Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS,...
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![Page 1: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/1.jpg)
Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases
Xia-Ji Liu
CAOUS, Swinburne University
Hawthorn, July.
![Page 2: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/2.jpg)
Outline
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Majorana Fermion
Probing Majorana Fermion in SO Coupled Fermi Gases
Manipulating Majorana Fermion in SO Coupled Fermi Gases
![Page 3: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/3.jpg)
Majorana Fermion
Majorana Fermion: particle is its own antiparticle
022
jj cc jkkj cc },{Fermion:
12 jkkj 2},{
Quantum statistics of Majorana Fermion: anyon
122121 || M
![Page 4: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/4.jpg)
Majorana Fermion
•Quasiparticles in fractional Quantum Hall effect at n=5/2 Moore Read 1991
Potential System Hosts for Majorana Fermion Bound States
•Unconventional superconductors -Sr2RuO4 Das Sarma, Nayak, Tewari 2006
•Proximity Effect Devices using ordinary s wave superconductors
-Topological Insulator devices Fu, Kene 2008 -Semiconductor/Magnet devices Sau, Lutchyn, Tewari, /das Sarma
2009
•Neutrinos Majorana 1937
•Supersymmetry: photino; neutral gauginos; Higgsinos
Condensed Matter System: quasiparticles
Current Status: Not Observed??
![Page 5: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/5.jpg)
Majorana Fermion
Ultracold Fermionic Atoms near Feshbach Resonance
Das SarmaT. Mizushima, K. Machida, M. Sato, Y. Takahashi, S. Fujimoto, C. Zhang, , et al..
Full Microscopic Calculation ?
Signature for Majorana Fermion ?
Question:
Suggestion:
![Page 6: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/6.jpg)
2D trapped ultracold Fermi gas with SO coupling
Hamiltonian
Single- Particle Hamiltonian
Interaction Hamiltonian
Renormalization
Rashba SO Coupling xyyx kk Dresselhaus SO Coupling xyyx kk
![Page 7: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/7.jpg)
2D trapped ultracold Fermi gas with SO coupling
MF BdG Equantion
Bogoliubov Transformation
BdG Hamiltonian
Gap Function 0Ur
Single VortexSingle Vortex
Quansiparticle wave function
Liu, Hu and Drummond, PRA75, 023614(2007)
![Page 8: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/8.jpg)
2D trapped ultracold Fermi gas with SO coupling
E
E
E
E
EE
0E 00 EE
“trival” “topological”
Majorana Fermion: Particle = Antiparticle
Particle-hole transformation
![Page 9: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/9.jpg)
2D trapped ultracold Fermi gas with SO couplingTopological Invariants
Topological variants
![Page 10: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/10.jpg)
2D trapped ultracold Fermi gas with SO coupling
Question: Does the Majorana fermion bound state exist?
There is not zero mode when the Zeeman field h=0
EE
n
n
n
n
u
v
v
uS-wave interaction without SO coupling 0 nn vuso
Mixed singlet and triplet pairings
![Page 11: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/11.jpg)
2D trapped ultracold Fermi gas with SO coupling
kE
kE
helicity basis k k
chh only Ek (-) is occuped
cvcucvcu0
cvcucvcu ****0
22 ch
p-wave symmetry zero mode bound state
* vu
Two solutions
01 11
* vu 02 i 22
210 i
Majorana fermion: particle is its own antiparticleFermion operator
Majorana fermion is a half of ordinary fermion
![Page 12: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/12.jpg)
2D trapped ultracold Fermi gas with SO couplingPhase diagram
Non-topological state phase separation state topological state
rrrhc22 22
2
1rmr
Fa EE 2.0 1/ FF Ek 0/ FTTparameters
topological state 022 h
![Page 13: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/13.jpg)
2D trapped ultracold Fermi gas with SO coupling
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)
Phase separation phase: “outer edge” and “inner edge”
Topological state: “outer edge” and “GdGM state”
h
![Page 14: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/14.jpg)
2D trapped ultracold Fermi gas with SO couplingWave Function
a bond and anti-bond hybridization and
* vu *
vu
quasiparticle tunneling energy splitting
PS phase: tunneling between two edge states
T state: tunneling between outer edge state and “GdGM state”
Exponentially small energy zeroatomN
![Page 15: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/15.jpg)
Probing Majorana Fermion
Experimental Signature
spin-up and spin-down densities at the trap center
)(0rnrn
)(0rnrn FEh 6.0
![Page 16: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/16.jpg)
Probing Majorana Fermion
Experimental Signature
EEvEEuEr 22 ||||2
1,local density of
state 22 ||||0, rvrur
rf-spectroscopy
40K, B=225.3G, Ea/EF=0.2 N=2000, kHzz 802 Hz1252 Kohl’s group PRL 2011
![Page 17: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/17.jpg)
Application:
Topological quantum computation using Majorana Fermions as qubits
![Page 18: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/18.jpg)
1D trapped ultracold Fermi gas with SO coupling
Hamiltonian
Rashba SO Coupling xyyx kk Dresselhaus SO Coupling xyyx kk
![Page 19: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/19.jpg)
1D trapped ultracold Fermi gas with SO coupling
Topological superfluid xxxhc22
![Page 20: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/20.jpg)
1D trapped ultracold Fermi gas with SO coupling
Phase diagram
![Page 21: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/21.jpg)
1D trapped ultracold Fermi gas with SO coupling
h/EF=0.5
![Page 22: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/22.jpg)
Manipulating Majorana Fermions
Transport Majorana Fermions: Zeeman field
h/EF=0.5h/EF=0.6
![Page 23: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/23.jpg)
Manipulating Majorana Fermions
![Page 24: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/24.jpg)
Manipulating Majorana Fermions
Create Majorana Fermions: Magnetic impurity potential xVimp
h/EF=0.5
![Page 25: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/25.jpg)
Manipulating Majorana Fermions
Magnetic impurity potential
![Page 26: Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649d945503460f94a7b50e/html5/thumbnails/26.jpg)
Manipulating Majorana Fermions
40K
SO Coupled ultracold atomic gases
Spielman’s group Nature Vol 471, 83 (2011)
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Open Question:
Topological quantum computation
SO coupled bosonic system
Topological superfluidity