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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/localized quantum walks mediated by a proper adjusting of aperiodic parameter. Both scenarios are studied by exploring typical quantities (inverse participation ratio and survival probability), 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 vanishing gap between two main bands, which justifies the the delocalized character observed for ν < 0.5. With increase of ν arises gaps and flat-bands on the energy spectra, which corroborates the suppresion of transport detected for ν > 0.5. For ν high enough we observe an energy spectra which resembles that described by the 1d 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 informations about the role played by aperiodicity on the coin-poisition 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.

We study the existence and charaterization of self-trapping phenomena in discrete-time quantum walks. By considering a Kerr-like nonlinearity, we associate an acquisition of the intensity-dependent phase to the walker while it propagates on the lattice. Adjusting the nonlinear parameter (χ) and the quantum gates (θ), we will show the existence of different quantum walking regimes, including those with travelling soliton-like structures or localized by self-trapping. This latter scenario is absent for quantum gates close enough to Pauli-X. It appears for intermediate configurations and becomes predominant as quantum gates get closer to Pauli-Z. By using χ versus θ diagrams, we will show that the threshold between quantum walks with delocalized or localized regimes exhibit an unusual aspect, in which an increment on the nonlinear strength can induce the system from localized to a delocalized regime.

We show that initially localized and uncorrelated two-particles quantum wavepackets evolving in a one-dimensional discrete lattice become strongly entangled while drifting under the action of an harmonic AC field resonant with doubled Bloch oscillations promoted by a static DC field. Although partial entanglement is achieved when the AC field is resonant with the single-particle Bloch oscillations, it is strongly limited by the survival of anti-correlated unbounded states. We further show that the phase dependence of the wavepacket centroid velocity is similar to the semiclassical behavior depicted by a single-particle. However, the drift velocity exhibits a non-trivial non-monotonic dependence on the interaction strength, vanishing in the limit of uncorrelated particles, that unveils its competing influence on unbounded and bounded states.Recent experiments investigating the behavior of few interacting atoms in optical lattices[1] opened the possibility to generate a variety of quantum entangled matter states that can have a great impact on the search for universal and more efficient quantum computation processes, quantum sensing and metrology [2][3][4]. It has been experimentally demonstrated that quantum entangled atom pairs perform Bloch oscillations (BOs) at twice the fundamental frequency in tilted optical lattices (TOLs) [1]. BO is the phenomenon of oscillatory motion of wavepackets placed in a periodic potential when driven by a constant force [5,6]. It has been observed in several physical contexts such as semiconductors superlattices [7,8], ultra-cold atoms[9-13], optical[8] and acoustic waves [14]. The coherent phenomenon of frequency doubling of BOs was predicted to occur in the presence of interaction [15][16][17][18][19] because two particles bind together and perform correlated tunneling. Fractional BOs at multiples of the fundamental BO frequency have also been demonstrated for larger clusters of interacting particles [20]. A photonic realization of the BOs frequency doubling has been proposed [21,22] and experimentally achieved in waveguide lattices [23]. Its experimental demonstration with ultra-cold atoms of bosonic 87 Rb in decoupled one-dimensional tubes of an optical lattice[1] represents an important step towards the investigation of essential features of quantum many-body states.Unidirectional transport and super-BOs can be induced when wavepackets are driven by superposed static and harmonic fields [24][25][26][27][28][29][30]. It is achieved when the harmonic field is resonant with the underlying BO frequency, which depends linearly on the strength of the static field. A small detuning from the resonant condition results in super-BOs due to an effective tunneling renormalization. This phenomenology has been experimentally demonstrated in a weakly interacting Bose-Einstein condensate of Cs atoms placed in a TOL under forced driving, achieving matter-wave transport over macroscopic distances [26]. It has been theoretically demonstrated that some features of super-BOs and unidirectional tra...

We investigate the influence of the on-site Hubbard interaction U on the eigenstates and dynamics of two electrons restricted to move in a linear chain with long-range correlated disorder. We solve the time-dependent Schrödinger equation to follow the time evolution of an initially localized Gaussian two-electron wave packet. In the regime of strongly correlated disorder, for which one-electron extended eigenstates emerge near the band center, the electron-electron coupling promotes the trapping of a finite portion of the wave packet. In the presence of a uniform electric field, the wave packet develops complex Bloch oscillations. The power spectrum of the centroid's velocity trace shows a splitting near the typical semiclassical Bloch frequency, as well as a frequency doubling phenomenon for intermediate couplings which is related to the bounded states components that are present in the wave packet. Finally, we show that localized and extended two-electron eigenstates coexist near the band center with the level spacing distribution showing a universal Poissonian form irrespective to the Hubbard coupling.

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