Download - Dynamical decoupling in solids
Dynamical decoupling in solids
报告人:王亚
导师:杜江峰
University of Science & Technology of China
2011.8.5
Suppressing decoherence
Anomalous decoherence effect
The application of DD in quantum metrology
Future work
Outline
B SBSH H H H decoherence
Decoherence suppression with DD
Decoherence suppression
1 2 1eff 1 22 1 nn iHiH iH iHe e e e
0SBH
/ 2
echo
ZZ k kS A I Z
Z k kS A I
Hahn spin echo
time π
time
k Zhf Z k k
Zhf Z k k
H S A I
H S A I
……
Spin bath system
03
3( )( )4
i jdd i ij j ij i j
ij
H S e S e S Sr
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 / 2 2TSin j N
Decoupling sequences
(2 1) / 2T j N
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 BathCoupling Solid State Computer
Electron spinNuclear spin
Electron Orbit
B
Magnetic Field
Crystal Lattice
Hyperfine:Fermi ContactDipole-Dipole
Spin-orbital
Nuclear spin
Electron spin
Dipole-dipole
Dipole-Dipole
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 & Nuclear-Nuclear 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
z z z NH S h S H
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
Decoherence by quantum entanglement
( )I t ( )I t
I
( ) ( )I t I t
*( ) ( ) ( )S t C C I t I t
( ) ( )
HC C I
C I t C I t
( ) iH tHI I t e I
t t
Decoherence under Dynamical decouling
H H
H H
DD under simulated noise
Michael J. Biercuk et al. Nature 458 996 (2009)
J.F Du et al. Nature 461 1265 (2009)
DD in solids: ensemble system
After 7 pulses, the coherence enhancement is saturated due to the electron-electron spin coupling.
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
Pulse imperfections in DD
C.A.Ryan et al. Phys. Rev. Lett 105, 200402 (2010)
Dynamical decoupling works in muti-qubit case ?
Nested DD in multi-qubits case
2
2
| | 0 0
0 0 0 0
0 | | 0
0 0 0 0
a ad
a d d
a d
… … ……
( 4)X UDD1( 2)X UDD 0 ( 1)X UDD
… … ……
( ( ))N NQ XDD N2 2( ( ))Q XDD N 1 1( ( ))Q XDD N
Commute or anti-commute
Single qubit operators, e.g. { , , ,0}ni i x y z
Phys. Rev. A 83, 022306 (2011)
Physical Review A 81, 012331(2010)Physical Review A 82, 052338(2010)
CW/Pulsed EPR sepctrometer
Anomalous Decoherence Effect in a Quantum Bath
Nitrogen Vacancy (NV) in Diamond
kcou
nts/
s
1μm
3E
3A2
Flu
ore
sce
nce
Op
tica
l Exc
itatio
n
N
V
Laser
MW
BC
C
C
CC
C
Energy level
3E
3A2
1A1
ms=0
ms=-1ms=1
ODMR spectrum Rabi Oscillation
ODMR setup
25
Optical Parts
26
Microwave and Electronic parts
Quantum Description of decoherence
( )0(0) 0- +Y = - + + + Äa a a J
( )0 0( ) ( ) 0 ( ) ( )j-
- - + +Y = - Ä + Ä + + Äi tt a J t a J t a e J t
( )( )( ) expaaº -J t iH t J
( )a a= +z BH b H
Coherence is lost as which-way information is recorded in the bath
0, 0
,
( ) ( ) ( )
( ) ( ) ( )
± ±
+ - + -
=
=
L t J t J t
L t J t J t
( )- 0iH te
( )+- iH te( )-- iH te
3 ways for nuclear spin of different electron state
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
2 22exp( / )*- t T
Anomalous Decoherence Effect in Muti-pulse DD
Quantum Nature of ADE
0,
ˆ( )a
a a a= ±
= Ä +å z BH b H
in single transition (0,+) case:
( )
0 0 ( )
0 0 ( )2 2
= + + + +
= + + - + +
z
z z
B B
B
H H b H
b bH
in double transition (+,-) case:
( )( ) ( )= - - - + + + + +
= + + - - - +
B B
z B
z zH b H b H
b H
demolished due to DD control
bath operator
back action: cause high frequency moise
Application of dynamical decoupling in Quantum metrology
Standard quantum limit and Heisenberg limit
Generalized uncertainty relation : 1/ 2iHU e h
2 1/ 2[ ]jj
h H
1 1
max
/ ]
1
2
2
1 [
M M m mN N
M m
M m
N
N
h
Vittorio Giovannetti et al. PRL 96, 010401 (2006)
1
2
1 [ ]
2
/
j M m M m
M mN
NH h
An example
11 0 0 1
2
1
1 0 0 12
ie 1
10 0
2N N
10 0
2iNN e N
1/ N
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); ……
Quantum metrology with entanglement
Quantum metrology without entanglement:Multi-round protocol
Vittorio Giovannetti et al. PRL 96, 010401 (2006)
B.L.Higgins et al. Nature 450 393 (2007)
Geometric phase(GP):AA phase
[NV]center in diamond
S = 1
Addressing NV centre
Phase estimation with single GP
Phase estimation with multi GP
φ
Prepare Read out
Repeated N timesClassical:
φ
Prepare Read outRepeated N timesQuantum:
Enhanced phase estimation with CPMG
π
π
π
2k GP
π π
π π
π π
π
ππ/2 π/2
k GP k GP
Analysis
4'
2 2
4'
2 2
2
4 2'
2 2
4'
2 2
( ( ) ( ))sin( )
( ( ) ( )) cos( )
/
( ( ) ( )) cos ( )
( ( ) ( ))
i i
i i
ii
ii
T TI Exp wt N
T T
T TI NExp wt N
T T
I I N
T TExp wt N
T T
T TExp
T T
Future work
Robust gate Dynamically corrected gate(DCG)
PRL 102,080501(2009)…
Combine DD with optimization control
…
Thank you for your attention