A two-qubit conditional quantum gate with single spins
F.Jelezko, J. WrachtrupI. Popa, T. Gaebel,M. Domhan, C.Wittmann
Univ. of Stuttgart
Outline
• Introduction
• Single spin states: Read-out, manipulation, coherence time
• CROT gate with single electron and nuclear spin in a solid
• Scaling up: Positioning of single N-V defects in diamond
Science 275 (1997) 350-365
History
„is very difficult to realize because of the highsensitivity required to see the small magneticinduction signal created by a single nucleus“1
A pure state (single spin EPR,NMR):
but see e.g. J. Wrachtrup, A. Gruber, L. Fleury, C. von Borczyskowski „Magnetic Resonance on single nuclei“ CPL 267 (1997) 179
Single spin read-out
2. Electrical detection
Durkan, C. & Welland, M. E. Appl. Phys. Lett. 80, 458-460 (2002) - STM
3. Optically detected ESR on single spin
See e.g. Jelezko et al. APL 81 (2002) 2160,
Jelezko & Wrachtrup Journal of Physics: Condensed Matter 16, R1089 (2004)
1. Magnetic Resonance Force MicroscopyRugar et al. Nature 430, 329 (2004);
M. Xiao, I. Martin, E. Yablonovitch, H. W. Jiang Nature 430, 435 - 439 (2004) - FET
J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, L. P. Kouwenhoven Nature 430, 431 - 435 (2004)
Optical readout
ESR (10-5 eV)
Optical transition (2 eV)
The number of scattered photonsdepends on spin stateBrossel and Bitter (1952) Phys. Rev. 86 308 (mercury vapours)Wrachtrup et al. Nature 363, 244–245 (1993) (single molecules)
300 nm
300
nm
Single defect detection:Optical microscopy
Set-up
MW and RF loop
500
Microwave resonator (D. Suter Univ. Dortmund)Typical value for ESR -pulse - 10 ns
Variable temperature microscopeOperating temperature – 1,6 – 300 KDetection yield – 1 percent
Magnetic field – up to 5 T
Optical microscope
MO, N. A. 0.85
Superconducting magnet
Nitrogen Vacancy (NV) center in diamond
3A
3E1A
E=
1.94
5eV
3 G
Hz
Diamond:-bandgap 6 eV-Tdebay: 2000KLong T2 of defects at RT
Optical detection of single defectsGruber A, Wrachtrup J et al, SCIENCE 276 2012 (1997)
Single N-V centers implantation
10 µmApp. 2 N iones/ N-V defect
Single center signature: photon antibunching
Photon stream
t
1
2
-100 -50 0 50 1000,0
0,2
0,4
0,6
0,8
1,0
g(2) ()
, ns
2
2
tI
tItIg
Single photon source:Weinfurter et al. PRL 85 (2000)Grangier et al. PRL 89 (2003)
Observation of single electron spin quantum jump at T=2K
ms=0
ms=±1
Relaxation time:T1:1-2 s (2 K)2 ms (300 K)
3E1A
ms=±10 2 4
0
10
I fl, Ct
s/10m
s
Time, s
ms=0
200 300 400
0
2
4
6
8
10
12
14
16
Flu
ore
sce
nce
, C
ts/
20
ms
Laser Detuning, MHz
Flu
ores
cenc
e/a.
u.
40MHz
E~3GHz
Single defects:Jelezko F et al. APL 81 , 2160 (2002)
Low temperature optical spectroscopy, bulk:D. Redman J. Opt. Soc. Am. B 9, No. 5, (1992).
Inhibition of coherent spin state evolution by measurement („ a watched pot never boils“)
Weak probe
MW pulse
ms=0
ms=±1
prob
e Spin system:T1~ 2msT2: ?
T=300K
1.5 2.0 2.5 3.0
2700
3000
3300
flu
ore
scen
ce, a.u
.
time [µs]
Strong probe
1,2 1,4 1,6 1,8 2,0 2,2
8000
9000
10000
11000
flu
ore
scen
ce, a.u
.
time, [µs]
Switch off the Laser light during manipulating the spin
time
IMW
Laser Laser
How large is T2?Hahn Echo
0,0 0,2 0,4 0,6 0,8 1,0
46
48
50
52
54
56
fluor
esce
nce,
a. u
.
t1, microseconds
= 0.3 s
/2 /2
t1
Hahn echo decay
0,0 0,5 1,0 1,51,1
1,2
1,3
1,6
1,7
1,8
H0=0.02 T
H0=0 T
fluor
esce
nce
inte
nsity
[a. u
.]
