Dynamical decoupling in solids 报告人:王亚 导师:杜江峰 University of Science Technology of china 201185
Dynamical decoupling in solids 报告人：王亚 导师：杜江峰 University of Science & Technology of China 2011.8.5
Outline Suppressing decoherence a Anomalous decoherence effect a The application of dd in quantum metrology 口 Future work
Suppressing decoherence Anomalous decoherence effect The application of DD in quantum metrology Future work Outline
Decoherence suppression with DD environment no access- system lo entanglement decoherence H=HS+HB+HsB decoherence Decoherence suppression H→>0 -iH'In.e iH. iHtm(x1+2+…+n e
H H H = + + S B HSB decoherence Decoherence suppression with DD Decoherence suppression ( ) 1 2 1 n 2 1 eff 1 2 n iH iH iH iH e e e e − − − − + + + 0 HSB →
Hahn spin echo echo S∑41S24 ……………”, …time time
/2 echo Z Z k k S A I Z Z k k −S A I Hahn spin echo time π time
Spin bath system Hn=S2∑4 Hn=2y(ses)-s·S)
k Z hf Z k k Z hf Z k k H S A I H S A I = = …… Spin bath system ( ) 0 3 3( )( ) 4 i j dd i ij j ij i j ij H S e S e S S r = • • − •
Decoupling sequences Dynamical decoupling(DD) Pulse sequence Reference method CPMG(PDD) 7(2j-1)/2N even l:p1→>P Concatenated dd(cdd) PRL95,180501(2005) odd l P1-1→>丌→>P-1 Optimal DD(UDD) TSin2(jiz/2N+2)PR98100504(2007 PRL101,180403(2008) Optimization of UDD locally optimized DD(LODD) sequence for given Nature458,996(2009) noise PRL103,040501(2009)
Dynamical decoupling(DD) method Pulse sequence Reference CPMG(PDD) Concatenated DD(CDD) PRL 95, 180501 (2005) Optimal DD(UDD) PRL 98, 100504 (2007) PRL 101, 180403 (2008) locally optimized DD (LODD) Optimization of UDD sequence for given noise Nature 458, 996 (2009) PRL 103, 040501 (2009) …… 1 1 1 1 : : l l l l even l p p odd l p p − − − − → → → ( ) 2 TSin j N / 2 2 + Decoupling sequences T j N (2 1) / 2 −
Impurity spin-based Quantum computer External field P doped in silicon Endohedral N@cso INVI center in diamond 6● 31 ⊙ S=12 S=32 S=1 ■■口■■■
Impurity spin-based Quantum computer [NV]− center in diamond S = 1 Endohedral N@C60 S = 3/2 N P doped in silicon S = 1/2 …… 0 1 External field
Interactions in an Electron Spin -Nuclear Bath Coupling solid State Computer Magnetic Field Electron Orbit Crystal lattice Spin orbital· Electron spin← Nuclear sp Nuclear spin Hyperfine: Fermi Contact Dipole-Dipole Dipdle-Dipole Electron spin Dipole-dipole
Interactions in an Electron Spin-Nuclear Bath Coupling Solid State Computer Electron spin Nuclear spin Electron Orbit B Magnetic Field Crystal Lattice Hyperfine: Fermi Contact Dipole-Dipole Spin-orbital Nuclear spin Electron spin Dipole-dipole Dipole-Dipole
Typical electron spin decoherence time in solids Interaction Decoherence Characterized time Crystal Lattice(phonons) ( Strongly dependent - ms(malonic acid @50K) on Temperature T) S(P: Si @6K) T* z5 hyperfine ns(P: Si or Quantum dots Interaction HS(NV center) S Hf Nuclear cus(malonic acid) Nuclear interaction ms(p: Si, nV center) (QD) Ti>>T2 spin bath is the main decoherence source
Interaction Decoherence Characterized time Crystal Lattice(phonons) T1 (Strongly dependent on Temperature T) T1 ~ms (malonic acid @50K) ~ s (P:Si @6K) Nuclear spin baths Hyperfine interaction T2 * T2 * ~ns(P:Si or Quantum dots) ~s (NV center) Hf & NuclearNuclear interaction T2 T2 ~s (malonic acid) ~ms (P:Si, NV center) ~s (QD) T1>>T2, spin bath is the main decoherence source Typical electron spin decoherence time in solids
Qubit-bath model for pure dephasing H=QS.+hS +Hx Nuclear spin interaction Zeeman energy (dipole-dipole, Zeeman Overhauser field energy, etc. a block diagonal hamiltonian for qubit H=|+(4|8H+-(-H
H S h S H = + + z z z N Zeeman energy Overhauser field Nuclear spin interaction (dipole-dipole, Zeeman energy, etc.) H H H + − = + + + − − A block diagonal Hamiltonian for qubit Qubit-bath model for pure dephasing