Liu, B. & Heller, E.J. Multiple Scattering and Plasmon Resonance in the Intermediate Regime. arXiv preprint arXiv:1403.4310 (2014). Publisher's VersionAbstract

The collective excitation of the conduction electrons in subwavelength structures gives rise to the Localized Surface Plasmon(LSP). The system consisting of two such LSPs, known as the dimer system,is of fundamental interest and is being actively investigated in the literature. Three regimes have been previously identified and they are the photonic regime, the strong coupling regime and the quantum tunneling regime. In this Letter, we propose a new regime for this intriguing systems, the intermediate regime. In this new regime, the quasistatic approximation, which is widely used to study such LSP systems, fails to capture the main physics: the multiple scattering of the electromagnetic waves between the two LSPs, which significantly modifies the properties of the resonant modes in the system. This intermediate regime provides a new route to explore in plasmonics, where controlling both the excited plasmon modes and the damping rates are of paramount significance.

Liu, B. & Heller, E.J. Shaping Electromagnetic Fields. arXiv preprint arXiv:1405.2807 (2014). Publisher's VersionAbstract

The ability to control electromagnetic fields on the subwavelength scale could open exciting new venues in many fields of science. Transformation optics provides one way to attain such control through the local variation of the permittivity and permeability of a material. Here, we demonstrate another way to shape electromagnetic fields, taking advantage of the enormous size of the configuration space in combinatorial problems and the resonant scattering properties of metallic nanoparticles. Our design does not require the engineering of a material's electromagnetic properties and has relevance to the design of more flexible platforms for probing light-matter interaction and many body physics.

Kotimäki, V., Räsänen, E., Hennig, H. & Heller, E.J. Fractal dynamics in chaotic quantum transport. Physical Review E 88, 022913 (2013). Publisher's VersionAbstract

Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis—a widely used method in time-series analysis—and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.

Räsänen, E. & Heller, E.J. Optimal control of quantum revival. The European Physical Journal B 86, (2013). Publisher's VersionAbstract


Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of quantum revival, i.e., periodic recurrence in the time evolution, can be restored almost completely by coupling the distorted system to an external field obtained from quantum optimal control theory. We demonstrate the procedure with wave-packet calculations in both one- and two-dimensional quantum wells, and analyze the required physical characteristics of the control field. Our results generally show that the inherent dynamics of a quantum system can be idealized at an extremely low cost.


Mason, D.J., Borunda, M.F. & Heller, E.J. Quantum flux and reverse engineering of quantum wave functions. EPL (Europhysics Letters) 102, 60005 (2013). Publisher's VersionAbstract

An interpretation of the probability flux is given, based on a derivation of its eigenstates and relating them to coherent-state projections on a quantum wave function. An extended definition of the flux operator is obtained using coherent states. We present a "processed Husimi" representation, which makes decisions using many Husimi projections at each location. The processed Husimi representation reverse engineers or deconstructs the wave function, yielding the underlying classical ray structure. Our approach makes possible interpreting the dynamics of systems where the probability flux is uniformly zero or strongly misleading. The new technique is demonstrated by the calculation of particle flow maps of the classical dynamics underlying a quantum wave function in simple model systems such as a circular billiard with and without a magnetic field.

Liu, B. & Heller, E.J. Stability of Branched Flow from a Quantum Point Contact. Physical Review Letters 111, 236804 (2013). Full TextAbstract
In classically chaotic systems, small differences in initial conditions are exponentially magnified over time. However, it was observed experimentally that the (necessarily quantum) ‘‘branched flow’’ pattern of electron flux from a quantum point contact (QPC) traveling over a random background potential in two- dimensional electron gases remains substantially invariant to large changes in initial conditions. Since such a potential is classically chaotic and unstable to changes in initial conditions, it was conjectured that the origin of the observed stability is purely quantum mechanical, with no classical analog. In this Letter, we show that the observed stability is a result of the physics of the quantum point contact and the nature of the experiment. We show that the same stability can indeed be reproduced classically, or quantum mechanically. In addition, we explore the stability of the branched flow with regards to changes in the eigenmodes of the quantum point contact.
Borunda, M.F., Hennig, H. & Heller, E.J. Ballistic versus diffusive transport in graphene. Physical Review B 88, 125415 (2013). Publisher's VersionAbstract

We investigate the transport of electrons in disordered and pristine graphene devices. Fano shot noise, a standard metric to assess the mechanism for electronic transport in mesoscopic devices, has been shown to produce almost the same magnitude (1/3) in ballistic and diffusive graphene devices and is therefore of limited applicability. We consider a two-terminal geometry where the graphene flake is contacted by narrow metallic leads. We propose that the dependence of the conductance on the position of one of the leads, a conductance profile, can give us insight into the charge flow, which can in turn be used to analyze the transport mechanism. Moreover, we simulate scanning probe microscopy (SPM) measurements for the same devices, which can visualize the flow of charge inside the device, thus complementing the transport calculations. From our simulations, we find that both the conductance profile and SPM measurements are excellent tools to assess the transport mechanism differentiating ballistic and diffusive graphene systems.

Kocia, L. & Heller, E.J. Generalized dephasing relation for fidelity and application as an efficient propagator. The Journal of Chemical Physics 139, 124110 (2013). Publisher's VersionAbstract

The dephasing relation (DR), a linearization of semiclassical fidelity, is generalized to include the overlap of “off-diagonal” elements. The accuracy of the formulation is tested in integrable and chaotic systems and its scaling with dimensionality is studied in a Caldeira-Leggett model with many degrees of freedom. It is shown that the DR is often in very good agreement with numerically analytic quantum results and frequently outperforms an alternative semiclassical treatment. Most importantly, since there is no computationally expensive prefactor, and Monte Carlo Metropolis sampling is used to facilitate the calculation, the DR is found to scale remarkably well with increasing dimension. We further demonstrate that a propagator based on the DR can include more quantum coherence and outperform other popular linearized semiclassical methods, such as forward-backward semiclassical dynamics (FBSD) and the linearized semiclassical initial value representation (LSC-IVR).

Blasi, T., Borunda, M.F., Räsänen, E. & Heller, E.J. Optimal local control of coherent dynamics in custom-made nanostructures. Physical Review B 87, 241303 (2013). Publisher's VersionAbstract

We apply quantum optimal control theory to establish a local voltage-control scheme that operates in conjunction with the numerically exact solution of the time-dependent Schrödinger equation. The scheme is demonstrated for high-fidelity coherent control of electronic charge in semiconductor double quantum dots. We find tailored gate voltages in the viable gigahertz regime that drive the system to a desired charge configuration with >99% yield. The results could be immediately verified in experiments and would play an important role in applications towards solid-state quantum computing.

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.