Parrondo's paradox for discrete-time quantum walks in momentum space

Abstract

We investigate the possibility of implementing a sequence of quantum walks whose probability distributions give an overall positive winning probability, while it is negative for the single walks (Parrondo's paradox). In particular, we have in mind an experimental realisation with a Bose-Einstein condensate in which the walker's space is momentum space. Experimental problems in the precise implementation of the coin operations for our discrete-time quantum walks are analysed in detail. We study time-dependent phase fluctuations of the coins as well as perturbations arising from the finite momentum width of the condensate. We confirm the visibility of Parrondo's paradox for experimentally available time scales of up to a few hundred steps of the walk.

References in corpus (4)

• Quantum resonances and decoherence for delta-kicked atoms
• Parrondo's game using a discrete-time quantum walk
• Hamiltonian ratchets with ultra-cold atoms
• Initial state dependence of a quantum-resonance ratchet

Cited by in corpus (5)

• Parrondo's effect in continuous-time quantum walks
• Parrondo's paradox in quantum walks with inhomogeneous coins
• Spontaneous-emission induced ratchet in atom-optics kicked rotor quantum walks
• Continuous-time quantum walks on a defective lattice: Boosting the spreading of delocalized states through Parrondo's strategy
• Enhanced spreading in continuous-time quantum walks using aperiodic temporal modulation of defects