Mason, D.J., Borunda, M.F. & Heller, E.J. Semiclassical deconstruction of quantum states in graphene. Physical Review B 88, 165421 (2013). Publisher's VersionAbstract

We present a method for bridging the gap between the Dirac effective field theory and atomistic simulations in graphene based on the Husimi projection, allowing us to depict phenomena in graphene at arbitrary scales. This technique takes the atomistic wave function as an input, and produces semiclassical pictures of quasiparticles in the two Dirac valleys. We use the Husimi technique to produce maps of the scattering behavior of boundaries, giving insight into the properties of wave functions at energies both close to and far from the Dirac point. Boundary conditions play a significant role to the rise of Fano resonances, which we examine using the processed Husimi map to deepen our understanding of bond currents near resonance.

Räsänen, E., Blasi, T., Borunda, M.F. & Heller, E.J. Optical control of entangled states in semiconductor quantum wells. Phys. Rev. B 86, 205308 (2012). Publisher's VersionAbstract

We present theory and calculations for coherent high-fidelity quantum control of many-particle states in semiconductor quantum wells. We show that coupling a two-electron double quantum dot to a terahertz optical source enables targeted excitations that are one to two orders of magnitude faster and significantly more accurate than those obtained with electric gates. The optical fields subject to physical constraints are obtained through quantum optimal control theory that we apply in conjunction with the numerically exact solution of the time-dependent Schrödinger equation. Our ability to coherently control arbitrary two-electron states, and to maximize the entanglement, opens up further perspectives in solid-state quantum information.

Li, Z. & Heller, E.J. Cold collisions of complex polyatomic molecules. The Journal of chemical physics 136, 054306 (2012). Publisher's VersionAbstract



Ruiz, A., Palao, J.P. & Heller, E.J. The activation of classical vibro-rotational resonances in diatom molecules through slow collision processes. Physics Letters A 375, 2555–2562 (2011). Publisher's VersionAbstract

Classical atom–diatom collisions at low velocities can be considered as a transient perturbation to the (integrable) diatomic system. We present an analysis that makes explicit the contributions of the terms of the Fourier expansion of the interaction potential to the changes in the molecular actions due to the collision process. Each term is associated with a resonance condition between the vibrational and rotational molecular frequencies, and leads to a vibrational, rotational or vibrotational contribution to the total action changes. The analysis is applied to the system View the MathML sourcesingle bondNe.

Mason, D.J., Prendergast, D., Neaton, J.B. & Heller, E.J. Algorithm for efficient elastic transport calculations for arbitrary device geometries. Physical Review B 84, 155401 (2011). Publisher's VersionAbstract

With the growth in interest in graphene, controlled nanoscale device geometries with complex form factors are now being studied and characterized. There is a growing need to understand new techniques to handle efficient electronic transport calculations for these systems. We present an algorithm that dramatically reduces the computational time required to find the local density of states and transmission matrix for open systems regardless of their topology or boundary conditions. We argue that the algorithm, which generalizes the recursive Green's function method by incorporating the reverse Cuthill-McKee algorithm for connected graphs, is ideal for calculating transmission through devices with multiple leads of unknown orientation and becomes a computational necessity when the input and output leads overlap in real space. This last scenario takes the Landauer-Buttiker formalism to general scattering theory in a computational framework that makes it tractable to perform full-spectrum calculations of the quantum scattering matrix in mesoscopic systems. We demonstrate the efficacy of these approaches on graphene stadiums, a system of recent scientific interest, and contribute to a physical understanding of Fano resonances which appear in these systems.

Borunda, M.F., Berezovsky, J., Westervelt, R.M. & Heller, E.J. Imaging Universal Conductance Fluctuations in Graphene. ACS nano 5, 3622–3627 (2011). Publisher's VersionAbstract

We study conductance fluctuations (CF) and the sensitivity of the conductance to the motion of a single scatterer in two-dimensional massless Dirac systems. Our extensive numerical study finds limits to the predicted universal value of CF. We find that CF are suppressed for ballistic systems near the Dirac point and approach the universal value at sufficiently strong disorder. The conductance of massless Dirac fermions is sensitive to the motion of a single scatterer. CF of order e2/h result from the motion of a single impurity by a distance comparable to the Fermi wavelength. This result applies to graphene systems with a broad range of impurity strength and concentration while the dependence on the Fermi wavelength can be explored via gate voltages. Our prediction can be tested by comparing graphene samples with varying amounts of disorder and can be used to understand interference effects in mesoscopic graphene devices.

