Propagation of Quantum Walks in Electric Fields

Cedzich, C.; Rybár, Tomáš; Werner, Albert H.; Alberti, Andrea; Genske, Maximilian; Werner, Reinhard

doi:10.1103/physrevlett.111.160601

Cited by 91 publications

(158 citation statements)

References 40 publications

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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%

Quantum walks and discrete gauge theories

2016

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A particular example is produced to prove that quantum walks can be used to simulate fullfledged discrete gauge theories. A new family of 2D walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac fermion coupled to arbitrary electromagnetic fields. The electromagnetic interpretation is extended beyond the continuous limit by proving that these DTQWs exhibit an exact discrete local U (1) gauge invariance and possess a discrete gauge-invariant conserved current. A discrete gauge-invariant electromagnetic field is also constructed and that field is coupled to the conserved current by a discrete generalization of Maxwell equations. The dynamics of the DTQWs under crossed electric and magnetic fields is finally explored outside the continuous limit by numerical simulations. Bloch oscillations and the so-called E × B drift are recovered in the weak-field limit. Localization is observed for some values of the gauge fields.

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Section: Simulations Outside the Continuous Limitmentioning

confidence: 99%

Quantum walks and discrete gauge theories

2016

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“…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%

Eigenvalue measurement of topologically protected edge states in split-step quantum walks

et al. 2019

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We study topological phenomena of quantum walks by implementing a novel protocol that extends the range of accessible properties to the eigenvalues of the walk operator. To this end, we experimentally realise for the first time a split-step quantum walk with decoupling, which allows for investigating the effect of a bulk-boundary while realising only a single bulk configuration. The experimental platform is implemented with the well-established time-multiplexing architecture based on fibre-loops and coherent input states. The symmetry protected edge states are approximated with high similarities and we read-out the phase relative to a reference for all modes. In this way we observe eigenvalues which are distinguished by the presence or absence of sign flips between steps. Furthermore, the results show that investigating a bulk-boundary with a single bulk is experimentally feasible when decoupling the walk beforehand.

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“…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.…”

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confidence: 99%

Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks

et al. 2017

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The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a simple time-dependent, Bloch-oscillating quantum walk enables the direct measurement of topological invariants. We consider two classes of one-dimensional quantum walks and connect the global phase imprinted on the walker with its refocusing behavior. By disentangling the dynamical and geometric contributions to this phase we describe a general strategy to measure the topological invariant in these quantum walks. As an example, we propose an experimental protocol in a circuit QED architecture where a superconducting transmon qubit plays the role of the coin, while the quantum walk takes place in the phase space of a cavity.Much like their classical stochastic counterparts, discrete-time quantum walks [1] have stimulated activity across a broad range of disciplines. In the context of computation, they provide exponential speedup for certain oracular problems and represent a universal platform for quantum information processing [2][3][4]. Quantum walks also exhibit features characteristic of a diverse set of physical phenomena, ranging from localization to molecule formation [5,6]. At their core, discrete-time quantum walks (DTQW) are dynamical protocols associated with spinful particles on a lattice, where the internal spin state controls the direction of motion [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Motivated by this intrinsic spin-orbit coupling, a tremendous body of recent work has focused on exploring the topological features of DTQWs both theoretically and experimentally [5,[11][12][13][14][15].A connection between quantum walks and topology has been made by mapping the unitary evolution of the DTQW protocol to stroboscopic evolution under an effective Hamiltonian. In certain cases-distinguished by a combination of symmetry and dimensionality-the effective Hamiltonian's bandstructure exhibits a quantized invariant, analogous to those found in topological insulators [5,11,12,14]. On one hand, these invariants have helped to enable a sharp classification of non-interacting topological phases, which unlike conventional symmetry breaking phases, do not exhibit any local order parameters [20,21]. On the other, they underly a multitude of exotic physical phenomena ranging from protected edge modes and quantized conductance to fractional charges and magnetic monopoles [22,23]. Despite their importance and owing to their non-locality, bulk topological invariants have been directly probed in only a handful of quantum optical systems [24][25][26][27] and a generic blueprint for their measurement remains an outstanding challenge.In this Letter, we demonstrate that the simulation platform associated with discrete-time quantum walks is naturally suited for the direct extraction of topolog- ical invariants. We analyze a time-dependent,"Blochoscillating" generalization of t...

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Propagation of Quantum Walks in Electric Fields

Cited by 91 publications

References 40 publications

Quantum walks and discrete gauge theories

Quantum walks and discrete gauge theories

Eigenvalue measurement of topologically protected edge states in split-step quantum walks

Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks

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