Abstract
We analytically investigate the analogy between a standard continuous-time quantum walk in one dimension and the evolution of the quantum kicked rotor at quantum resonance conditions. We verify that the obtained probability distributions are equal for a suitable choice of the kick strength of the rotor. We further discuss how to engineer the evolution of the walk for dynamically preparing experimentally relevant states. These states are important for future applications of the atom-optics kicked rotor for the realization of ratchets and quantum search.
Highlights
IntroductionQuantum walks (QWs) are the quantum-mechanical analogue of classical random walks [1]
Speaking, quantum walks (QWs) are the quantum-mechanical analogue of classical random walks [1]
We revisited in detail the analogy of the continuous-time quantum walk (CTQW) in momentum space and the quantum kicked rotor (QKR)
Summary
Quantum walks (QWs) are the quantum-mechanical analogue of classical random walks [1]. Whilst there is no stochastic component in QW prior to measurements, QWs are characterized by the interference of many paths in the walker’s space, shaping the obtained probability distributions The engineering of these distributions, or more generally of the amplitudes that result in them, may find practical applications for the creation of specific initial states. Similar observations on the interference patterns in the resonant quantum kicked rotor and possible analogies with quantum walks were reported in, e.g., [20,21,22,23,24,25,26,27] We discuss their equivalence from a general viewpoint first, showing a direct connection between the Hamiltonians describing the two processes and by studying the probability distributions explicitly for exemplary initial states.
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