Self-trapped quantum walks

Abstract

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.

Universal dynamical scaling laws in three-state quantum walks

“…The key point here is that there are endless forms to set those rules and thus different routes to travel through the Hilbert space, what drives progress in assessing hard computational problems [15]. From that point of view, discrete-time quantum walks are also a powerful tool for quantum simulation of complex phenomena such as quantum phase transitions [16][17][18], nonlinear dynamics [19][20][21][22], topological phases of matter [23][24][25], localization [26][27][28][29], and many others.…”

Asymptotic stability of small bound state of nonlinear quantum walks

“…The importance of solitons can also be seen by soliton resolution conjecture [58], which claims generic solutions decouple into scattering waves and solitons, as in RAGE theorem for the linear case [20,51]. Indeed, many papers studying nonlinear QWs numerically observe solitonic behavior of the solution and focus on the study of its dynamics [8,9,17,34,37,45,63]. For the stability analysis of bound states, related to the study of topological phases [3,4,10,11,28,29,40,60,61,62], Gerasimenko, Tarasinski, and Beenakker [22], followed by Mochizuki, Kawakami and Obuse [44] studied the linear stability of bound states bifurcating from linear bound states.…”

Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics

“…Nonlinear phenomena on DTQWs have also been investigated, in which its source emerges from different frameworks [29][30][31][32][33][34][35]. An anomalous slow diffusion has been reported for feed-forward DTQWs, a nonlinear quantum walk in which the coin operator depends on the coin states of the nearest-neighbor sites [29].…”

“…Restricted only to Hadamard quantum gates, nondispersive pulses and chaoticlike dynamics has been reported. Detailed study exploring other quantum gates reveal a rich setof dynamical profiles, including the self-trapped quantum walks, a localized regime in which the quantum walker remains localized around its initial position [35]. An interesting mathematical treatment on nonlinear DTQWs is described in Ref.…”