008

T-matrix calculation via discrete-dipole approximation, point matching and exploiting symmetry

We present a method of incorporating the discrete dipole approximation (DDA) method with the point matching method to formulate the T-matrix for modeling arbitrarily shaped micro-sized objects. The \emph{T}-matrix elements are calculated using point matching between fields calculated using vector spherical wave functions and DDA. When applied to microrotors, their discrete rotational and mirror symmetries can be exploited to reduce memory usage and calculation time by orders of magnitude; a number of optimization methods can be employed based on the knowledge of the relationship between the azimuthal mode and phase at each discrete rotational point, and mode redundancy from Floquet's theorem. A 'reduced-mode' T-matrix can also be calculated if the illumination conditions are known.

physics.optics↗

arXiv2008

Versatile two-dimensional potentials for ultra-cold atoms

We propose and investigate a technique for generating smooth two-dimensional potentials for ultra-cold atoms based on the rapid scanning of a far-detuned laser beam using a two-dimensional acousto-optical modulator (AOM). We demonstrate the implementation of a feed-forward mechanism for fast and accurate control of the spatial intensity of the laser beam, resulting in improved homogeneity for the atom trap. This technique could be used to generate a smooth toroidal trap that would be useful for static and dynamic experiments on superfluidity and persistent currents with ultra-cold atoms.

physics.atom-ph↗

arXiv2007

Optical trapping of a cube

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.

physics.optics↗

arXiv2007

Nanotrapping and the thermodynamics of optical tweezers

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.

physics.optics↗

arXiv2007

Forces from highly focused laser beams: modeling, measurement and application to refractive index measurements

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.

physics.optics↗

arXiv2006

Towards efficient modelling of optical micromanipulation of complex structures

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.

physics.optics↗

arXiv2006

Atom counting in ultra-cold gases using photoionisation and ion detection

We analyse photoionisation and ion detection as a means of accurately counting ultra-cold atoms. We show that it is possible to count clouds containing many thousands of atoms with accuracies better than $N^{-1/2}$ with current technology. This allows the direct probing of sub-Poissonian number statistics of atomic samples. The scheme can also be used for efficient single atom detection with high spatio-temporal resolution. All aspects of a realistic detection scheme are considered, and we discuss experimental situations in which such a scheme could be implemented.

cond-mat.other↗

arXiv2006

Fringe spacing and phase of interfering matter waves

We experimentally investigate the outcoupling of atoms from Bose-Einstein condensates using two radio-frequency (rf) fields in the presence of gravity. We show that the fringe separation in the resulting interference pattern derives entirely from the energy difference between the two rf fields and not the gravitational potential difference. We subsequently demonstrate how the phase and polarisation of the rf radiation directly control the phase of the matter wave interference and provide a semi-classical interpretation of the results.

cond-mat.other↗

arXiv2004

Foil-based atom chip for Bose-Einstein condensates

We describe a novel method of fabricating atom chips that are well suited to the production and manipulation of atomic Bose-Einstein condensates. Our chip was created using a silver foil and simple micro-cutting techniques without the need for photolithography. It can sustain larger currents than conventional chips, and is compatible with the patterning of complex trapping potentials. A near pure Bose-Einstein condensate of 4 $\times$ 10$^4$ $^{87}$Rb atoms has been created in a magnetic microtrap formed by currents through wires on the chip. We have observed the fragmentation of atom clouds in close proximity to the silver conductors. The fragmentation has different characteristic features to those seen with copper conductors.

cond-mat.other↗

arXiv2003

Mechanical effects of optical vortices

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.

physics.optics↗

arXiv2003

Optical trapping of absorbing particles

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.

physics.optics↗

arXiv2003

Optical torque controlled by elliptical polarization

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.

physics.optics↗

arXiv2003

Calculation and optical measurement of laser trapping forces on non-spherical particles

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.

physics.optics↗

arXiv2003

Multipole expansion of strongly focussed laser beams

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.

physics.optics↗

arXiv2003

Calculation of the T-matrix: general considerations and application of the point-matching method

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.

physics.optics↗

arXiv2003

Optical alignment and spinning of laser-trapped microscopic particles

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.

physics.optics↗