Localization of quantum walks on finite graphs

We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probability distribution vectors of quantum walks in infinite and finite graphs in the presence of static disorder respectively, and get the distance between these two vectors. We find that when the steps taken are small and the boundary condition is tight, the localization between the infinite and finite cases is greatly different. However, the difference is negligible when the steps taken are large or the boundary condition is loose. It means quantum walks on a one-dimensional finite graph may also suffer from localization in the presence of static disorder. Our approach and results can be generalized to analyze the localization of quantum walks in higher-dimensional cases.     

Hanle effect driven by weak localization

The influence of weak localization on the Hanle effect in a two-dimensional system with a spin-split spectrum is considered. We show that weak localization drastically changes the dependence of a stationary spin polarization S on an external magnetic field B. In particular, the nonanalytic dependence of S on B is predicted for III-V-based quantum wells grown in the [110] direction and for the [100]-grown quantum wells having equal strengths of Dresselhaus and Bychkov-Rashba spin-orbit coupling. It is shown that in a weakly localized regime the components of S are discontinuous at B = 0. At low B, the magnetic field-induced rotation of the stationary polarization is determined by quantum interference effects. This implies that the Hanle effect in such systems is totally driven by weak localization.     

Bringing order through disorder: localization of errors in topological quantum memories

Anderson localization emerges in quantum systems when randomized parameters cause the exponential suppression of motion. Here we consider this phenomenon in topological models and establish its usefulness for protecting topologically encoded quantum information. For concreteness we employ the toric code. It is known that in the absence of a magnetic field this can tolerate a finite initial density of anyonic errors, but in the presence of a field anyonic quantum walks are induced and the tolerable density becomes zero. However, if the disorder inherent in the code is taken into account, we demonstrate that the induced localization allows the topological quantum memory to regain a finite critical anyon density and the memory to remain stable for arbitrarily long times. We anticipate that disorder inherent in any physical realization of topological systems will help to strengthen the fault tolerance of quantum memories.     

Dynamic localization of two electrons in AC-driven triple quantum dots and quantum dot shuttles

We analyze the dynamic localization of two interacting electrons induced by alternating current electric fields in triple quantum dots and triple quantum dot shuttles. The calculation of the long-time averaged occupation probability shows that both the intra-and inter-dot Coulomb interaction can increase the localization of electrons even when the AC field is not very large. The mechanical oscillation of the quantum dot shuttles may keep the localization of electrons at a high level within a range if its frequency is quite a bit smaller than the AC field. However, the localization may be depressed if the frequency of the mechanical oscillation is the integer times of the frequency of the AC field. We also derive the analytical condition of two-electron localization both for triple quantum dots and quantum dot shuttles within the Floquet formalism.     

Atom localization in a four-level atomic system with an assisting radio-frequency driven field

We propose a scheme for atom localization in a four-level atomic system by means of a radio-frequency field driving a hyperfine transition within the two ground states. It is found that, due to the quantum disturbed effect induced by the radio-frequency field, the property of atom localization can be significantly controlled. This scheme shows some characteristics that other schemes of atom localization do not have, which may provide some possibilities for the technological applications in atom nano-lithography.     

Dynamical Localization Simulated on Actual Quantum Hardware

Quantum computers are invaluable tools to explore the properties of complex quantum systems. We show that dynamical localization of the quantum sawtooth map, a highly sensitive quantum coherent phenomenon, can be simulated on actual, small-scale quantum processors. Our results demonstrate that quantum computing of dynamical localization may become a convenient tool for evaluating advances in quantum hardware performances.     

Role of orbital dynamics in spin relaxation and weak antilocalization in quantum dots

We develop a semiclassical theory for spin-dependent quantum transport to describe weak (anti)localization in quantum dots with spin-orbit coupling. This allows us to distinguish different types of spin relaxation in systems with chaotic, regular, and diffusive orbital classical dynamics. We find, in particular, that for typical Rashba spin-orbit coupling strengths, integrable ballistic systems can exhibit weak localization, while corresponding chaotic systems show weak antilocalization. We further calculate the magnetoconductance and analyze how the weak antilocalization is suppressed with decreasing quantum dot size and increasing additional in-plane magnetic field.     

Periodic-orbit theory of anderson localization on graphs

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an aperiodic Kronig-Penney model in one dimension. The exact expression for the probability to return to an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families, are performed analytically using advanced combinatorial methods.     

Conformal Symmetry and Quantum Relativity

The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincare symmetry of field theory can be extended to the larger conformal symmetry. We use these symmetries to define quantum observables associated with positions in space-time, in the spirit of Einstein theory of relativity. This conception of localization may be applied to massive as well as massless fields. Localization observables are defined as to obey Lorentz covariant commutation relations and in particular include a time observable conjugated to energy. While position components do not commute in the presence of a nonvanishing spin, they still satisfy quantum relations which generalize the differential laws of classical relativity. We also give of these observables a representation in terms of canonical spatial positions, canonical spin components, and a proper time operator conjugated to mass. These results plead for a new representation not only of space-time localization but also of motion.     

