Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin bath

Avoiding the loss of coherence of quantum mechanical states is an important prerequisite for quantum information processing. Dynamical decoupling (DD) is one of the most effective experimental methods for maintaining coherence, especially when one can access only the qubit system and not its environment (bath). It involves the application of pulses to the system whose net effect is a reversal of the system-environment interaction. In any real system, however, the environment is not static, and therefore the reversal of the system-environment interaction becomes imperfect if the spacing between refocusing pulses becomes comparable to or longer than the correlation time of the environment. The efficiency of the refocusing improves therefore if the spacing between the pulses is reduced. Here, we quantify the efficiency of different DD sequences in preserving different quantum states. We use C-13 nuclear spins as qubits and an environment of H-1 nuclear spins as the environment, which couples to the qubit via magnetic dipole-dipole couplings. Strong dipole-dipole couplings between the proton spins result in a rapidly fluctuating environment with a correlation time of the order of 100 mu s. Our experimental results show that short delays between the pulses yield better performance if they are compared with the bath correlation time. However, as the pulse spacing becomes shorter than the bath correlation time, an optimum is reached. For even shorter delays, the pulse imperfections dominate over the decoherence losses and cause the quantum state to decay.

Negative differential capacitance in n-GaN/p-Si heterojunctions

Negative differential capacitance (NDC) has been observed in n-GaN/p-Si heterojunctions grown by plasma assisted molecular beam epitaxy (PAMBE). The NDC is observed at low frequencies 1 and 10 kilohertz (kHz) and disappeared at a higher testing frequency of 100 kHz. The NDC is also studied with temperature and found that it has disappeared above 323 degrees C. Current-Voltage (I-V) characteristics of n-GaN /p-Si heterojunction were measured at different temperatures and are attributed to the space-charge-limited current (SCLC). A simple model involving two quantum states is proposed to explain the observed NDC behavior. (C) 2010 Elsevier Ltd. All rights reserved.

Direct Observation of Valley Hybridization and Universal Symmetry of Graphene with Mesoscopic Conductance Fluctuations

In graphene, the valleys represent spinlike quantities and can act as a physical resource in valley-based electronics to produce novel quantum computation schemes. Here we demonstrate a direct route to tune and read the valley quantum states of disordered graphene by measuring the mesoscopic conductance fluctuations. We show that the conductance fluctuations in graphene at low temperatures are reduced by a factor of 4 when valley triplet states are gapped in the presence of short-range potential scatterers at high carrier densities. We also show that this implies a gate tunable universal symmetry class that outlines a fundamental feature arising from graphene's unique crystal structure.

Universal Conductance Fluctuations as a direct probe to valley coherence and universality class of disordered graphene

We demonstrate that the universal conductance fluctuations (UCF) can be used as a direct probe to study the valley quantum states in disordered graphene. The UCF magnitude in graphene is suppressed by a factor of four at high carrier densities where the short-range disorder essentially breaks the valley degeneracy of the K and K' valleys, leading to a density dependent crossover of symmetry class from symplectic near the Dirac point to orthogonal at high densities.

Long-lived oscillatory incoherent electron dynamics in molecules: trans-polyacetylene oligomers

We identify an intriguing feature of the electron-vibrational dynamics of molecular systems via a computational examination of trans-polyacetylene oligomers. Here, via the vibronic interactions, the decay of an electron in the conduction band resonantly excites an electron in the valence band, and vice versa, leading to oscillatory exchange of electronic population between two distinct electronic states that lives for up to tens of picoseconds. The oscillatory structure is reminiscent of beating patterns between quantum states and is strongly suggestive of the presence of long-lived molecular electronic coherence. Significantly, however, a detailed analysis of the electronic coherence properties shows that the oscillatory structure arises from a purely incoherent process. These results were obtained by propagating the coupled dynamics of electronic and vibrational degrees of freedom in a mixed quantum-classical study of the Su-Schrieffer-Heeger Hamiltonian for polyacetylene. The incoherent process is shown to occur between degenerate electronic states with distinct electronic configurations that are indirectly coupled via a third auxiliary state by vibronic interactions. A discussion of how to construct electronic superposition states in molecules that are truly robust to decoherence is also presented

Degree of fourth-order coherence by double Hanbury Brown-Twiss detections

Photon quantum statistics of light can be shown by the high-order coherence. The fourth-order coherences of various quantum states including Pock states, coherent states, thermal states and squeezed vacuum states are investigated based on a double Banbury Brown Twiss (HBT) scheme. The analytical results are obtained by taking the overall efficiency and background into account.

