universal dynamical decoupling of single electron spins in...
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Universal dynamical decoupling of single electron spins in diamond
D. Ristè, R. Hanson (TU Delft, Netherlands)Z. Wang, V. Dobrovitski (Ames Laboratory, ISU)
Gijs de Lange
Why do dynamical decoupling?
Need to mitigate decoherence Exploit high fidelity control of quantum systems
sensor
substrate
Exploit coherence of a single quantum system for:
Quantum information
Metrology
Ultra sensitive probes (magnetometry)
t
δB(t) fluctuating field (environment)
δB(t)y(t,T) effective field+1
t
y(t,T)
T
π
-1
ππ
total free evolution time
filter function
Pulse sequence
Sequence of π-pulses to suppress fluctuations in δB(t)
Recoherence: Dynamical Decoupling
System under study: Defect centers in Diamond
• Paramagnetic spin 1• Zero field splitting D = 2.87 GHz• Optical polarization• Optical read out
CC
CC
N
C
C
C
Central spin: Nitrogen Vacancy center Bath spins: Nitrogen impurities
• Paramagnetic impurity with electron spin1/2
• No fluorescence
2ˆ ˆ
ˆˆ
NV zH DS
A
γ= +
+
B S
I S
g
g1
ˆPH γ= B Sg
C CC
CC
C
N
V
ΔE
Bz100 G
Quantum control on an NV center in a spin bath
NV 1
NV 2
12 µm
C CC
CC
C
N
V
Quantum control on an NV center in a spin bath
NV 1
NV 2
12 µm
C CC
CC
C
N
V
0 20 40 60 80 100
0
1
microwave burst length (ns)
0P
-1
0
1
Ixσ
yσzσ
zσyσ
xσI
πx:
0.99ﾻF
-1
0
1
Ixσ
yσzσ
zσyσ
xσI
πy:
Probing the local NV environment
3( / )free SEt Te−:
0
0
1
0.0 0.2 0.4 0.6 0.8
P
2 2
2
b t
e−
:DecayDecay
Spin echo Ramsey fringes
free evolution time (µs)0 2 4 6free evolution time (µs)
0.5
1
sta
te f
ide
lity
Probing the local NV environment
1 J. Klauder, P. Anderson Phys. Rev. 125, 912 (1962)
3( / )free SEt Te−:
0
0
1
0.0 0.2 0.4 0.6 0.8
P
2 2
2
b t
e−
:DecayDecay
Spin echo Ramsey fringes
cτ
free evolution time (µs)0 2 4 6free evolution time (µs)
0.5
1
sta
te f
ide
lity
Slow bath:( ) ( ) | / |20 ctB B t b e τδ δ −=f
spectral density
-1
2.6 μs
3.6 μs
25 μs
SE
c
T
b
τ
=
=
=
Bath dynamics1:
1/ cτ
2cb τ
Dynamical decoupling of a single spin
0 2 4 6
N=4N=8
N=2N=1
free evolution time (µs)
0.5
1
sta
te f
ide
lity
N=12 pulses
0 5 10 15
1
free evolution time (µs)
x
y
simulation0.6
sta
te f
ide
lity
Not universal
x
y x
y
CPMG:πx
N/2
τ 2τ τpreparation readout
πx
CPMG:
G. de Lange et al., Science. 330, 60 (2010)
Dynamical decoupling of a single spin
XY4:πx
N/4
τ 2τ τpreparation readoutπyπy πx
2τ 2τ
-1
0
1
Ixσ
yσzσ
zσyσ
xσI
Ixσ
yσzσ
zσyσ
xσI
-1
0
1
Re(χ) Im(χ)
Universal decoupling!
Preserving an arbitrary state:
T = 5.1 μs
F = 0.98
x
y
z
x
y
T. Gullion et al., J. Mag. Res. 89, 479 (1990)
"CPMG-like" timing
free evolution time (µs)0 5 10 15
1
x
y
simulation0.6
sta
te f
ide
lity
XY4
12 pulses
Going to higher number of pulses
1 10 100
0.5
1
free evolution time (µs)
SE N = 4 N = 16 N = 72
sta
te fi
de
lity
Re(χ) Im(χ)
-1
0
1
Ixσ
yσzσ
zσyσ
xσI
-1
0
1
Ixσ
yσzσ
zσyσ
xσI
Universal decoupling!
T = 8 μs
72 pulses
F = 0.98
XY4:πx
N/4
τ 2τ τπyπy πx
2τ 2τ
x
y
z
x
y
"CPMG-like" timing
G. de Lange et al., Science. 330, 60 (2010)
Scaling with N
1 10 100
100
10
number of pulses N
1/e
de
cay
time
(μs
)
NV2XY4SE
NV1XY8XY4 CXY4SE
2/3=N SET N T
Scaling with N:
1 10 100
0.5
1
free evolution time (µs)
SE N = 4 N = 16 N = 72
sta
te f
ide
lity
3 2 / 3 3(2 / ) [2 /( )]SE SEN
T N N Te eτ τ− −� � =� �Free evolution time
G. de Lange et al., Science. 330, 60 (2010)
A first application: Magnetometry
Why an NV center:• High spatial resolution• Room-temperature operation• Not toxic• Tunable sensitivity with DD sequences
Challenge: detection of single spins (nuclei, protons...)
sensor
substrate
Dipolar interaction ~1/r3
AC-Magnetometry
2τ
y
t = 6τ
x
y
t = 4τ
xx
y
t = 2τt = 0
y
x
t0
+Bz
-Bz
lab frametoggling frame
π π π
∆π
Bz1/(2f)
0 40 80 120-0.5
0.0
0.5
<S x>
N
1.7 μT, 1 MHzzB f= =
With pulses
G. de Lange et al., arXiv:1008.4395 (2010)
Increased sensitivity!
0 40 80
0.0
0.1
0.2
<S
x>
554 kHz 658 kHz 769 kHz
N
linear regime
/ const=zNB f
mindBη = T
Sensitivity = minimum detectable field in 1 s
0 40 80
250
500
η(n
T H
z-1/2)
554 kHz 658 kHz 769 kHz
N
AC-signal in phase with sequence
arXiv:1008.4395
G. de Lange et al., arXiv:1008.4395 (2010)
Concluding
0 40 80
250
500
η(n
T H
z-1/2)
554 kHz 658 kHz 769 kHz
N
A first application: Increased sensitivity for magnetometry
Universal dynamical decoupling of
a single solid state spin
Re(χ) Im(χ)
-1
0
1
Ixσ
yσzσ
zσyσ
xσI
-1
0
1
Ixσ
yσzσ
zσyσ
xσI
SE N = 4 N = 16 N = 72
increased coherence time: 2/3=N SET N T
(26x for N=136)
G. de Lange et al., arXiv:1008.4395 (2010)