Floquet Majorana Fermions for Topological Qubits in Superconducting Devices and Cold-Atom Systems

Liu, Dong E.; Levchenko, Alex; Baranger, Harold U.

doi:10.1103/physrevlett.111.047002

Cited by 172 publications

(147 citation statements)

References 40 publications

(62 reference statements)

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“…These modes could be useful for future quantum information applications 48 . Finally, we also showed that this gives rise to a proliferation of Dirac cones in the quasienergy spectrum, a finding which may be useful for simulating static chiral-symmetric Hamiltonians with many Dirac cones.…”

Section: Discussionmentioning

confidence: 99%

“…Our numerics also reveal that as certain parameters of the ORDKR model are tuned up, a large number of these topological edge modes occurs, together with a proliferation of Dirac cones in the quasienergy spectrum. This finding may be useful for quantum information processing with Floquet Majorana modes 48 and the study of Dirac cones [49][50][51][52][53][54] . So far as we know, this paper is the first to consider weak topological effects in driven systems.…”

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confidence: 99%

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Topological effects in chiral symmetric driven systems

Gong

2014

Phys. Rev. B

108

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Recent years have seen a strong interest in topological effects within periodically driven systems.In this work, we explore topological effects in two closely related 2-dimensional driven systems described by Floquet operators possessing chiral symmetry (CS). Our numerical and analytical results suggest the following. Firstly, the CS is associated with the existence of the anomalous counter-propagating (ACP) modes reported recently. Specifically, we show that a particular form of CS protects the ACP modes occurring at quasienergies of ±π. We also find that these modes are only present along selected boundaries, suggesting that they are a weak topological effect. Secondly, we find that CS can give rise to protected 0 and π quasienergy modes, and that the number of these modes may increase without bound as we tune up certain system parameters. Like the ACP modes, these 0 and π modes also appear only along selected boundaries and thus appear to be a weak topological effect. To our knowledge, this work represents the first detailed study of weak topological effects in periodically driven systems. Our findings add to the still-growing knowledge on driven topological systems.

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

Topological effects in chiral symmetric driven systems

Gong

2014

Phys. Rev. B

108

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“…An important example is the case of periodically driven one-dimensional topological superconductors, where the bulk Z 2 invariant is replaced by a pair of Z 2 invariants, whose calculation necessitates information beyond that represented by the Floquet Hamiltonian [10]. The edge states then are Floquet Majorana fermions, with potential applications in quantum information processing [11]. Such states, not predicted by the bulk Floquet Hamiltonian, have also been observed in optical realization of a one-dimensional quantum walk [12].…”

Section: Introductionmentioning

confidence: 99%

Chiral symmetry and bulk-boundary correspondence in periodically driven one-dimensional systems

2014

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In periodically driven lattice systems, the effective (Floquet) Hamiltonian can be engineered to be topological; then, the principle of bulk-boundary correspondence guarantees the existence of robust edge states. However, such setups can also host edge states not predicted by the Floquet Hamiltonian. The exploration of such edge states and the corresponding unique bulk topological invariants has only recently begun. In this work we calculate these invariants for chiral symmetric periodically driven one-dimensional systems. We find simple closed expressions for these invariants, as winding numbers of blocks of the unitary operator corresponding to a part of the time evolution. This gives a robust way to tune these invariants using sublattice shifts. We illustrate our ideas on the periodically driven Su-Schrieffer-Heeger model, which, as we show, can realize a discrete-time quantum walk; this opens a useful connection between periodically driven lattice systems and discrete-time quantum walks. Our work helps interpret the results of recent simulations where a large number of Floquet Majorana fermions in periodically driven superconductors have been found.

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“…Note that Floquet MMs are a particular class of MMs associated with the Floquet quasi-energy bands of a periodically driven system: 44 they may be used for topological quantum computation as "normal" MMs do. 48 Specifically, we propose to generate multiple Floquet MMs by switching (periodic quenching) a Hamiltonian from H 1 for the first half-period to H 2 for the second one. The Floquet operator U is then…”

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confidence: 99%

Generating many Majorana modes via periodic driving: A superconductor model

et al. 2013

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Realizing Majorana modes (MMs) in condensed-matter systems is of vast experimental and theoretical interests, and some signatures of MMs have been measured already. To facilitate future experimental observations and to explore further applications of MMs, generating many MMs at ease in an experimentally accessible manner has become one important issue. This task is achieved here in a one-dimensional p-wave superconductor system with the nearest-and next-nearest-neighbor interactions. In particular, a periodic modulation of some system parameters can induce an effective long-range interaction (as suggested by the Baker-Campbell-Hausdorff formula) and may recover time-reversal symmetry already broken in undriven cases. By exploiting these two independent mechanisms at once we have established a general method in generating many Floquet MMs via periodic driving.

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Floquet Majorana Fermions for Topological Qubits in Superconducting Devices and Cold-Atom Systems

Cited by 172 publications

References 40 publications

Topological effects in chiral symmetric driven systems

Topological effects in chiral symmetric driven systems

Chiral symmetry and bulk-boundary correspondence in periodically driven one-dimensional systems

Generating many Majorana modes via periodic driving: A superconductor model

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