Electric Quantum Walks with Individual Atoms

Genske, Maximilian; Alt, Wolfgang; Steffen, Andreas; Werner, Albert H.; Werner, Reinhard; Meschede, Dieter; Alberti, Andrea

doi:10.1103/physrevlett.110.190601

Cited by 182 publications

(218 citation statements)

References 30 publications

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“…This makes them valuable in quantum search algorithms [2] or even for general quantum computing [3]. Experiments on quantum walks range from realizations on trapped ions [4][5][6], to cold atoms in optical lattices [7][8][9], to light on an optical table [10][11][12][13][14][15], but there have been many other experimental proposals [16,17].…”

Section: Introductionmentioning

confidence: 99%

Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk

Rakovszky

Asbóth

2015

Phys. Rev. A

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Quantum walks are promising for information processing tasks because in regular graphs they spread quadratically more rapidly than random walks. Static disorder, however, can turn the tables: unlike random walks, quantum walks can suffer Anderson localization, with their wave function staying within a finite region even in the infinite time limit, with a probability exponentially close to 1. It is thus important to understand when a quantum walk will be Anderson localized and when we can expect it to spread to infinity even in the presence of disorder. In this work we analyze the response of a one-dimensional quantum walk-the split-step walk-to different forms of static disorder. We find that introducing static, symmetry-preserving disorder in the parameters of the walk leads to Anderson localization. In the completely disordered limit, however, a delocalization transition occurs, and the walk spreads subdiffusively to infinity. Using an efficient numerical algorithm, we calculate the bulk topological invariants of the disordered walk and find that the disorder-induced Anderson localization and delocalization transitions are governed by the topological phases of the quantum walk.

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Section: Introductionmentioning

confidence: 99%

Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk

Rakovszky

Asbóth

2015

Phys. Rev. A

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“…Discrete-time quantum walks (DTQW) 6 , quantum mechanical generalizations of random walks, have in the recent years enjoyed increasing attention from both theoretical and experimental [7][8][9][10][11][12][13] physicists. The hallmark property of DTQWs is that they spread faster than classical random walks: on a regular graph, the variance of the position of the walker scales as O(t 2 ) with the number t of timesteps, rather than O(t) as in the classical case.…”

Section: Introductionmentioning

confidence: 99%

Quantized recurrence time in unital iterated open quantum dynamics

et al. 2015

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The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of systems that includes classical Markov chains and unitary discrete time quantum walks on networks. Starting from a pure state, the time evolution is induced by repeated applications of a general quantum channel, in each timestep followed by a measurement to detect whether the system has returned to the original state. We prove that if the superoperator is unital in the relevant Hilbert space (the part of the Hilbert space explored by the system), then the expectation value of the return time is an integer, equal to the dimension of this relevant Hilbert space. We illustrate our results on partially coherent quantum walks on finite graphs. Our work connects the previously known quantization of the expected return time for bistochastic Markov chains and for unitary quantum walks, and shows that these are special cases of a more general statement. The expected return time is thus a quantitative measure of the size of the part of the Hilbert space available to the system when the dynamics is started from a certain state.

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“…For example, Felix Bloch predicted in his seminal paper 5 that a crystal electron carries out an oscillatory motion under the influence of an external static electric field. While scattering of the electron prevents Bloch oscillations in bulk crystals, they have been observed in a number of equivalent systems, such as semiconductor superlattices 6 , atomic systems 7,8 , arrays of coupled dielectric waveguides 9,10 and periodic dielectric systems 11 . Other examples for the ability to map wave phenomena among different physical systems are Zener tunnelling in optical lattices 12,13 , as well as the analogy between the ballistic motion of an electronic wave packet in a tight-binding lattice 14 and discrete diffraction of light in a waveguide array 15,16 .…”

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confidence: 99%

Bloch oscillations in plasmonic waveguide arrays

et al. 2014

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The combination of modern nanofabrication techniques and advanced computational tools has opened unprecedented opportunities to mold the flow of light. In particular, discrete photonic structures can be designed such that the resulting light dynamics mimics quantum mechanical condensed matter phenomena. By mapping the time-dependent probability distribution of an electronic wave packet to the spatial light intensity distribution in the corresponding photonic structure, the quantum mechanical evolution can be visualized directly in a coherent, yet classical wave environment. On the basis of this approach, several groups have recently observed discrete diffraction, Bloch oscillations and Zener tunnelling in different dielectric structures. Here we report the experimental observation of discrete diffraction and Bloch oscillations of surface plasmon polaritons in evanescently coupled plasmonic waveguide arrays. The effective external potential is tailored by introducing an appropriate transverse index gradient during nanofabrication of the arrays. Our experimental results are in excellent agreement with numerical calculations.

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Electric Quantum Walks with Individual Atoms

Cited by 182 publications

References 30 publications

Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk

Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk

Quantized recurrence time in unital iterated open quantum dynamics

Bloch oscillations in plasmonic waveguide arrays

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