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 ($\chi$) and the quantum gates ($\theta$), 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 $\chi$ versus $\theta$ 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.

7 pages, 6 figures with fig 1 (a-h), fig 2 (a-b), fig 3 (a-h), fig 4 (a-d), fig 5 (a-b), fig 6 (a-b)

References in corpus (28)

• Theory of Bose-Einstein condensation in trapped gases
• A Quantum Random Walk Search Algorithm
• Universal computation by quantum walk
• Solitons in nonlinear lattices
• Photons Walking the Line: A quantum walk with adjustable coin operations
• Observation of the topological soliton state in the Su-Schrieffer-Heeger model
• Anderson localization of entangled photons in an integrated quantum walk
• Quantum walk on the line as an interference phenomenon
• Self-trapping and stable localized modes in nonlinear photonic crystals
• A passive CPHASE gate via cross-Kerr nonlinearities
• Josephson and Persistent Spin Currents in Bose-Einstein Condensates of Magnons
• Optical Cavity Implementations of the Quantum Walk
• Symmetries and noise in quantum walk
• Robust self-trapping of vortex beams in a saturable optical medium
• Nonlinear optical Galton board
• Solitary Waves in Optical Fibers Governed by Higher Order Dispersion
• Universal Nonlinear Disordered Wave Packet Subdiffusion: 12 Decades
• Discrete-time quantum walk with feed-forward quantum coin
• Quantum walk as a simulator of nonlinear dynamics: Nonlinear Dirac equation and solitons
• Aperiodic space-inhomogeneous quantum walks: localization properties, energy spectra and enhancement of entanglement
• Attractor-repeller pair of topological zero-modes in a nonlinear quantum walk
• Limitations of two-level emitters as non-linearities in two-photon controlled phase gates
• Universal Selftrapping in Nonlinear Tight-binding Lattices
• Effect of nonlinearity on the dynamics of a particle in dc field-induced systems
• Discrete-time quantum walks on one-dimensional lattices
• Edge states in a two-dimensional quantum walk with disorder
• Almost compact moving breathers with fine-tuned discrete time quantum walks
• Self-trapped pulsed beams with finite power in pure cubic Kerr media excited by time-diffracting, space-time beams

Cited by in corpus (10)

• Bloch-like super-oscillations and unidirectional motion of phase driven quantum walkers
• Rogue waves in discrete-time quantum walks
• Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics
• Dynamics of discrete-time quantum walk with time-correlated unitary noise
• Nonlinear flip-flop quantum walks through potential barriers
• Discrete-time quantum walk dispersion control through long-range correlations
• One-dimensional quantum walks driven by two-entangled-qubit coins
• Asymptotic stability of small bound state of nonlinear quantum walks
• Nonlinear three-state quantum walks
• Universal dynamical scaling laws in three-state quantum walks