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Abstract

Two methods of quantifying the spatial resolution of a camera are described, performed, and compared, with the objective of designing an imaging-system experiment for students in an undergraduate optics laboratory. With the goal of characterizing the resolution of a typical digital single-lens reflex (DSLR) camera, we motivate, introduce, and show agreement between traditional test-target contrast measurements and the technique of using Fourier analysis to obtain the modulation transfer function (MTF). The advantages and drawbacks of each method are compared. Finally, we explore the rich optical physics at work in the camera system by calculating the MTF as a function of wavelength and f-number. For example, we find that the Canon 40D demonstrates better spatial resolution at short wavelengths, in accordance with scalar diffraction theory, but is not diffraction-limited, being significantly affected by spherical aberration. The experiment and data analysis routines described here can be built and written in an undergraduate optics lab setting.

Abstract

We report on the design, construction, and characterisation of a new class of in-vacuo optical levitation trap optimised for use in high-intensity, high-energy laser interaction experiments. The system uses a focused, vertically propagating continuous wave laser beam to capture and manipulate micro-targets by photon momentum transfer at much longer working distances than commonly used by optical tweezer systems. A high speed (10 kHz) optical imaging and signal acquisition system was implemented for tracking the levitated droplets position and dynamic behaviour under atmospheric and vacuum conditions, with ±5 μm spatial resolution. Optical trapping of 10 ± 4 μm oil droplets in vacuum was demonstrated, over timescales of >1 h at extended distances of ~40 mm from the final focusing optic. The stability of the levitated droplet was such that it would stay in alignment with a ~7 μm irradiating beam focal spot for up to 5 min without the need for re-adjustment. The performance of the trap was assessed in a series of high-intensity (\(10^{17}\) W cm) laser experiments that measured the X-ray source size and inferred free-electron temperature of a single isolated droplet target, along with a measurement of the emitted radio-frequency pulse. These initial tests demonstrated the use of optically levitated microdroplets as a robust target platform for further high-intensity laser interaction and pointsourcestudies.

Abstract

We present a microfabricated surface-electrode ion trap with a pair of integrated waveguides that generate a standing microwave field resonant with the 171Yb+ hyperfine qubit. The waveguides are engineered to position the wave antinode near the center of the trap, resulting in maximum field amplitude and uniformity along the trap axis. By calibrating the relative amplitudes and phases of the waveguide currents, we can control the polarization of the microwave field to reduce off-resonant coupling to undesired Zeeman sublevels. We demonstrate single-qubit π-rotations as fast as 1 μs with less than 6% variation in Rabi frequency over an 800 μm microwave interaction region. Fully compensating pulse sequences further improve the uniformity of X-gates across this interaction region.

Abstract

In heteroepitaxy, lattice mismatch between the deposited material and the underlying surface strongly affects nucleation and growth processes. The effect of mismatch is well studied in atoms with growth kinetics typically dominated by bond formation with interaction lengths on the order of one lattice spacing. In contrast, less is understood about how mismatch affects crystallization of larger particles, such as globular proteins and nanoparticles, where interparticle interaction energies are often comparable to thermal fluctuations and are short ranged, extending only a fraction of the particle size. Here, using colloidal experiments and simulations, we find particles with short-range attractive interactions form crystals on isotropically strained lattices with spacings significantly larger than the interaction length scale. By measuring the free-energy cost of dimer formation on monolayers of increasing uniaxial strain, we show the underlying mismatched substrate mediates an entropy-driven attractive interaction extending well beyond the interaction length scale. Remarkably, because this interaction arises from thermal fluctuations, lowering temperature causes such substrate- mediated attractive crystals to dissolve. Such counterintuitive results underscore the crucial role of entropy in heteroepitaxy in this technologically important regime. Ultimately, this entropic component of lattice mismatched crystal growth could be used to develop unique methods for heterogeneous nucleation and growth of single crystals for applications ranging from protein crystallization to controlling the assembly of nanoparticles into ordered, functional superstructures. In particular, the construction of substrates with spatially modulated strain profiles would exploit this effect to direct self-assembly, whereby nucleation sites and resulting crystal morphology can be controlled directly through modifications of the substrate.

Abstract

We present a simple cryostat purpose built for use with surface-electrode ion traps, designed around an affordable, large cooling power commercial pulse tube refrigerator. A modular vacuum enclosure with a single vacuum space facilitates interior access and enables rapid turnaround and flexibility for future modifications. Long rectangular windows provide nearly 360 degrees of optical access in the plane of the ion trap, while a circular bottom window near the trap enables NA 0.4 light collection without the need for in-vacuum optics. We evaluate the system's mechanical and thermal characteristics and we quantify ion trapping performance by trapping 40Ca+, finding small stray electric fields, long ion lifetimes, and low ion heating rates.

Abstract

A definition of quantum singularity for the case of static spacetimes has has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed and then applied to a class of spherically symmetric, conformally static spacetimes, including as special cases those studied by Roberts, by Fonarev, and by Husain et al. We use solutions of the generally coupled, massless Klein-Gordon equation as test fields. In this way we find the ranges of metric parameters and coupling coefficients for which classical timelike singularities in these spacetimes are healed quantum mechanically.