time [µs]
0 10 20 30 400
2
4
am
plitu
de frequency [MHz]
0 10 20 30 400
5
10
frequency [MHz]
am
plitu
de
F. Jelezko et al PRL 92 (2004) 076401
„first data“: T2 0.3-0.5 s Decoherence due to P1 centers ?(P1 - single substitutional nitrogen,100 ppm in HPHT Ib diamond)
Hahn echo decay of single N-V center in IIa type diamond
0 20 40 60 80 100 120 140 160 1800,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06T
2= 0.35 ms, T= 300 K
Flu
ores
cenc
e, a
. u.
2, µs
/2 /2
1 2
pulse – 8 nsT2/Tgate = 105
Hyperfine splitting A1,2,3 = 130 MHz
Optical single nuclear spin read-out (13C diamond)
BI g I AS S DS S B g Hi n ni i i e e Fine Structure:Splittting: 3 GHz
1
23
13C spins as qubits: Wrachtrup Opt. Spectr. 91 429 (2001) – optical spectroscopy
Ab initio calculations:M.Luszczek et al. Physica B 348, 292 (2004)
Experimental realization using ESR:Jelezko et al. Phys. Rev. Lett. 93, 130501 (2004)
2800 2850 2900 2950
coupling to single 13C
127 MHz
Flu
ore
scen
ce, a
. u.
MW frequency, MHz
Gates: qubits
A B
C
00
1 0
1 0
11
4
2
3
1
D
1st qubit: electron spin of N-V2nd qubit: nuclear spin of 13C
A:2800 MHzB:2940 MHz
C:130 MHzD:10 MHz
ESR NMR (ENDOR)
Rabi nutation of single electron and single 13C spin – single qubit operations
C
Averages over 105 Cycles
0 1 2 3 4 5 6 7
0,70
0,75
0,80
0,85
norm
aliz
ed fl
uore
scen
ce
pulse length, µs
0,0 0,2 0,4 0,6 0,8 1,0
0,85
0,90
0,95
1,00
ESR (transition A)
ENDOR (transition C)
A
C
00
1 0
1 0
11
4
2
3
1
CROT-gatea two qubit gate
1000
0100
0001
0010
CROT
flips the nuclear spin dependent on the orientation of the electron spin
with π/2(z) equivalent to the CNOT-gate
Experimental: selective NMR π-pulse
OutputInput
00
1 0
1 0
11
4
2
3
1 π
Tomography of state after CROT
14
23
32
11
22
33
12 13
21 24
31 34
42 44 4431
ρ
statestate
Initial state:
00
1 0
1 0
11
4
2
3
1
Ideal result: ρ
statestate
π
Tomography of state after CROT
Parameters for calculation:
ESR: 15 ns; T2e=1.2 s; NMR:400 ns; T2n=3.6 s;
Experiment Theory
0.1 0.16 0.04 0
0.16 0.9 0.12 0
0.04 0.12 0 0
0 0 0 0
CROT=
Jelezko et al. quant-ph/0402087
Scaling up
13C spin cluster is scalable up to 3-12 qubits
1
23
Fully scalable architecture – coupled NV defects
N+
beam5 nmDiamond
NV defect
Coupling: magnetic dipole (short range)Optical dipole (long range)
Positioning accuracy limitations
N+ ions, 2MeV
N+ ions
1,1µm
surface of sample
target depth~500nm FWHM
1 nm accuracy for 1 keV ions possible
Summary single spin QC
1 and 2 Qbit operation ( 3. Qbit 14N not used in experiment)
Single electron and nuclear spin state read-out and coherent manipulation
scaling requires coupling of defects (nm positioning)
Acknowledgment
In collaboration with:S.Kilin, A. Nizovtsev (Minsk)J. Twamley (University of Ireland)J. Buttler (NRL Washington)JD. Suter (Dortmund)J. Meyer (Bochum)J. Rabeau, S. Prawer (Melbourne)
DFG, EU (QIPDDF ROSES) Landesstiftung BW
at U niversity o f S tuttgartat U niversity o f S tuttgart
The S ingle M olecule G roupThe S ingle M olecule G roup
3. Institute of PhysicsUniversity of Stuttgart
J. Wrachtrup
I. Popa
T. Gaebel,
M. Domhan
C.Wittmann
A. Gruber*
* currently at University of Chemnitz