### 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

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 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

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.

### Abstract

We derive criteria for whether two cosmological events can have a shared causal past or a shared causal future, assuming a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe with best-fit cosmological parameters from the Planck satellite. We further derive criteria for whether either cosmic event could have been in past causal contact with our own worldline since the time of the hot “big bang,” which we take to be the end of early-universe inflation. We find that pairs of objects such as quasars on opposite sides of the sky with redshifts $$z \ge 3.65$$ have no shared causal past with each other or with our past worldline. More complicated constraints apply if the objects are at different redshifts from each other or appear at some relative angle less than 180°, as seen from Earth. We present examples of observed quasar pairs that satisfy all, some, or none of the criteria for past causal independence. Given dark energy and the recent accelerated expansion, our observable Universe has a finite conformal lifetime, and hence a cosmic event horizon at current redshift $$z = 1.87$$. We thus constrain whether pairs of cosmic events can signal each other’s worldlines before the end of time. Lastly, we generalize the criteria for shared past and future causal domains for FLRW universes with nonzero spatial curvature.

### Abstract

We experimentally study the ghost critical field (GCF), a magnetic field scale for the suppression of superconducting fluctuations, using Hall effect and magnetoresistance measurements on a disordered superconducting thin film near its transition temperature $$T_c$$. We observe an increase in the Hall effect with a maximum in field that tracks the upper critical field below $$T_c$$, vanishes near $$T_c$$, and returns to higher fields above $$T_c$$. Such a maximum has been observed in studies of the Nernst effect and identified as the GCF. Magnetoresistance measurements near Tc indicate quenching of superconducting fluctuations, agree with established theoretical descriptions, and allow us to extract the GCF and other parameters. Above $$T_c$$, the Hall peak field is quantitatively distinct from the GCF, and we contrast this finding with ongoing studies of the Nernst effect and superconducting fluctuations in unconventional and thin-film superconductors.

### Abstract

Recent advances in quantum information processing with trapped ions have demonstrated the need for new ion trap architectures capable of holding and manipulating chains of many (>10) ions. Here we present the design and detailed characterization of a new linear trap, microfabricated with scalable complementary metal-oxide-semiconductor (CMOS) techniques, that is well-suited to this challenge. Forty-four individually controlled dc electrodes provide the many degrees of freedom required to construct anharmonic potential wells, shuttle ions, merge and split ion chains, precisely tune secular mode frequencies, and adjust the orientation of trap axes. Microfabricated capacitors on dc electrodes suppress radio-frequency pickup and excess micromotion, while a top-level ground layer simplifies modeling of electric fields and protects trap structures underneath. A localized aperture in the substrate provides access to the trapping region from an oven below, permitting deterministic loading of particular isotopic/elemental sequences via species-selective photoionization. The shapes of the aperture and radio-frequency electrodes are optimized to minimize perturbation of the trapping pseudopotential. Laboratory experiments verify simulated potentials and characterize trapping lifetimes, stray electric fields, and ion heating rates, while measurement and cancellation of spatially-varying stray electric fields permits the formation of nearly-equally spaced ion chains

### Abstract

We have studied the Hall effect in superconducting tantalum nitride films. We find a large contribution to the Hall conductivity near the superconducting transition, which we can track to temperatures well above $$T_c$$ and magnetic fields well above the upper critical field, $$\mathrm{H}_{c2}(0)$$. This contribution arises from Aslamazov-Larkin superconducting fluctuations, and we find quantitative agreement between our data and recent theoretical analysis based on time dependent Ginzburg-Landau theory.

### Abstract

The helical coiling of plant tendrils has fascinated scientists for centuries, yet the underlying mechanism remains elusive. Moreover, despite Darwin’s widely accepted interpretation of coiled tendrils as soft springs, their mechanical behavior remains unknown. Our experiments on cucumber tendrils demonstrate that tendril coiling occurs via asymmetric contraction of an internal fiber ribbon of specialized cells. Under tension, both extracted fiber ribbons and old tendrils exhibit twistless overwinding rather than unwinding, with an initially soft response followed by strong strain-stiffening at large extensions. We explain this behavior using physical models of prestrained rubber strips, geometric arguments, and mathematical models of elastic filaments. Collectively, our study illuminates the origin of tendril coiling, quantifies Darwin’s original proposal, and suggests designs for biomimetic twistless springs with tunable mechanical responses.

#### 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

# Recent Publications

Student authorFaculty author

41. John R. Savage, Stefan F. Hopp, Rajesh Ganapathy, Sharon Gerbode, Andreas Heuer, and I. Cohen Entropy-Driven Crystal Formation on Highly Strained Substrates Proceedings of the National Academy of Sciences 110 (2013) 9301-9304. Thomas Helliwell and D. A. Konkowski Quantum singularities in spherically symmetric, conformally static spacetimes Physical Review D 87 (2013) 104041. C. M. Shappert, J. T. Merrill, K. R. Brown, J. M. Amini, C. Volin, Charlie 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 Journal of Physics 15 (2013) 083503. K. Wright, J. M. Amini, D. L. Faircloth, C. Volin, Charlie 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 Journal of Physics 15 (2013) 033004. Andrew S Friedman, David I Kaiser, and Jason Gallicchio The shared causal pasts and futures of cosmological events Physical Review D 88 (2013) . Nicholas P. Breznay and Aharon Kapitulnik Observation of the ghost critical field for superconducting fluctuations in a disordered TaN thin film Physical Review B 88 (2013) 223. Charlie Doret, J. M. Amini, K. Wright, C. Volin, T. Killian, A. Ozakin, D. Denison, H. Hayden, C. -S. Pai, R. E. Slusher, and A. W. Harter Controlling trapping potentials and stray electric fields in a microfabricated ion trap through design and compensation New Journal of Physics 14 (2012) 073012. Nicholas P. Breznay, Karen Michaeli, Konstantin S Tikhonov, Alexander M Finkel'stein, Mihir Tendulkar, and Aharon Kapitulnik Hall conductivity dominated by fluctuations near the superconducting transition in disordered thin films Physical Review B 86 (2012) 014514. Sharon Gerbode, Joshua R. Puzey, A. G. McCormick, and L. Mahadevan How the cucumber tendril coils and overwinds Science 337 (2012) 1087. John S. Townsend A Modern Approach to Quantum Mechanics, Second Edition University Science Books, Sausalito, 2012.