Dynamical decoupling in solids

1
Dynamical decoupling in solids

• ?????
• ?????

University of Science Technology of China

2011.8.5
2
Outline

• Suppressing decoherence
• Anomalous decoherence effect
• The application of DD in quantum metrology
• Future work

3
Decoherence suppression with DD
Decoherence suppression
4
Hahn spin echo
echo
5
Spin bath system

6
Decoupling sequences
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)

7
Impurity spin-based Quantum computer

8
Interactions in an Electron Spin-Nuclear
Bath Coupling Solid State Computer
9
Typical electron spin decoherence time in solids
Interaction Interaction Decoherence Characterized time
Crystal Lattice(phonons) Crystal Lattice(phonons) T1 (Strongly dependent on Temperature T) T1 ms (malonic acid _at_50K) s (PSi _at_6K)
Nuclear spin baths Hyperfine interaction T2 T2 ns(PSi or Quantum dots) ms (NV center)
Nuclear spin baths Hf Nuclear-Nuclear interaction T2 T2 ms (malonic acid) ms (PSi, NV center) ms (QD)
T1gtgtT2, spin bath is the main decoherence source
10
Qubit-bath model for pure dephasing
Nuclear spin interaction (dipole-dipole, Zeeman
energy, etc.)
Zeeman energy
Overhauser field
A block diagonal Hamiltonian for qubit
11
Decoherence by quantum entanglement
12
Decoherence under Dynamical decouling
13
DD under simulated noise
Michael J. Biercuk et al. Nature 458 996 (2009)
14
DD in solids ensemble system
J.F Du et al. Nature 461 1265 (2009)
After 7 pulses, the coherence enhancement is
saturated due to the electron-electron spin
coupling.
15
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, 200402
(2010)
17
Dynamical decoupling works in muti-qubit case ?
18
Nested DD in multi-qubits case
Physical Review A 81, 012331(2010) Physical
Review A 82, 052338(2010)
Phys. Rev. A 83, 022306 (2011)
19
(No Transcript)
20
CW/Pulsed EPR sepctrometer
21
Anomalous Decoherence Effect in a Quantum Bath
22
Nitrogen Vacancy (NV) in Diamond
1µm
Fluorescence
Optical Excitation
23
Energy level
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 decay envelop
L0, L,-
T23.97µs T21.82µs
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, 010401 (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, 1165-1169(2010)

35
Quantum metrology without entanglementMulti-roun
d protocol
Vittorio Giovannetti et al. PRL 96, 010401 (2006)
B.L.Higgins et al. Nature 450 393 (2007)
36
Geometric phase(GP)AA phase
37
Addressing NV centre
38
Phase estimation with single GP
39
Phase estimation with multi GP
40
Enhanced phase estimation with CPMG
2k GP
k GP
k GP
p
p
p
p
p
p
p
p
p
p/2
p/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