The Budapest Quantum Optics Group

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Chiral symmetry and Majorana fermions in periodically driven quantum wires

János Asbóth

(MTA Wigner RCP SZFI)

Time: Tue Mar 11 10:00:00 2014
Location: Building 1, Room 114, Auditorium

Topological insulators are materials that host low energy states at their boundaries, the number of these states being given by topological invariants of the bulk lattice system. Recent experimental proposals have shown that these invariants can be tuned by subjecting a solid state system to a periodic drive, i.e., a time-periodic change of some parameters [1]. Apart from altering the values of the topological invariants, the periodic drive allows for completely new types of invariants as well, with new types of corresponding protected states at the boundary. In the case of a one-dimensional particle-hole symmetric system, these are Majorana fermions at pi energy, in natural units where the period of the drive and hbar are set to 1 [2]. Understanding the bulk invariants controlling the number of these Majorana fermions is especially important since they are related to the Majorana fermions in non-driven quantum wires, which offer a promising road towards quantum information processing [3]. We show how chiral symmetry can be induced in a periodically driven system, and what the associated bulk topological invariants are that predict the number of zero and pi energy Majorana fermion-like states at the ends of the wire. As in the case of discrete-time quantum walks [4], these invariants combine the information from different, time-delayed descriptions of the system. We illustrate our findings on the simplest periodically driven 1D system, the driven SSH model, which in a limiting case maps to a discrete-time quantum walk.

References:

  1. J. Cayssol, B. Dóra, F. Simon, and R Moessner, Floquet topological insulators, Phys. Status Solidi RRL, 7, 101‒108 (2013)
  2. L. Jiang, T. Kitagawa, J. Alicea, A. R. Akhmerov, D. Pekker, G. Refael, J. I. Cirac, E. Demler, M. D. Lukin, and P. Zoller, Majorana fermions in equilibrium and driven cold atom quantum wires, Phys. Rev. Lett. 106, 220402 (2011)
  3. J. Alicea, Y. Oreg, G. Refael, F. von Oppen, M. P. A. Fisher, Non-Abelian statistics and topological quantum information processing in 1D wire networks, Nature Physics 7, 412‒417 (2011)
  4. J. K. Asbóth and H. Obuse, Bulk-boundary correspondence for chiral symmetric quantum walks, Phys. Rev. B 88, 121406(R) (2013) [arXiv]