A theoretical study of the phenomenon of Anderson localization in a generalized discrete time quantum walk will be reported. The generalized discrete time quantum walk is controlled by a quantum coin unitary matrix on each step of particle motion. The quantum coin matrix depends on four angles that can be engineered with microwave pulses in qubit chains. In the absence of disorder in quantum coins parameters the quantum walk dynamics is determined by two-bands dispersion relationship which becomes completely flat in the limit of vanishing kinetic energy. Various types of disorder result in the localization of quantum particle. In particular, kinetic energy disorder leads to logarithmic divergence of the localization length at spectral symmetry points. By making use of the transfer matrix technique we were able to obtain analytical expressions for the frequency dependent localization length in two limits, i.e. weak and strong disorder, and we anticipate that it will be useful for various applications.
A theoretical study of the phenomenon of Anderson localization in a generalized discrete time quantum walk will be reported. The generalized discrete time quantum walk is controlled by a quantum coin unitary matrix on each step of particle motion. The quantum coin matrix depends on four angles that can be engineered with microwave pulses in qubit chains. In the absence of disorder in quantum coins parameters the quantum walk dynamics is determined by two-bands dispersion relationship which becomes completely flat in the limit of vanishing kinetic energy. Various types of disorder result in the localization of quantum particle. In particular, kinetic energy disorder leads to logarithmic divergence of the localization length at spectral symmetry points. By making use of the transfer matrix technique we were able to obtain analytical expressions for the frequency dependent localization length in two limits, i.e. weak and strong disorder, and we anticipate that it will be useful for various applications.
We study Anderson localization in a generalized discrete-time quantum walk---a unitary map related to a Floquet driven quantum lattice. It is controlled by a quantum coin matrix which depends on four angles with the meaning of potential and kinetic energy, and external and internal synthetic flux. Such quantum coins can be engineered with microwave pulses in qubit chains. The ordered case yields a two-band eigenvalue structure on the unit circle, which becomes completely flat in the limit of vanishing kinetic energy. Disorder in the external magnetic field does not impact localization. Disorder in all the remaining angles yields Anderson localization. In particular, kinetic-energy disorder leads to logarithmic divergence of the localization length at spectral symmetry points. Strong disorder in potential and internal magnetic field energies allows one to obtain analytical expressions for spectrally independent localization length, which is highly useful for various applications.
We study the interplay of two interacting discrete time quantum walks in the presence of disorder. Each walk is described by a Floquet unitary map defined on a chain of two-level systems. Strong disorder induces a novel Anderson localization phase with a gapless Floquet spectrum and one unique localization length ${\ensuremath{\xi}}_{1}$ for all eigenstates for noninteracting walks. We add a local contact interaction which is parametrized by a phase shift $\ensuremath{\gamma}$. A wave packet is spreading subdiffusively beyond the bounds set by ${\ensuremath{\xi}}_{1}$ and saturates at a new length scale ${\ensuremath{\xi}}_{2}\ensuremath{\gg}{\ensuremath{\xi}}_{1}$. In particular we find ${\ensuremath{\xi}}_{2}\ensuremath{\sim}{\ensuremath{\xi}}_{1}^{1.2}$ for $\ensuremath{\gamma}=\ensuremath{\pi}$. We observe a nontrivial dependence of ${\ensuremath{\xi}}_{2}$ on $\ensuremath{\gamma}$, with a maximum value observed for $\ensuremath{\gamma}$ values which are shifted away from the expected strongest interaction case $\ensuremath{\gamma}=\ensuremath{\pi}$. The novel Anderson localization regime indicates violation of single parameter scaling for both interacting and noninteracting walks.
We study the evolution of a system performing a one-dimensional quantum walk in the presence of static phase disorder. The same model also describes the propagation of classical light pulses in photonic mesh lattices. We study the interplay between the coupling (i.e. the bias of the "quantum coin") and disorder. We provide an exact analytical expression for the localization length for two limiting cases of strong and weak phase disorder. In all the cases of interest we supply numerical simulations for participation ratio, Lyapunov exponent and the return probability as functions of the coupling parameter.
The interplay between disorder and topology triggers interesting effects for the propagation of quantum particles in low-dimensional network structures. For instance, the occurrence of Anderson localization, a commonly observed effect in a quantum network with static disorder, can be suppressed by introducing topology-a phenomenon dubbed as topological Anderson localization transition [1] . In one-dimensional systems, for example, disorder induces localization on a short length scale while topology counters that through long-range correlations, yielding divergent correlation length and extremely slow spreading at quantum criticality. However, its experimental demonstration still remains an outstanding challenge as that would require, in contrast to Anderson localization transition, addi¬tional control over internal degrees of freedom, which is hard to implement, for instance, in cold-atom systems [2] . Quantum walks (QWs), a quantum analog of random walks, comprising quantum coin toss and conditioned step operations are already established for studying quantum transport phenomena, such as, disorder and topology [5] . Based on our theoretical proposal [3] , here, we provide an experimental route using time-multiplexed quantum walk [4] for evidencing the targeted phenomenon.
Quantum Walk (QW) has very different transport properties to its classical counterpart due to interference effects. Here we study the discrete-time quantum walk (DTQW) with on-site static/dynamic phase disorder following either binary or uniform distribution in both one and two dimensions. For one dimension, we consider the Hadamard coin; for two dimensions, we consider either a 2-level Hadamard coin (Hadamard walk) or a 4-level Grover coin (Grover walk) for the rotation in coin-space. We study the transport properties e.g. inverse participation ratio (IPR) and the standard deviation of the density function (σ) as well as the coin-position entanglement entropy (EE), due to the two types of phase disorders and the two types of coins. Our numerical simulations show that the dimensionality, the type of coins, and whether the disorder is static or dynamic play a pivotal role and lead to interesting behaviors of the DTQW. The distribution of the phase disorder has very minor effects on the quantum walk.
We study the localization properties, energy spectra, and coin-position entanglement of the aperiodic discrete-time quantum walks. The aperiodicity is described by spatially dependent quantum coins distributed on the lattice, whose distribution is neither periodic (Bloch-like) nor random (Anderson-like). Within transport properties we identified delocalized and localized quantum walks mediated by a proper adjusting of aperiodic parameter. Both scenarios are studied by exploring typical quantities (inverse participation ratio, survival probability, and wave packet width), as well as the energy spectra of an associated effective Hamiltonian. By using the energy spectra analysis, we show that the early stage the inhomogeneity leads to a vanishing gap between two main bands, which justifies the predominantly delocalized character observed for ν<0.5. With increase of ν arise gaps and flat bands on the energy spectra, which corroborates the suppression of transport detected for ν>0.5. For ν high enough, we observe an energy spectra, which resembles that described by the one-dimensional Anderson model. Within coin-position entanglement, we show many settings in which an enhancement in the ability to entangle is observed. This behavior brings new information about the role played by aperiodicity on the coin-position entanglement for static inhomogeneous systems, reported before as almost always reducing the entanglement when comparing with the homogeneous case. We extend the analysis in order to show that systems with static inhomogeneity are able to exhibit asymptotic limit of entanglement.