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