Abstract

We report the design, fabrication and characterization of a microfabricated surface-electrode ion trap that supports controlled transport through the two-dimensional intersection of linear trapping zones arranged in a 90° cross. The trap is fabricated with very large scalable integration techniques which are compatible with scaling to a large quantum information processor. The shape of the radio-frequency electrodes is optimized with a genetic algorithm to reduce axial pseudopotential barriers and minimize ion heating during transport. Seventy-eight independent dc control electrodes enable fine control of the trapping potentials. We demonstrate reliable ion transport between junction legs and determine the rate of ion loss due to transport. Doppler-cooled ions survive more than \( 10^5 \) round-trip transits between junction legs without loss and more than 65 consecutive round trips without laser cooling.

From the Cover…

.. epigraph:: “Townsend is the best book I know for advanced undergraduate quantum mechanics. It is clear, contemporary, and compact. My students used it as a wonderful springboard to graduate school.” -- Ralph D. Amado, University of Pennsylvania .. epigraph:: “With this second edition, Townsend has succeeded in making a clear and pedagogical textbook on undergraduate quantum mechanics even better.” -- Charles Gale, McGill University

Abstract

The role of petal spurs and specialized pollinator interactions has been studied since Darwin. Aquilegia petal spurs exhibit striking size and shape diversity, correlated with specialized pollinators ranging from bees to hawkmoths in a textbook example of adaptive radiation. Despite the evolutionary significance of spur length, remarkably little is known about Aquilegia spur morphogenesis and its evolution. Using experimental measurements, both at tissue and cellular levels, combined with numerical modelling, we have investigated the relative roles of cell divisions and cell shape in determining the morphology of the Aquilegia petal spur. Contrary to decades-old hypotheses implicating a discrete meristematic zone as the driver of spur growth, we find that Aquilegia petal spurs develop via anisotropic cell expansion. Furthermore, changes in cell anisotropy account for 99 per cent of the spur-length variation in the genus, suggesting that the true evolutionary innovation underlying the rapid radiation of Aquilegia was the mechanism of tuning cell shape.

Abstract

We study the primary root growth of wild-type Medicago truncatula plants in heterogeneous environments using 3D time-lapse imaging. The growth medium is a transparent hydrogel consisting of a stiff lower layer and a compliant upper layer. We find that the roots deform into a helical shape just above the gel layer interface before penetrating into the lower layer. This geometry is interpreted as a combination of growth-induced mechanical buckling modulated by the growth medium and a simultaneous twisting near the root tip. We study the helical morphology as the modulus of the upper gel layer is varied and demonstrate that the size of the deformation varies with gel stiffness as expected by a mathematical model based on the theory of buckled rods. Moreover, we show that plant-to-plant variations can be accounted for by biomechanically plausible values of the model parameters.

Recent Publications

Student authorFaculty author

1. Calvin Leung and Thomas D. Donnelly, “Measuring the spatial resolution of an optical system in an undergraduate optics laboratory”, Am. J. Phys. 85 (2017) 429-438.
2. C. J. Price, Thomas D. Donnelly, S. Giltrap, N. H. Stuart, S. Parker, S. Patankar, H. F. Lowe, D. Drew, E. T. Gumbrell, and R. A. Smith, “An in-vacuo optical levitation trap for high-intensity laser interaction experiments with isolated microtargets”, Rev. Sci. Inst. 86 (2015) 033502.
3. C. M. Shappert, J. T. Merrill, K. R. Brown, J. M. Amini, C. Volin, S. C. Doret, H. Hayden, C. -S. Pai, K. R. Brown, and A. W. Harter, “Spatially uniform single-qubit gate operations with near-field microwaves and composite pulse compensation”, New J. Phys. 15 (2013) 083503.
4. John R. Savage, Stefan F. Hopp, Rajesh Ganapathy, Sharon J. Gerbode, Andreas Heuer, and I. Cohen, “Entropy-Driven Crystal Formation on Highly Strained Substrates”, PNAS 110 (2013) 9301-9304.
5. G. Vittorini, K. Wright, K. R. Brown, A. W. Harter, and S. C. Doret, “Modular cryostat for ion trapping with surface-electrode ion traps”, Rev. Sci. Inst. 84 (2013) 043112.
6. Thomas M. Helliwell and D. A. Konkowski, “Quantum singularities in spherically symmetric, conformally static spacetimes”, Phys. Rev. D 87 (2013) 104041.
7. K. Wright, J. M. Amini, D. L. Faircloth, C. Volin, S. C. Doret, H. Hayden, C. -S. Pai, D. W. Landgren, D. Denison, T. Killian, R. E. Slusher, and A. W. Harter, “Reliable transport through a microfabricated X-junction surface-electrode ion trap”, New J. Phys. 15 (2013) 033004.
8. John S. Townsend, A Modern Approach to Quantum Mechanics, Second Edition, University Science Books, Sausalito (2012).
9. L. Mahadevan, Sharon J. Gerbode, E. M. Kramer, S. A. Hodges, and J. R. Puzey, “Evolution of spur-length diversity in Aquilegia petals is achieved solely through cell-shape anisotropy”, Proc. R. Soc. B 273:1733 (2012) 1640.
10. J. L. Silverberg, R. N. Noar, M. Packer, M. Harrison, I. Cohen, C. Henley, and Sharon J. Gerbode, “3D Imaging and mechanical modeling of helical buckling in Medicago truncatula plant roots”, PNAS 109 (2012) 16794.