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.


When matter falls past the horizon of a large black hole, the expectation from string theory is that the configuration thermalizes and the information in the probe is rather quickly scrambled away. The traditional view of a classical unique spacetime near a black hole horizon conflicts with this picture. The question then arises as to what spacetime does the probe actually see as it crosses a horizon, and how does the background geometry imprint its signature onto the thermal properties of the probe. In this work, we explore these questions through an extensive series of numerical simulations of D0 branes. We determine that the D0 branes quickly settle into an incompressible symmetric state—thermalized within a few oscillations through a process driven entirely by internal nonlinear dynamics. Surprisingly, thermal background fluctuations play no role in this mechanism. Signatures of the background fields in this thermal state arise either through fluxes, i.e. black hole hair; or if the probe expands to the size of the horizon—which we see evidence of. We determine simple scaling relations for the D0 branes’ equilibrium size, time to thermalize, lifetime, and temperature in terms of their number, initial energy, and the background fields. Our results are consistent with the conjecture that black holes are the fastest scramblers as seen by matrix theory.


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.

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 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


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.


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.


A popular method for generating micron-sized aerosols is to submerge ultrasonic ( *ω* ~ MHz) piezoelectric oscillators in a water bath. The submerged oscillator atomizes the fluid, creating droplets with radii proportional to the wavelength of the standing wave at the fluid surface. Classical theory for the Faraday instability predicts a parametric instability driving a capillary wave at the subharmonic (*ω*/2) frequency. For many applications it is desirable to reduce the size of the droplets; however, using higher frequency oscillators becomes impractical beyond a few MHz. Observations are presented that demonstrate that smaller droplets may also be created by increasing the driving amplitude of the oscillator, and that this effect becomes more pronounced for large driving frequencies. It is shown that these observations are consistent with a transition from droplets associated with subharmonic ( *ω*/2) capillary waves to harmonic (*ω*) capillary waves induced by larger driving frequencies and amplitudes, as predicted by a stability analysis of the capillary waves.

Recent Publications

Student authorFaculty author


Jason Gallicchio and Matthew D Schwartz

Quark and gluon jet substructure

Journal of High Energy Physics 2013 (2013) .

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.
PDF document

Paul L. Riggins and Vatche Sahakian

Black hole thermalization, D0 brane dynamics, and emergent spacetime

Physical Review D 86 (2012) 046005.
PDF document

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.

John S. Townsend

A Modern Approach to Quantum Mechanics, Second Edition

University Science Books, Sausalito, 2012.

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.
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J. L. Silverberg, R. N. Noar, M. Packer, M. Harrison, I. Cohen, C. Henley, and Sharon Gerbode

3D Imaging and mechanical modeling of helical buckling in Medicago truncatula plant roots

Proceedings of the National Academy of Sciences 109 (2012) 16794.
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Sharon Gerbode, Joshua R. Puzey, A. G. McCormick, and L. Mahadevan

How the cucumber tendril coils and overwinds

Science 337 (2012) 1087.
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Andrew P. Higginbotham, Andrew J. Bernoff, Aaron M. Guillen, Thomas D. Donnelly, and Nathan Jones

Evidence of the harmonic Faraday instability in ultrasonic atomization experiments with a deep, inviscid fluid

Journal of the Acoustical Society of America 130 (2011) 2694-2699.
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Jason Gallicchio and Matthew D Schwartz

Pure samples of quark and gluon jets at the LHC

Journal of High Energy Physics 2011 (2011) .