Resonant Quantum Kicked Rotor as A Continuous-Time Quantum Walk

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.

Spatial Search on Johnson Graphs by Continuous-Time Quantum Walk

“…Benedetti et al [8] described CTQW on dynamical percolation graphs with the goal of analyzing the effect of noise produced by randomly adding or removing graph edges. Delvecchio et al [9] analytically investigated the analogy between the CTQW in one dimension and the evolution of the quantum kicked rotor at quantum resonance conditions.…”

Many Body Quantum Chaos

“…Finally, the quantum kicked rotor has recently found still another application, namely in the realization of quantum walks [30][31][32]. Our contribution [33] proves the analogy between a continuous-time quantum walk [34] with the kicked-rotor evolution at quantum resonance conditions [12], a research motivated by my joint work with Shmuel!…”

Quantum search with a continuous-time quantum walk in momentum space

“…This procedure is discussed in detail in Ref. [8]. Figures 1(b,c,d) show data for several momentum distributions obtained by the initial states of width three.…”

“…In Ref. [8] some of us observed that the QKR at resonance conditions realizes a simple one-dimensional continuous-time quantum walk (CTQW). In the jargon of QWs, a CTQW is characterized by the absence of the degree arXiv:2002.09139v1 [quant-ph] 21 Feb 2020 of freedom given by the coin, as described, e.g., by [3,9].…”