Majorana modes and p-wave superfluids for fermionic atoms in optical lattices

The quest for realization of non-Abelian phases of matter, driven by their possible use in fault-tolerant topological quantum computing, has been spearheaded by recent developments in p-wave superconductors. The chiral p(x)+ip(y)-wave superconductor in two-dimensions exhibiting Majorana modes provides the simplest phase supporting non-Abelian quasiparticles and can be seen as the blueprint of fractional topological order. Alternatively, Kitaev's Majorana wire has emerged as an ideal toy model to understand Majorana modes. Here we present a way to make the transition from Kitaev's Majorana wires to two-dimensional p-wave superconductors in a system with cold atomic gases in an optical lattice. The main idea is based on an approach to generate p-wave interactions by coupling orbital degrees of freedom with strong s-wave interactions. We demonstrate how this design can induce Majorana modes at edge dislocations in the optical lattice, and we provide an experimentally feasible protocol for the observation of the non-Abelian statistics.

[1]  P. Zoller,et al.  Repulsively bound atom pairs in an optical lattice , 2006, Nature.

[2]  S. Simon,et al.  Non-Abelian Anyons and Topological Quantum Computation , 2007, 0707.1889.

[3]  M. Lewenstein,et al.  Engineering p-wave interactions in ultracold atoms using nanoplasmonic traps , 2013, Nature Communications.

[4]  M. Lewenstein,et al.  Creating p-wave superfluids and topological excitations in optical lattices , 2009, 0908.4568.

[5]  Markus Greiner,et al.  A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice , 2009, Nature.

[6]  Immanuel Bloch,et al.  Single-atom-resolved fluorescence imaging of an atomic Mott insulator , 2010, Nature.

[7]  Liang Fu,et al.  Topological insulators in three dimensions. , 2006, Physical review letters.

[8]  G. Refael,et al.  Helical liquids and Majorana bound states in quantum wires. , 2010, Physical review letters.

[9]  S. Fujimoto,et al.  Non-Abelian topological order in s-wave superfluids of ultracold fermionic atoms. , 2009, Physical review letters.

[10]  Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures , 1996, cond-mat/9602137.

[11]  E. Rico,et al.  Majorana modes in driven-dissipative atomic superfluids with a zero Chern number. , 2012, Physical review letters.

[12]  Jason Alicea,et al.  Majorana fermions in a tunable semiconductor device , 2009, 0912.2115.

[13]  Alexei Kitaev,et al.  Anyons in an exactly solved model and beyond , 2005, cond-mat/0506438.

[14]  p-wave Cooper pairing of fermions in mixtures of dilute Fermi and Bose gases , 2001, cond-mat/0108045.

[15]  C. Beenakker,et al.  Search for Majorana Fermions in Superconductors , 2011, 1112.1950.

[16]  N. Cooper,et al.  Structure and consequences of vortex-core states in p-wave superfluids , 2010, 1006.0924.

[17]  A. Kitaev.  Unpaired Majorana fermions in quantum wires , 2000, cond-mat/0010440.

[18]  N. Nagaosa,et al.  Topological indices, defects, and Majorana fermions in chiral superconductors , 2012, 1203.6707.

[19]  N. Cooper,et al.  Stable topological superfluid phase of ultracold polar fermionic molecules. , 2009, Physical review letters.

[20]  Chuanwei Zhang,et al.  px+ipy superfluid from s-wave interactions of fermionic cold atoms. , 2008, Physical review letters.

[21]  K. West,et al.  Magnetic-field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at ν = 5/2. , 2013, Physical review letters.

[22]  Liang Fu,et al.  Topological insulators with inversion symmetry , 2006, cond-mat/0611341.

[23]  R. A. Williams,et al.  Synthetic Partial Waves in Ultracold Atomic Collisions , 2012, Science.

[24]  Xiaopeng Li,et al.  Chiral superfluidity with p-wave symmetry from an interacting s-wave atomic Fermi gas , 2014, Nature Communications.

[25]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[26]  P. Zoller,et al.  Majorana edge States in atomic wires coupled by pair hopping. , 2013, Physical review letters.

[27]  Y. Castin,et al.  Three fully polarized fermions close to a p-wave Feshbach resonance , 2007, 0708.0610.

[28]  Swee-Ping Chia,et al.  AIP Conference Proceedings , 2008 .

[29]  N. Cooper,et al.  Stability of fermionic gases close to a p -wave Feshbach resonance , 2008, 0808.1304.

[30]  S. Tewari,et al.  Quantum computation using vortices and majorana zero modes of a px + ipy superfluid of fermionic cold atoms. , 2006, Physical review letters.

[31]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[32]  Shinsei Ryu,et al.  Classification of topological insulators and superconductors in three spatial dimensions , 2008, 0803.2786.

[33]  N. Read,et al.  Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect , 1999, cond-mat/9906453.

[34]  P Zoller,et al.  Atomic quantum simulator for lattice gauge theories and ring exchange models. , 2005, Physical review letters.

[35]  L. Duan,et al.  Probing non-abelian statistics of Majorana fermions in ultracold atomic superfluid. , 2010, Physical review letters.

[36]  E. Bakkers,et al.  Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices , 2012, Science.

[37]  Resonantly-paired fermionic superfluids , 2006, cond-mat/0611022.

[38]  Y. Oreg,et al.  Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions , 2012, Nature Physics.

[39]  E. Schonbrun,et al.  Optical vortices for localized optical lattice site manipulation , 2006 .

[40]  Gregory W. Moore,et al.  Nonabelions in the fractional quantum Hall effect , 1991 .

[41]  A. Kitaev.  Fault tolerant quantum computation by anyons , 1997, quant-ph/9707021.

[42]  Cheng Chin,et al.  Feshbach resonances in ultracold gases , 2008, 0812.1496.

[43]  A. Leggett,et al.  Exotic Properties of Superfluid 3He , 1992 .

[44]  Antoine Browaeys,et al.  Single-Atom Trapping in Holographic 2D Arrays of Microtraps with Arbitrary Geometries , 2014, 1402.5329.

[45]  D. Jin,et al.  p-Wave Feshbach molecules. , 2007, Physical review letters.

[46]  Xiaopeng Li,et al.  Chiral superfluidity with p-wave symmetry from an interacting s-wave atomic Fermi gas , 2014, Nature Communications.

[47]  P. Zoller,et al.  Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms , 2003, quant-ph/0304038.

[48]  A. R. Akhmerov.  Topological quantum computation away from the ground state using Majorana fermions , 2010 .

[49]  S. Simon,et al.  Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect , 2011, 1112.3400.

[50]  Alexei Kitaev,et al.  Periodic table for topological insulators and superconductors , 2009, 0901.2686.

[51]  Y. Maeno,et al.  Spin-triplet superconductivity in Sr2RuO4 identified by 17O Knight shift , 1998, Nature.

[52]  Stabilization of the p-wave superfluid state in an optical lattice. , 2009, Physical review letters.

[53]  M. Lukin,et al.  Engineering superfluidity in Bose-Fermi mixtures of ultracold atoms , 2004, cond-mat/0410494.

[54]  S Das Sarma,et al.  Generic new platform for topological quantum computation using semiconductor heterostructures. , 2009, Physical review letters.