Kotimäki, V., Räsänen, E., Hennig, H. & Heller, E.J. Fractal dynamics in chaotic quantum transport.
Physical Review E 88, 022913 (2013).
Publisher's VersionAbstractDespite 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 VersionAbstractAn 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 TextAbstractIn 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 VersionAbstractWe 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 VersionAbstractThe 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).
PDF 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 VersionAbstractWe 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 VersionAbstractWe 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.