Qian, J., Halperin, B.I. & Heller, E.J. Imaging and manipulating electrons in a one-dimensional quantum dot with Coulomb blockade microscopy. Physical Review B 81, 125323 (2010). Publisher's VersionAbstract

Motivated by recent experiments by the Westervelt group, which used a mobile tip to probe the electronic state of a segmented nanowire, we calculate shifts in Coulomb blockade peak positions, as a function of tip location, which we term “Coulomb blockade microscopy.” We show that if the tip can be brought sufficiently close to the nanowire, one can distinguish a high-density electronic liquid state from a Wigner-crystal state by microscopy with a weak-tip potential. In the opposite limit of a strongly negative tip potential, the potential depletes the electronic density under it and divides the quantum wire into two partitions. There the tip can push individual electrons from one partition to the other and the Coulomb blockade micrograph can clearly track such transitions. We show that this phenomenon can be used to qualitatively estimate the relative importance of the electron interaction compared to one-particle potential and kinetic energies. Finally, we propose that a weak-tip Coulomb blockade micrograph focusing on the transition between electron number N=0 and N=1 states may be used to experimentally map the one-particle potential landscape produced by impurities and inhomogeneities.

Berezovsky, J., Borunda, M.F., Heller, E.J. & Westervelt, R.M. Imaging coherent transport in graphene (part I): mapping universal conductance fluctuations. Nanotechnology 21, 274013 (2010). Publisher's VersionAbstract

Graphene provides a fascinating testbed for new physics and exciting opportunities for future applications based on quantum phenomena. To understand the coherent flow of electrons through a graphene device, we employ a nanoscale probe that can access the relevant length scales—the tip of a liquid-He-cooled scanning probe microscope (SPM) capacitively couples to the graphene device below, creating a movable scatterer for electron waves. At sufficiently low temperatures and small size scales, the diffusive transport of electrons through graphene becomes coherent, leading to universal conductance fluctuations (UCF). By scanning the tip over a device, we map these conductance fluctuations versus scatterer position. We find that the conductance is highly sensitive to the tip position, producing δG ~ e2/h fluctuations when the tip is displaced by a distance comparable to half the Fermi wavelength. These measurements are in good agreement with detailed quantum simulations of the imaging experiment and demonstrate the value of a cooled SPM for probing coherent transport in graphene.

Sanders, S.N., Mintert, F. & Heller, E.J. Matter-wave scattering from ultracold atoms in an optical lattice. Physical review letters 105, 035301 (2010). Publisher's VersionAbstract

We study matter-wave scattering from an ultracold, many-body atomic system trapped in an optical lattice. The angular cross section of the target lattice for a matter wave is determined and is demonstrated to have a strong dependence on the many-body phase, superfluid, or Mott insulator. Analytical approaches are employed deep in the superfluid and Mott-insulator regimes, while intermediate points in the phase transition are treated numerically. Matter-wave scattering offers a convenient method for nondestructively probing the quantum many-body phase transition of atoms in an optical lattice.

Kramer, T., Krueckl, V., Heller, E.J. & Parrott, R.E. Self-consistent calculation of electric potentials in Hall devices. Physical Review B 81, 205306 (2010). Publisher's VersionAbstract

Using a first-principles classical many-body simulation of a Hall bar, we study the necessary conditions for the formation of the Hall potential: (i) Ohmic contacts with metallic reservoirs, (ii) electron-electron interactions, and (iii) confinement to a finite system. By propagating thousands of interacting electrons over million time-steps we capture the build-up of the self-consistent potential. The microscopic model sheds light on the current injection process and directly links the Hall effect to specific boundary conditions at the particle reservoirs.

Kramer, T., et al. Theory of the quantum Hall effect in finite graphene devices. Physical Review B 81, 081410 (2010). Publisher's VersionAbstract

We study the quantum Hall effect (QHE) in graphene based on the current injection model, which takes into account the finite rectangular geometry with source and drain electrodes. In our model, the presence of disorder, the edge-state picture, extended states, and localized states, which are believed to be indispensable ingredients in describing the QHE, do not play an important role. Instead the boundary conditions during the injection into the graphene sheet, which are enforced by the presence of the Ohmic contacts, determine the current-voltage characteristics.

Ruiz, A., Palao, J.P. & Heller, E.J. Classical and quantum analysis of quasiresonance in grazing atom-surface collisions. Physical Review A 79, 052901 (2009). Publisher's VersionAbstract

Quasiresonance is a general effect that may arise from the coupling between approximately resonant degrees of freedom in a system perturbed by some transient interaction. In a process induced by a slowly switching on and off of the coupling interaction, quasiresonance is characterized by the existence of significant ranges of initial states in the perturbed system over which some very specific and efficient transfer of energy between the approximately resonant degrees of freedom occurs. This work presents a classical and quantum analysis of quasiresonant processes in grazing incident angle atom-surface collisions. The momentum transfer between the normal components to an index direction is investigated. For fast atoms with grazing angle of incidence there is an interval of azimuthal angles around the index directions, the quasiresonance region, in which the energy transfer can be very efficient. This effect is reflected in quantum diffraction patterns with large nonspecular peaks, associated with the parallel to the surface and normal to the index direction momentum component. We demonstrate the essentially classical underlying mechanism for the persistence of a pattern of diffraction peak intensities for incidence close to an index direction. The analysis also shows that the size of the quasiresonance region is approximately equal to the spectral width of the diffraction pattern.

