Preparing and probing atomic Majorana fermions and topological order in optical lattices

Kraus, Christina V.; Diehl, Sebastian; Zoller, P.; Baranov, M. A.

doi:10.1088/1367-2630/14/11/113036

Cited by 56 publications

(74 citation statements)

References 41 publications

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“…Explicitly, the nearest and NNN hopping (t a ) can be realized by a simple zigzag chain lattice, 34 with the hopping strength adjustable by the lattice geometry. The chemical potential (µ) is controllable through the optical trap potential or a radio frequency detuning.…”

Section: Cos(ak) and Cos(ementioning

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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Section: Cos(ak) and Cos(ementioning

confidence: 99%

Generating many Majorana modes via periodic driving: A superconductor model

et al. 2013

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“…In these experimental settings, the quasi-topological phase can be characterized using both correlation function and spectral properties, as discussed above. The nature of the edge modes can be demonstrated using a variety of techniques [52]. In particular, time-of-flight imaging and edge spectroscopy can be used to demonstrate the existence of zero-energy modes and their inherent correlations.…”

mentioning

confidence: 99%

Majorana Quasiparticles Protected by Z2 Angular Momentum Conservation

et al. 2017

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We show how angular momentum conservation can stabilise a symmetry-protected quasitopological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated by density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe -spin-orbit coupling and strong inter-orbital interactions -have been experimentally realized over the last two years.PACS numbers: 37.10. Jk, 05.10.Cc, 71.10.Pm Introduction. -The past two decades have witnessed an impressive progress in understanding how to harness quantum systems supporting topological order, one of the ultimate goals being the observation of quasi-particles with non-Abelian statistics -non-Abelian anyons [1][2][3][4][5]. A pivotal role in this search has been the formulation of a model for one-dimensional (1D) p-wave superconductors [6], that supports a symmetry-protected topological phase with Majorana quasi-particles (MQPs) as edge modes. The key element for the stability of such edge modes is the presence of a Z 2 parity symmetry. At the mean-field level, this can be realized via proximityinduced superconductivity in solid-state settings [7][8][9][10][11][12], or via coupling to molecular Bose-Einsten condensates in cold atoms [13]. Remarkably, it is possible to stabilize MQPs even taking fully into account quantum fluctuations by considering canonical settings [14][15][16][17][18], where the parity symmetry emerges via, e.g., engineered pairtunneling between pairs of wires [19][20][21]. However, it is an open challenge to understand whether, in these number-conserving setups, there exist fundamental microscopic symmetries that can serve as a pristine mechanism for the realization of MQPs, that is genuinely distinct from reservoir-induced superconductivity.Here, we show how angular momentum conservation enables the realization of a symmetry-protected quasitopological phase supporting MQPs in one-dimensional number-conserving systems [22]. In particular, we show how a combination of spin-exchange interactions and crossed spin-orbit couplings in orbital Hubbard models (see Fig. 1a-b) naturally gives rise to a Z 2 spin symmetry. This symmetry serves as the enabling tool to realize (1) describes tunneling (Ht), spin-orbit-coupling (Hso), and spin-exchange processes (HW ). In cold atom settings, the spin degree of freedom is represented by different Zeeman states with nuclear spin mF , mF + 1, while the orbital degree of freedom is encoded in different electronic states, 1 S0 and 3 P0. ...

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“…The result of the braiding, therefore, can be checked by measuring the change of the Majorana correlation functions in Time-of-Flight or spectroscopic experiments [45], or by measuring the parity of the wires by counting the number of fermions modulo two [23]. …”

Section: A Ideal Casementioning

confidence: 99%

Hybrid topological quantum computation with Majorana fermions: A cold-atom setup

et al. 2014

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In this paper we present a hybrid scheme for topological quantum computation in a system of cold atoms trapped in an atomic lattice. A topological qubit subspace is defined using Majorana fermions which emerge in a network of atomic Kitaev one-dimensional wires. We show how braiding can be efficiently implemented in this setup and propose a direct way to demonstrate the non-Abelian nature of Majorana fermions via a single parity measurement. We then introduce a proposal for the efficient, robust and reversible mapping of the topological qubits to a conventional qubit stored in a single atom. There, well-controlled standard techniques can be used to implement the missing gates required for universal computation. Our setup is complemented with an efficient non-destructive protocol to check for errors in the mapping.

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Preparing and probing atomic Majorana fermions and topological order in optical lattices

Cited by 56 publications

References 41 publications

Generating many Majorana modes via periodic driving: A superconductor model

Generating many Majorana modes via periodic driving: A superconductor model

Majorana Quasiparticles Protected by Z2 Angular Momentum Conservation

Hybrid topological quantum computation with Majorana fermions: A cold-atom setup

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