Binding energy of localized trions in quantum wires

We present a finite difference calculation of the binding energies of localized trions in quasi-one-dimensional quantum wires (QWRs). It is found that both the lateral confinement and the localization potential have a strong effect on the relative stability of the trions. It is confirmed that a weak localization potential not only enhances the binding energy but also changes the relative stability of the positive and negative trions. Our theoretical model is in good accord with a recent experiment regarding photoluminescence in disordered QWRs.     

Quantum Arnol'd diffusion in a rippled waveguide

We study the quantum Arnol'd diffusion for a particle moving in a quasi-1D waveguide bounded by a periodically rippled surface, in the presence of the time-periodic electric field. It was found that in a deep semiclassical region the diffusion-like motion occurs for a particle in the region corresponding to a stochastic layer surrounding the coupling resonance. The rate of the quantum diffusion turns out to be less than the corresponding classical one, thus indicating the influence of quantum coherent effects. Another result is that even in the case when such a diffusion is possible, it terminates in time due to the mechanism similar to that of the dynamical localization. The quantum Arnol'd diffusion represents a new type of quantum dynamics, and may be experimentally observed in measurements of a conductivity of low-dimensional mesoscopic structures.     

Dynamical localization effect in a coupled quantum dot array driven by an AC magnetic field

We have studied the transport properties of a ring-coupled quantum dot array driven by an AC magnetic field, which is connected to two leads, and we give the response of the transport current to the dynamical localization. We found that when the ratio of the magnetic flux to the total quantum dots number is a root of the zeroth order Bessel function, dynamical localization and collapse of quasi-energy occurs and importantly, the transport current displays a dip which is the signal of dynamical localization. The dynamical localization effect is strengthened as a result of the increase of the quantum dot number, and it is weakened on account of the increase of the dots-lead hopping rate.     

Transport of charge-density waves in the presence of disorder: classical pinning versus quantum localization

We consider the interplay of the elastic pinning and the Anderson localization in the transport properties of a charge-density wave in one dimension, within the framework of the Luttinger model in the limit of strong repulsion. We address a conceptually important issue of which of the two disorder-induced phenomena limits the mobility more effectively. We argue that the interplay of the classical and quantum effects in transport of a very rigid charge-density wave is quite nontrivial: the quantum localization sets in at a temperature much smaller than the pinning temperature, whereas the quantum localization length is much smaller than the pinning length.     

Controlling two-dimensional electron localization via phase-controlled absorption and gain in the three-coupled quantum wells

We investigate two-dimensional (2D) electron localization via phase-controlled absorption and gain of a weak probe field in an asymmetric semiconductor three-coupled quantum well (TCQW) with a closed loop under the action of two orthogonal standing-wave fields. It is found that we can achieve high-precision and high-resolution 2D electron localization via properly varying the parameters of the system. The influences of direct one-photon transition and indirect three-photon transition on the precision of probe absorption–gain spectra are also discussed in details. Thus, the proposed scheme shows the underlying probability for the formation of the 2D electron localization in a solid.     

Interpreting Observables in a Quantum World from the Categorial Standpoint

We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime.     

Quantum localization of the kicked rydberg atom

We investigate the quantum localization of the one-dimensional Rydberg atom subject to a unidirectional periodic train of impulses. For high frequencies of the train the classical system becomes chaotic and leads to fast ionization. By contrast, the quantum system is found to be remarkably stable. We find this quantum localization to be directly related to the existence of "scars" of the unstable periodic orbits of the system. The localization length is given by the energy excursion along the periodic orbits.     

Exciton polaritons and their one-dimensional localization in disordered quantum-well structures

A theory of the Anderson localization of light in randomly arranged ultrathin layers (quantum wells) uniform in lateral dimensions and possessing intrinsic optical resonances is put forward. To solve the multiple-scattering problem, a model of layers with a δ-function resonance dielectric polarization is proposed. The model is an electromagnetic counterpart of the electronic model of zero-radius potentials. Interlayer disorder is included under the assumption of a low average concentration of identical layers in order to calculate analytically the one-and two-photon characteristics of electromagnetic-radiation transport, in particular, the average energy density and the Anderson localization length of light. The analysis is carried out for a structure with randomly distributed quantum wells in which quasi-two-dimensional excitons of different quantum wells are in resonance while their wave functions do not overlap. It is shown that the average electromagnetic field propagates through this disordered structure in the form of polaritons but are produced in exciton reemission between quantum wells. The localization length of light in the polariton spectral region decreases substantially, because the scattering (reflection) of light by individual quantum wells grows near the excitonic resonance.     

Competition between weak localization and antilocalization in topological surface states

A magnetoconductivity formula is presented for the surface states of a magnetically doped topological insulator. It reveals a competing effect of weak localization and weak antilocalization in quantum transport when an energy gap is opened at the Dirac point by magnetic doping. It is found that, while random magnetic scattering always drives the system from the symplectic to the unitary class, the gap could induce a crossover from weak antilocalization to weak localization, tunable by the Fermi energy or the gap. This crossover presents a unique feature characterizing the surface states of a topological insulator with the gap opened at the Dirac point in the quantum diffusion regime.