Method for measuring two-qubit entanglement of formation by local operations and classical communication

We present a parametrically efficient method for measuring the entanglement of formation E-f in an arbitrarily given unknown two-qubit state rho(AB) by local operations and classical communication. The two observers, Alice and Bob, first perform some local operations on their composite systems separately, by which the desired global quantum states can be prepared. Then they estimate seven functions via two modified local quantum networks supplemented a classical communication. After obtaining these functions, Alice and Bob can determine the concurrence C and the entanglement of formation E-f.

Qubit Residence Time Measurements with a Bose-Einstein Condensate

We show that an electrostatic qubit located near a Bose-Einstein condensate trapped in a symmetric double-well potential can be used to measure the duration the qubit has spent in one of its quantum states. The strong, medium, and weak measurement regimes are analyzed. The analogy between the residence and the traversal (tunnelling) times is highlighted.

Effect of interparticle interaction in a free-oscillation atomic interferometer

We investigate the dynamics of two interacting bosons repeatedly scattering off a beam-splitter in a free oscillation atom interferometer. Using the interparticle scattering length and the beam-splitter probabilites as our control parameters, we show that even in a simple setup like this a wide range of strongly correlated quantum states can be created. This in particular includes the NOON state, which maximizes the quantum Fisher information and is a foremost state in quantum metrology. DOI: 10.1103/PhysRevA.87.043630

Joint measurements on qubits and cloning of observables

Cloning of observables, unlike standard cloning of states, aims at copying the information encoded in the statistics of a class of observables rather then on quantum states themselves. In such a process the emphasis is on the quantum operation (evolution plus measurement) necessary to retrieve the original information. We analyze, for qubit systems, the cloning of a class generated by two noncommuting observables, elucidating the relationship between such a process and joint measurements. This helps in establishing an optimality criterion for cloning of observables. We see that, even if the cloning machine is designed to act on the whole class generated by two noncommuting observables, the same optimal performances of a joint measurement can be attained. Finally, the connection with state dependent cloning is enlightened.

A first principles study of CH3 dehydrogenation on Ni(111)

Density functional theory with gradient corrections and spin polarization has been used to study the dehydrogenation of CH3 on Ni(111), a crucial step in many important catalytic reactions. The reaction, CH3(ads)--> CH2(ads)+H-(ads), is about 0.5 eV endothermic with an activation energy of more than 1 eV. The overall reaction pathway is rather intriguing. The C moiety translates from a hcp to a fcc site during the course of the reaction. The transition state of the reaction has been identified. The CH3 species is highly distorted, and both C and the active H are centered nearly on top of a row of Ni atoms with a long C-H bond length of 1.80 Angstrom. The local density of states coupled with examination of the real space distribution of individual quantum states has been used to analyze the reaction pathway. (C) 2000 American Institute of Physics. [S0021-9606(00)30218-5].

