Nonlinear optical Galton board
arXiv:quant-ph/0604084 · doi:10.1103/PhysRevA.75.062333
Abstract
We generalize the concept of optical Galton board (OGB), first proposed by Bouwmeester et al. {[}Phys. Rev. A \textbf{61}, 013410 (2000)], by introducing the possibility of nonlinear self--phase modulation on the wavefunction during the walker evolution. If the original Galton board illustrates classical diffusion, the OGB, which can be understood as a grid of Landau--Zener crossings, illustrates the influence of interference on diffusion, and is closely connected with the quantum walk. Our nonlinear generalization of the OGB shows new phenomena, the most striking of which is the formation of non-dispersive pulses in the field distribution (soliton--like structures). These exhibit a variety of dynamical behaviors, including ballistic motion, dynamical localization, non--elastic collisions and chaotic behavior, in the sense that the dynamics is very sensitive to the nonlinearity strength.
8 pages, 8 figures
References in corpus (17)
- Quantum random walks - an introductory overview
- Quantum Computation and Decision Trees
- From quantum cellular automata to quantum lattice gases
- Quantum walk on the line as an interference phenomenon
- Quantum quincunx in cavity quantum electrodynamics
- Classical wave-optics analogy of quantum information processing
- Spatial search and the Dirac equation
- Entanglement in coined quantum walks on regular graphs
- A random walk approach to quantum algorithms
- Quantum walks based on an interferometric analogy
- Simulation of quantum random walks using interference of classical field
- Quantum Walk with a time-dependent coin
- Optical Cavity Implementations of the Quantum Walk
- Complementarity and quantum walks
- Implementing the one-dimensional quantum (Hadamard) walk using a Bose-Einstein Condensate
- Generalized Quantum Walk in Momentum Space
- Optical implementability of the two-dimensional Quantum Walk
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