Session A52: Using Chaos to Control Quantum Systems

Regularization of tunneling rates in quantum chaotic systems

Prototypical systems of two potential wells separated by a tunneling barrier exhibit the unexpected and counter-intuitive results that regular, non-chaotic systems have tunneling rates that fluctuate with energy dramatically over several orders of magnitude whereas the fully chaotic wells have orders of magnitude smaller fluctuations. All calculations were found from the Schrodinger equation using the Boundary Element Method. A random, plane wave theory explains the magnitude of the average tunneling rates as well as their fluctuations. We show that we can tune the amount of variance in tunneling rates by changing the shape of the quantum wells implying possible device design capabilities for nanodevices that operate in the electron ballistic regime.   

Relativistic quantum Darwinism in Dirac fermion and graphene systems

We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which are signatures of relativistic quantum Darwinism (RQD). These localized states suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of quantum tunneling. Qualitatively similar phenomena have been observed in graphene. A physical theory is developed to explain relativistic quantum Darwinism and its effects based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the open cavity system.   

Relativistic quantum chaos----an analytic Dirac equation approach

Relativistic quantum chaos has attracted much attention since the discovery of graphene in 2004. Using graphene billiard as an apparatus of relativistic quantum particles, relativistic quantum scars, level spacing statistics, and relativistic quantum scattering have been widely investigated recently. However, since graphene has two non-equivalent Dirac points which can be coupled together by various processes, it has been wondered that whether the observed phenomena are inherent to the relativistic movement or caused by the discrete graphene lattice structure and boundary terminations. Based on Berry et al.'s work on neutrino billiards, we developed a conformal transformation method to solve the 2D Dirac equation in a confined region resembling chaotic billiards in the classical limit. This method solves both the eigen-energies and the eigen-wavefunctions of the 2D massless Dirac fermions. Level spacing statistics and relativistic quantum scars for a heart-shaped billiard are investigated and comparisons with graphene billiards are made.   

Using Local Perturbations To Manipulate and Control Pointer States in Quantum Dot Systems

Recently, scanning gate microscopy (SGM) was used to image scarred wave functions in an open InAs quantum dot[1]. The SGM tip provides a local potential perturbation and imaging is performed by measuring changes in conductance. Scarred wave functions, long associated with quantum chaos, have been shown in open dots to correspond to pointer states[2], eigenstates that survive the decoherence process that occurs via coupling to the environment. Pointer states modulate the conductance, yielding periodic fluctuations and the scars, normally thought unstable, are stabilized by quantum Darwinism [3]. We shall show that, beyond probing, pointer states can be manipulated by local perturbations. Particularly interesting effects occur in coupled quantum dot arrays, where a pointer state localized in one dot can be shifted over into another with a perturbation in a completely different part of the system. These nonlocal effects may perhaps be exploited to give such systems an exotic functionality. [1] A. M. Burke, R. Akis, T. E. Day, Gil Speyer, D. K. Ferry, and B. R. Bennett, Phys. Rev. Lett. 104, 176801 (2010). [2] D. K. Ferry, R. Akis, and J. P. Bird, Phys. Rev. Lett. 104, 176801 (2004). [3] R. Brunner, R. Akis,D. K. Ferry, F. Kuchar,and R. Meisels, Phys. Rev. Lett. 101, 024102 (2008).   

Periodic Orbit Scar in Propagation of Wave Packet

The scar-like enhancement is found in the accumulation of the time-evolving wave packet in stadium billiard. The time-average of the absolute square of the time-evolving wave functions in the stadium billiard is investigated numerically and semiclassically. Nowadays nano- or subnano-sized devices are getting more and more available. This kind of dynamical properties is essential, when the devices actually work. The enhancement appears along an unstable periodic orbit, when the Gaussian wave packet is launched as the initial state along the orbit. Introducing the window function which is closely related to the eigenfunction expansion coefficients of the wave packet, the localization around the periodic orbit is clarified by the semiclassical approximation that it is due to essentially the same mechanism of the scar states in stationary states. The ``smooothed'' window function is well estimated by the intensity spectrum in Prof. Heller's theory of the long-time semiclassical dynamics. The key parameters that determine its shape are actually classical quantities: the size of the initial wave packet and the Lyapunov exponent.   

Chaotic Ionization of Bidirectionally Kicked Rydberg Atoms

A highly excited quasi one-dimensional Rydberg atom exposed to periodic alternating external electric ?eld pulses exhibits chaotic behavior. The ionization of this system is governed by a geometric structure of phase space called a homoclinic tangle and its turnstile. We present and explain the results from an experiment designed to probe the structure of the phase space turnstile. We create time-dependent Rydberg wave packets, subject them to alternating applied electric fields (kicks), and measure the survival probability. We show that the survival probability of the electron depends not only on the initial electron energy, but also on the phase space position of the electron with respect to the turnstile--the portion of the electron wave packet inside the turnstile ionizes quickly, after one period of the applied field, while that portion outside the turnstile ionizes after multiple kicking periods. Finally, we use the turnstile geometry to explain the dependence of ionization on the kicking period. This procedure describes a very robust yet simple way to control chaotic ionization of an atomic system.   