Density functional theory study of the interaction between CO and on a Pt surface:CO/Pt(111), O/Pt(111), and CO/O/Pt(111)

Ab initio total energy calculations within the Density Functional Theory framework were carried out for Pt(111), Pt(111)-p(2x2)-CO, Pt(111)-p(2x2)-O, and Pt(111)-p(2x2)-(CO+O) to provide an insight into the interaction between CO and O on metal surfaces, an important issue in CO oxidation, and also in promotion and poisoning effects of catalysis. The geometrical structures of these systems were optimized with respect to the total energy, the results of which agree with existing experimental values very well. It is found that (i) the local structures of Pt(111)-p(2x2)-(CO+O), such as the bond lengths of C-O, C-Pt, and O-Pt (chemisorbed O atom with Pt), are almost the same as that in Pt(111)-p(2x2)-CO and Pt(111)-p(2x2)-O, respectively, (ii) the total valence charge density distributions in Pt(111)-p(2x2)-(CO+O) are very similar to that in Pt(111)-p(2x2)-CO, except in the region of the chemisorbed oxygen atom, and also nearly identical to that in Pt(111)-p(2x2)-O, apart from in the region of the chemisorbed CO, and (iii) the chemisorption energy of CO on a precovered Pt(111)-p(2x2)-O and the chemisorption energy of O on a precovered Pt(111)-p(2x2)CO are almost equal to that in Pt(111)-p(2x2)-CO and Pt(111)-p(2x2)-O, respectively. These results indicate that the interaction between CO and chemisorbed oxygen on a metal surface is mainly shore range in nature. The discussions of Pt-CO and Pt-O bonding and the interaction between CO and the chemisorbed oxygen atom on Pt(111) are augmented by local densities of states and real space distributions of quantum states.

Comportement des systèmes de référence quantiques pour le moment cinétique

Le domaine des systèmes de référence quantiques, dont les dernière avancées sont brièvement présentées au chapitre 1, est extrêmement pertinent à la compréhension de la dégradation des états quantiques et de l’évolution d’instruments de mesures quantiques. Toutefois, pour arriver à comprendre formellement ces avancées et à apporter une contribution originale au domaine, il faut s’approprier un certain nombre de concepts physiques et mathématiques, in- troduits au chapitre 2. La dégradation des états quantiques est très présente dans le contrôle d’états utiles à l’informatique quantique. Étant donné que ce dernier tente de contrôler des sys- tèmes à deux états, le plus souvent des moments cinétiques, l’analyse des systèmes de référence quantiques qui les mesurent s’avère opportune. Puisque, parmi les plus petits moments ciné- tiques, le plus connu est de s = 1 et que son état le plus simple est l’état non polarisé, l’étude 2 du comportement d’un système de référence mesurant successivement ce type de moments ci- nétiques constitue le premier pas à franchir. C’est dans le chapitre 3 qu’est fait ce premier pas et il aborde les questions les plus intéressantes, soit celles concernant l’efficacité du système de référence, sa longévité et leur maximum. La prochaine étape est de considérer des états de moments cinétiques polarisés et généraux, étape qui est abordée dans le chapitre 4. Cette fois, l’analyse de la dégradation du système de référence est un peu plus complexe et nous pouvons l’inspecter approximativement par l’évolution de certains paramètres pour une certaine classe d’états de système de référence. De plus, il existe une interaction entre le système de référence et le moment cinétique qui peut avoir un effet sur le système de référence tout à fait comparable à l’effet de la mesure. C’est cette même interaction qui est étudiée dans le chapitre 5, mais, cette fois, pour des moments cinétiques de s = 1. Après une comparaison avec la mesure, il devient manifeste que les ressemblances entre les deux processus sont beaucoup moins apparentes, voire inexistantes. Ainsi, cette ressemblance ne semble pas générale et semble accidentelle lorsqu’elle apparaît.

Local character of magnetic coupling in ionic solids

Magnetic interactions in ionic solids are studied using parameter-free methods designed to provide accurate energy differences associated with quantum states defining the Heisenberg constant J. For a series of ionic solids including KNiF3, K2NiF4, KCuF3, K2CuF4, and high- Tc parent compound La2CuO4, the J experimental value is quantitatively reproduced. This result has fundamental implications because J values have been calculated from a finite cluster model whereas experiments refer to infinite solids. The present study permits us to firmly establish that in these wide-gap insulators, J is determined from strongly local electronic interactions involving two magnetic centers only thus providing an ab initio support to commonly used model Hamiltonians.