Netanel H. Lindner

Floquet topological insulator in semiconductor quantum wells

Topological phases of matter have captured our imagination over the past few years, with tantalizing properties such as robust edge modes and exotic non-Abelian excitations, and potential applications ranging from semiconductor spintronics to topological quantum computation. Despite recent advancements in the field, our ability to control topological transitions remains limited, and usually requires changing material or structural properties. We show, using Floquet theory, that a topological state can be induced in a semiconductor quantum well, initially in the trivial phase. This can be achieved by irradiation with microwave frequencies, without changing the well structure, closing the gap and crossing the phase transition. We show that the quasi-energy spectrum exhibits a single pair of helical edge states. We discuss the necessary experimental parameters for our proposal. This proposal provides an example and a proof of principle of a new non-equilibrium topological state, the Floquet topological insulator, introduced in this paper.

Entanglement on demand through time reordering

Entangled photons can be generated on demand in a novel scheme involving unitary time reordering of the photons emitted in a radiative decay. This scheme can be applied to the biexciton cascade in quantum dots.

Fractionalizing Majorana fermions: non-Abelian Statistics on the Edges of Abelian Quantum Hall States

We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of

Universal topological quantum computation from a superconductor-abelian quantum hall heterostructure

\nu= 1/m

Proposal for pulsed on-demand sources of photonic cluster state strings.

, while electrons of the opposite spin occupy a similar state with

Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump

\nu = -1/m

Universal transport signatures of Majorana fermions in superconductor-Luttinger liquid junctions

. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-abelian anyon of quantum dimension

Disorder-induced Floquet topological insulators.

\sqrt{2m}

Topological Quantum Computation—From Basic Concepts to First Experiments

. We calculate the unitary transformations that are associated with braiding of these anyons, and show that they are able to realize a richer set of non-abelian representations of the braid group than the set realized by non-abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation.

Deterministic generation of a cluster state of entangled photons

Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Greens observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the Z_3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that---unlike Ising anyons---allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kanes construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a two-fold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types yet depending on non-universal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.