Quantized Intrinsically Localized Modes

We have calculated the quantized $n=2$ breather spectra of both the $\beta$ and the $\alpha$ Fermi-Pasta-Ulam lattices. The breather spectra are composed of resonances in the two-phonon continuum and branches of infinitely long-lived excitations. The non-linear attributes of these excitations become more pronounced at elevated temperatures. The calculated $n=2$ breather and the resonance of the $\beta$-lattice hybridize and exchange identity at the zone boundary, and are in reasonable agreement with the results of previous calculations using the number conserving approximation. However, by contrast the breather spectrum the $\alpha$-lattice couples resonantly with the single-phonon spectrum and cannot be calculated within a number conserving approximation. Furthermore we show that, for sufficiently strong non-linearity, the $\alpha$-lattice breathers can be observed directly through the single-phonon inelastic neutron scattering spectrum. As the temperature is increased, the single-phonon dispersion relation for the $\alpha$-lattice becomes progressively softer as the lattice instability is approached. We compare our theoretical results with the recent experimental observation of breathers in NaI by Manley {\it et al}.   

Using quantum chaos to control the production of bipartite entangled states

Recently, we have shown that it is possible for the entanglement dynamics to depend on the global classical dynamical regime instead of the local classical behavior. We observe that as the corresponding classical system becomes more chaotic, the rate of entanglement production increases with the emergence of larger entanglement entropy in the steady state. This suggests that quantum chaos can be used to control the generation of highly entangled quantum states, which are typically more robust against the effects of decoherence from the environment. Furthermore, the dependence of our system on the global classical dynamical regime indicates that the mode of production is insensitive to errors in the preparation of the initial separable coherent states. In this talk, I will present our recent results of using the additional control of quantum squeezing to further enhance the entanglement of the dynamically generated quantum states. I will show that the concomitant application of quantum squeezing and quantum chaos leads to a more entangled state at a faster production rate relative to squeezing without quantum chaos.   

Entanglement Entropy and Entanglement Spectrum for Two-Dimensional Classical Spin Configuration

In quantum spin chains at criticality, two types of scaling for the entanglement entropy exist: one comes from conformal field theory (CFT), and the other is for entanglement support of matrix product state (MPS) approximation. On the other hand, quantum spin-chain models can be mapped onto two-dimensional (2D) classical ones. Motivated by the scaling and the mapping, we introduce new entanglement entropy for 2D classical spin configuration as well as entanglement spectrum, and examine their basic properties in the Ising and the three-state Potts models on the square lattice. They are defined by the singular values of the reduced density matrix for a Monte Carlo snapshot. We find scaling relations of the entropy analogous to the CFT and the MPS results. At criticality, the spin configuration is fractal, and various sizes of ordered clusters coexist. Then, the original snapshot can be decomposed into a set of images, and they have different length scales, respectively. This is the origin of the scaling. Based on these observations as well as calculation of the entanglement spectrum, we conclude that the amount of information of only one snapshot at criticality is equal to that of 1D quantum critical systems.   

Fluctuation theorem for a double quantum dot coupled to a point-contact electrometer

We study the fluctuation theorem in single-electron sequential tunneling regime. We consider single-electron transport through a double quantum dot (DQD) monitored by a capacitively coupled quantum point-contact (QPC) electrometer. In this setup it is possible to perform a direction resolved real-time electron counting experiment. We derive the full counting statistics for the coupled DQD - QPC system and obtain the joint probability distribution of the charges transferred through the DQD and the QPC. We show that the joint probability distribution satisfies the fluctuation theorem for 4-terminal system. For two-terminal DQD, the effective temperature should be introduced to recover the fluctuation theorem. The system can be described by a master equation with tunneling rates depending of the counting fields and satisfying a generalized local detailed-balance relation. Furthermore, we derive universal relations between the non-linear corrections to the current and noise, which can be verified in experiment.   

Electromagnetic fluctuations in non-equilibrium: Casimir forces and heat transfer

It is well known that quantum Casimir forces play an important role in micro- or nanostructures. Recently, the role of temperature in thermal non-equilibrium raised theoretical as well as experimental interest. If the objects are held at different temperatures, the interactions depend on all temperatures in the system, and show many effects which are absent in equilibrium. Additionally, the objects exchange thermal energy by electromagnetic fields, known as radiative heat transfer, which is fundamentally different from macroscopic cases described by the well known laws of Planck or Stefan-Boltzmann. We discuss recent theoretical progress describing such effects, and illustrate the dependence of both quantities on the shapes as well as the distances of the objects.   

A First-Principles Method of Determining van der Waals Forces in Dissipative Media

Lifshitz theory of van der Waals (vdW) force and energy between two planar objects is strictly valid when the medium separating two planar objects is vacuum. Generalization of Lifshitz theory to the case when intervening medium is a dissipative material, as opposed to vacuum, is a surprisingly difficult undertaking because there is no expression for the electromagnetic stress tensor in dissipative materials. Here, we derive the expression for vdW energy and pressure in planar multilayered dissipative media by computing the work done in assembling the multilayered structure from its constituent thin films. In doing so, we avoid any calculations of the Maxwell stress tensor in any medium but vacuum. Even though this work has proven to be a corroboration of Dzyaloshinskii, Lifshitz, and Pitaevskii, it has thrown new light on our understanding of vdW forces and suggests that it should be possible to achieve the similar result for objects with arbitrary shapes.   

Heat radiation from long cylindrical objects

The heat radiated by objects small or comparable to the thermal wavelength can be very different from the classical blackbody radiation as described by the laws of Planck and Stefan-Boltzmann. We derive methods based on scattering of electromagnetic waves to explore the dependence on size, shape, as well as material properties. In particular, we discuss the radiation from a long cylinder at uniform temperature, describing in detail the degree of polarization of the emitted radiation by nanowires and carbon nanotubes.