Non-Abelian Topological Order ins-Wave Superfluids of Ultracold Fermionic Atoms

Abstract

It is proposed that in s-wave superfluids of cold fermionic atoms with laser-field-generated effective spin-orbit interactions, a topological phase with gapless edge states and Majorana fermion quasiparticles obeying non-Abelian statistics is realized in the case with a large Zeeman magnetic field. Our scenario provides a promising approach to the realization of quantum computation based on the manipulation of non-Abelian anyons via an s-wave Feshbach resonance. PACS numbers:Introduction -Recently, there has been considerable interest in topological phases of quantum many-body systems, which are characterized by the following features [1,2,3,4,5,6,7,8]: (i) there are topologicallyprotected gapless edge states on surface boundaries of the systems, which are stable against local perturbations, (ii) for two-dimensional (2D) systems, there are quasiparticles with fractional quantum numbers (e.g., fractional charges) termed "anyons". To this time, the possibility of realizing topological phases has been studied for various states realized in condensed matter systems, such as quantum (spin) Hall states [2,3,4,5,6], vortex states of p + ip superconductors [9,10,11,12], and spin liquid states [7,13], and for cosmological systems such as axion strings [14]. The feature (ii) is particularly of interest in connection with the realization of fault-tolerant quantum computation based on the manipulation of non-Abelian anyons [7,13,15,16,17,18]. Since topological phases provide not only a novel paradigm of quantum ground states but also a potential breakthrough for technological advance, it is desirable to pursue various possible schemes for their realization.

Topological states in a ladder-like optical lattice containing ultracold atoms in higher orbital bands

“…ð À 1Þ j C w j . Topologically nontrivial band structure of this sp orbital ladder, which shall be shown analytically next, may be heuristically speculated from the following comparison: the staggered quantum tunnelling t sp P j ½C w j ð À is y ÞC j þ 1 þ h:c: resembles spin-orbit interaction [18][19][20][21]23 , when the s and p orbital states are mapped to pseudo-spin-(1/2) states. Such a staggered tunnelling can also naturally arise in the checkerboard optical lattice already engineered in the experiment 6 by increasing the laser strength in one direction to reach the quasi-1D limit.…”

“…Remarkably, the edge states persist upon dimensional crossover, which makes it promising to realize in optical lattice experiments. This route of achieving topological band insulators and superfluids is distinct from previous proposals that require rotation of the gas 15,16 , artificial gauge fields 17 , spin-orbital coupling [18][19][20][21] or p-wave triplet pairing 22 .…”

Probing a topological quantum critical point in semiconductor-superconductor heterostructures

“…For numerical calculations in this paper, we have assumed μ = 0 (Fermi surface at the bottom of the top-most band), = 0.5 meV, α = 0.3 meV, so that c = 0.5 meV. The existence of Majorana fermions at defects, and also the fact that the high-state is isomorphic to a spinless p x + ip y superconductor, 10,21,22 make the highstate a topological superconductor.…”

Superconducting Sn1–xInxTe Nanoplates

“…[2][3][4] The search for TSCs is a hot topic in physics and offers interesting opportunities for chemistry. While topological superconducting states can be realized in many different systems, [5][6][7][8][9][10][11][12] degeneratelydoped topological insulators or topological crystalline insulators [13][14][15][16] with strong spin-orbit coupling are considered to be a promising platform. [17][18][19][20][21] In this regard, the topological crystalline insulator SnTe doped with In, Sn1-xInxTe, is one of the candidates of TSCs.…”