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Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases

Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases. CAOUS, Swinburne University. Xia-Ji Liu. Hawthorn, July. Majorana Fermion. 1. Outline. Probing Majorana Fermion in SO Coupled Fermi Gases. 2. Manipulating Majorana Fermion in SO Coupled Fermi Gases. 3.

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Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases

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  1. Probing and Manipulating Majorana Fermionsin SO Coupled Atomic Fermi Gases CAOUS, Swinburne University Xia-Ji Liu Hawthorn, July.

  2. Majorana Fermion 1 Outline Probing Majorana Fermion in SO Coupled Fermi Gases 2 Manipulating Majorana Fermion in SO Coupled Fermi Gases 3

  3. Majorana Fermion: particle is its own antiparticle Majorana Fermion Quantum statistics of Majorana Fermion: anyon Fermion:

  4. Potential System Hosts for Majorana Fermion Bound States • Neutrinos Majorana 1937 Majorana Fermion • Supersymmetry: photino; neutral gauginos; Higgsinos Condensed Matter System: quasiparticles •Quasiparticles in fractional Quantum Hall effect at n=5/2Moore Read 1991 •Unconventional superconductors-Sr2RuO4Das Sarma, Nayak, Tewari 2006 • Proximity Effect Devices using ordinary s wave superconductors • -Topological Insulator devicesFu, Kene 2008 • -Semiconductor/Magnet devicesSau, Lutchyn, Tewari, /das Sarma 2009 Current Status: Not Observed??

  5. Suggestion: Ultracold Fermionic Atoms near Feshbach Resonance Das Sarma T. Mizushima, K. Machida, M. Sato, Y. Takahashi, S. Fujimoto, C. Zhang, ,et al.. Majorana Fermion Question: Full Microscopic Calculation ? Signature for Majorana Fermion ?

  6. Hamiltonian Single- Particle Hamiltonian 2D trapped ultracold Fermi gas with SO coupling Interaction Hamiltonian Renormalization Rashba SO Coupling Dresselhaus SO Coupling

  7. MF BdG Equantion Bogoliubov Transformation 2D trapped ultracold Fermi gas with SO coupling BdG Hamiltonian Gap Function Single Vortex Liu, Hu and Drummond, PRA75, 023614(2007) Quansiparticle wave function

  8. Particle-hole transformation “topological” “trival” 2D trapped ultracold Fermi gas with SO coupling Majorana Fermion: Particle = Antiparticle

  9. Topological Invariants 2D trapped ultracold Fermi gas with SO coupling Topological variants

  10. Question: Does the Majorana fermion bound state exist? S-wave interaction without SO coupling so 2D trapped ultracold Fermi gas with SO coupling There is not zero mode when the Zeeman field h=0 Mixed singlet and triplet pairings

  11. helicity basis 2D trapped ultracold Fermi gas with SO coupling only Ek (-) is occuped p-wave symmetry zero mode bound state Two solutions Majorana fermion: particle is its own antiparticle Fermion operator Majorana fermion is a half of ordinary fermion

  12. Phase diagram 2D trapped ultracold Fermi gas with SO coupling Non-topological state phase separation state topological state parameters topological state

  13. Low-Lying Quasiparticle Spectrum Three branches with small energy spacing appear: “Outer edge” state “Inner edge” state Vortex core GdGM state (garoli-de Gennes-Matricon) 2D trapped ultracold Fermi gas with SO coupling Phase separation phase: “outer edge” and “inner edge” Topological state: “outer edge” and “GdGM state”

  14. Wave Function a bond and anti-bond hybridization and quasiparticle tunneling energy splitting 2D trapped ultracold Fermi gas with SO coupling PS phase: tunneling between two edge states T state: tunneling between outer edge state and “GdGM state” Exponentially small energy zero

  15. Experimental Signature spin-up and spin-down densities at the trap center Probing Majorana Fermion

  16. Experimental Signature local density of state Probing Majorana Fermion rf-spectroscopy Kohl’s group PRL 2011 40K, B=225.3G, Ea/EF=0.2 N=2000,

  17. Application: Topological quantum computation using Majorana Fermions as qubits

  18. Hamiltonian 1D trapped ultracold Fermi gas with SO coupling Rashba SO Coupling Dresselhaus SO Coupling

  19. Topological superfluid 1D trapped ultracold Fermi gas with SO coupling

  20. Phase diagram 1D trapped ultracold Fermi gas with SO coupling

  21. h/EF=0.5 1D trapped ultracold Fermi gas with SO coupling

  22. Transport Majorana Fermions: Zeeman field h/EF=0.5 h/EF=0.6 Manipulating Majorana Fermions

  23. Manipulating Majorana Fermions

  24. Create Majorana Fermions: Magnetic impurity potential Manipulating Majorana Fermions h/EF=0.5

  25. Magnetic impurity potential Manipulating Majorana Fermions

  26. 40K Manipulating Majorana Fermions SO Coupled ultracold atomic gases Spielman’s groupNature Vol 471, 83 (2011)

  27. Topological quantum computation SO coupled bosonic system Topological superfluidity Open Question:

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