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