2013
DOI: 10.1103/physrevlett.111.160601
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Propagation of Quantum Walks in Electric Fields

Abstract: We study one-dimensional quantum walks in a homogenous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion, and Anderson localization, depend very sensitively on the value of the electric field, Φ, e.g., on whether Φ/(2π) is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with fin… Show more

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Cited by 92 publications
(158 citation statements)
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“…Previous work on DTQWs coupled to electric or magnetic fields [26,27,33] have shown that walks with field values which are rational multiples of 2π ('rational fields') follow very peculiar dynamics. Fig.…”
Section: Simulations Outside the Continuous Limitmentioning
confidence: 99%
“…Previous work on DTQWs coupled to electric or magnetic fields [26,27,33] have shown that walks with field values which are rational multiples of 2π ('rational fields') follow very peculiar dynamics. Fig.…”
Section: Simulations Outside the Continuous Limitmentioning
confidence: 99%
“…Moreover, quantum walks exhibit a rich variety of single-particle quantum effects such as Landau-Zener tunnelling [28], the Klein paradox [29] or the formation of molecules [30]. Recently, a uniform framework for coupling external gauge fields to quantum walks has been established [31] which contains the one-dimensional electric walks studied in [32] as a special case. Possible experimental implementations include nuclear magnetic resonance [33,34], trapped ions [35,36] and atoms [37,38].…”
Section: Introductionmentioning
confidence: 99%
“…Solid lines correspond to analytic formulae derived in [31], which capture the deviations from ideal refocusing behavior. Points correspond to P ↑↓ as computed from Eq.…”
mentioning
confidence: 99%