1. Dynamical decoupling in solids
报告人：王亚
导师：杜江峰
University of Science & Technology of China

2. Outline Suppressing decoherence Anomalous decoherence effect
The application of DD in quantum metrology
Future work

3. Decoherence suppression with DD

4. Hahn spin echo
echo π
time
time

5. Spin bath system ……

6. Dynamical decoupling(DD) method
Decoupling sequences
Dynamical decoupling(DD) method
Pulse sequence
Reference
CPMG(PDD)
Concatenated DD(CDD)
PRL 95, (2005)
Optimal DD(UDD)
PRL 98, (2007)
PRL 101, (2008)
locally optimized DD (LODD)
Optimization of UDD sequence for given noise
Nature 458, 996 (2009)
PRL 103, (2009) ……

7. Impurity spin-based Quantum computer
External field
[NV]- center in diamond
S = 1
P doped in silicon
S = 1/2
Endohedral
S = 3/2 N ……

8. 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
Dipole-dipole

9. Typical electron spin decoherence time in solids
Interaction
Decoherence
Characterized time
Crystal Lattice(phonons) T1
(Strongly dependent on Temperature T)
~ms (malonic
~ s
Nuclear spin baths
Hyperfine interaction
T2*
~ns(P:Si or Quantum dots)
~ms (NV center)
Hf & Nuclear-Nuclear interaction T2
~ms (malonic acid)
~ms (P:Si, NV center)
~ms (QD)
T1>>T2, spin bath is the main decoherence source

10. Ren-Bao Liu (CUHK Physics)
2008/12/02
Qubit-bath model for pure dephasing
Nuclear spin interaction (dipole-dipole, Zeeman energy, etc.)
Zeeman energy
Overhauser field
A block diagonal Hamiltonian for qubit
USTC

11. Ren-Bao Liu (CUHK Physics)
2008/12/02
Decoherence by quantum entanglement
USTC

12. Decoherence under Dynamical decouling

13. DD under simulated noise
Michael J. Biercuk et al. Nature (2009)

14. DD in solids: ensemble system
J.F Du et al. Nature (2009)
After 7 pulses, the coherence enhancement is saturated due to the electron-electron spin coupling.

15. Up to 136 pulses, no limit is found to the coherence enhancement
DD in solids: single electron spin
G. Lange et. Al., Science 330, 60 (2010)
Up to 136 pulses, no limit is found
to the coherence enhancement

16. Pulse imperfections in DD
C.A.Ryan et al. Phys. Rev. Lett 105, (2010)

17. Dynamical decoupling works in muti-qubit case ?

18. Nested DD in multi-qubits case
Physical Review A 81, (2010)
Physical Review A 82, (2010) …
Phys. Rev. A 83, (2011) …
Commute or anti-commute
Single qubit operators, e.g.

20. CW/Pulsed EPR sepctrometer

21. Anomalous Decoherence Effect in a Quantum Bath

22. Nitrogen Vacancy (NV) in Diamond
kcounts/s
1μm 3E
3A2 N V
Laser MW B C
Fluorescence
Optical Excitation

23. Energy level 3E
3A2
1A1
ms=0
ms=-1
ms=1
ODMR spectrum
Rabi Oscillation

24. ODMR setup

25. Optical Parts

26. Microwave and Electronic parts

27. Quantum Description of decoherence
Coherence is lost as which-way
information is recorded in the bath
3 ways for nuclear spin
of different electron state

28. Decoherence without DD
Observation of free induced decay of single- and multi-transition in NV
decay envelop
L0,+
L+,-
T2*=3.97μs
T2*=1.82μs

29. Anomalous Decoherence Effect in Muti-pulse DD

30. Quantum Nature of ADE in single transition (0,+) case:
in double transition (+,-) case:
demolished due to
DD control
bath operator
back action: cause high frequency moise

31. Application of dynamical decoupling in Quantum metrology

32. Standard quantum limit and Heisenberg limit
Vittorio Giovannetti et al. PRL 96, (2006)

33. An example

34. Quantum metrology with entanglement
J. M. Geremia, J. K. Stockton, H. Mabuchi, Science 304,270 (2004);
D. Leibfried , et al., Nature 438, 639 (2005);
Tomohisa Nagata, et al. Science 316, 726 (2007);
Jonathan A. Jones, et al., Science 324, 1166 (2009)
C. Gross, et al . , Nature 464, (2010); ……

35. Quantum metrology without entanglement: Multi-round protocol
Vittorio Giovannetti et al. PRL 96, (2006)
B.L.Higgins et al. Nature (2007)

36. Geometric phase(GP):AA phase
[NV]- center in diamond
S = 1

37. Addressing NV centre

38. Phase estimation with single GP

39. Phase estimation with multi GPφ
Prepare
Read out
Repeated N times
Classical: φ
Prepare
Read out
Repeated N times
Quantum:

40. Enhanced phase estimation with CPMG
k GP
2k GP
k GP π π π π π π π π π π
π/2
π/2

41. Analysis

42. Future work Robust gate
Dynamically corrected gate(DCG) PRL 102,080501(2009)…
Combine DD with optimization control …

43. Thank you for your attention