Sanders, S.N., Mintert, F. & Heller, E.J. Coherent scattering from a free gas. Physical Review A 79, 023610 (2009). Publisher's VersionAbstract

We investigate decoherence in atom interferometry due to scattering from a background gas and show that the supposition that residual coherence is due to near-forward scattering is incorrect. In fact, the coherent part is completely unscattered, although it is phase shifted. This recoil-free process leaves both the atom and the gas in an unchanged state, but allows for the acquisition of a phase shift. This is essential to understanding decoherence in a separated-arm atom interferometer, where a gas of atoms forms a refractive medium for a matter wave. Our work elucidates the actual microscopic, many-body, quantum-mechanical scattering mechanism that gives rise to prior phenomenological results for the phase shift and decoherence.

Ruiz, A., Palao, J.P. & Heller, E.J. Nearly resonant multidimensional systems under a transient perturbative interaction. Physical Review E 80, 066606 (2009). Publisher's VersionAbstract

We analyze the response of a classical system with N2 internal degrees of freedom satisfying R(N1) approximated resonance conditions to an external perturbative transient interaction. Under certain assumptions on the system internal frequencies and on the coupling interaction, we show the precise NR adiabatic invariants and obtain an estimate of the span of the domain defined by the intersecting resonances. The results are illustrated considering a system of three anharmonic oscillators transiently coupled by an explicitly time-dependent interaction, and applied to the low energy vibro-rotationally inelastic collisions between two diatomic molecules.

Landry, B.R., Wasserman, A. & Heller, E.J. Semiclassical Ground-State Energies of Many-Electron Systems. Physical review letters 103, 066401 (2009). Publisher's VersionAbstract

A new semiclassical method is proposed to obtain accurate ground-state energies for many-electron systems. The method borrows its semiclassical character from Thomas-Fermi (TF) theory, but improves upon it by including exchange-correlation effects, at least approximately. We illustrate our method (correlated TF method) on simple models of 1D-interacting electrons, showing that it yields dramatic improvements over TF theory, particularly in the strongly correlated regime.

Mintert, F. & Heller, E.J. Simulation of open quantum systems. EPL (Europhysics Letters) 86, 50006 (2009). Publisher's VersionAbstract

We present an approach for the semiclassical treatment of open quantum systems. An expansion into localized states allows restriction of a simulation to a fraction of the environment that is located within a predefined vicinity of the system. Adding and dropping environmental particles during the simulation yields an effective reduction of the size of the system that is being treated.

Kramer, T., Heller, E.J. & Parrott, R.E. An efficient and accurate method to obtain the energy-dependent Green function for general potentials. Journal of Physics: Conference Series 99, 012010 (2008). Publisher's VersionAbstract

Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results and a variety of numerical methods have been developed to solve the time-dependent Schrödinger equation. The time-dependent methods work for nearly arbitrarily shaped potentials, including sources and sinks via complex-valued potentials. Many quantities are measured at fixed energy, which is seemingly not well suited for a time-dependent formulation. Very few methods exist to obtain the energy-dependent Green function for complicated potentials without resorting to ensemble averages or using certain lead-in arrangements. Here, we demonstrate in detail a time-dependent approach, which can accurately and effectively construct the energy-dependent Green function for very general potentials. The applications of the method are numerous, including chemical, mesoscopic, and atomic physics.

Wasserman, A., Maitra, N.T. & Heller, E.J. Investigating interaction-induced chaos using time-dependent density-functional theory. Physical Review A 77, 042503 (2008). Publisher's VersionAbstract

Systems whose underlying classical dynamics are chaotic exhibit signatures of the chaos in their quantum mechanics. We investigate the possibility of using the linear response formalism of time-dependent density functional theory (TDDFT) to study the case when chaos is induced by electron-interaction alone. Nearest-neighbor level-spacing statistics are in principle exactly and directly accessible from TDDFT. We discuss how the TDDFT linear response procedure can reveal information about the mechanism of chaos induced by electron-interaction alone. A simple model of a two-electron quantum dot highlights the necessity to go beyond the adiabatic approximation in TDDFT.

Heller, E.J. & Tomsovic, S. Postmodern quantum mechanics. Physics Today 46, 38–46 (2008). Publisher's VersionAbstract


Postmodern movements are well known in the arts. After a major artistic revolution, and after the “modern” innovations have been assimilated, the threads of premodern thought are always reconsidered. Much of value may be rediscovered and put to new use. The modern context casts new light on premodern thought, which in turn shades perspectives on modernism.

Recent progress in semiclassical theory has overcome barriers posed by classical chaos and cast light on the correspondence principle. Semiclassical ideas have also become central to new experiments in atomic, molecular, microwave and mesoscopic physics.


Heller, E.J. Surface physics: Electron wrangling in quantum corrals. Nature Physics 4, 443 - 444 (2008). Publisher's VersionAbstract
The article reports on the discovery of image electron waves' ability to propagate along a metal surface by Don Eigler, Christopher Lutz, and Michael Crommie at IBM Almaden in 1990. Eigler, Lutz, and Crommie noticed unexpectedly long and periodic undulations in the scanning tunnelling microscope (STM) conductance signal as a function of tip position. The undulations were recognized as the signature of surface confined electron waves whose de Broglie wavelength is bigger than the lattice.