Singleshot readout of one electron spin QIP Workshop

Single-shot read-out of one electron spin QIP Workshop Newton Institute, Cambridge 27 -30 Sep. 2004 Lieven Vandersypen Jeroen Elzerman Ronald Hanson Laurens Willems van Beveren Frank Koppens Ivo Vink Wouter Naber Leo Kouwenhoven 1

A seven-spin NMR quantum computer 2 F F 1 6 12 C 13 C 7 13 C F 4 Fe C 5 H 5 F CO 12 C F 3 Vandersypen et al. , Nature 414, 883 (2001) Vandersypen & Chuang, RMP, Oct 2004. 15 = 3 x 5 5 CO 2

Quantum computing with electron spins Loss & Di. Vincenzo, PRA 1998 Vandersypen et al. , Proc. MQC 02 (quant-ph/0207059) Initialization 1 electron, low T, high B 0 H 0 ~ S wi szi Read-out convert spin to charge SL SR then measure charge ESR pulsed microwave magnetic field HRF ~ S Ai(t) cos(wi t) sxi SWAP exchange interaction HJ ~ S Jij (t) si · sj Coherence measure coherence time in 2 DEG: T 2 > 100 ns (Kikkawa&Awschalom, 1998) 3

Electrical single-shot spin measurement Convert spin to charge, then measure charge Loss & Di. Vincenzo, PRA 1998 4

Outline (1) one-electron quantum dots… (3) …fast charge detection… (2) …two-level system… EZ = gm. BB (4) …. single spin measurement! 5

Outline: we need… (1) one-electron double dots… (3) …fast charge detection… (2) …two-level system… EZ = gm. BB (4) …. single spin measurement! 6

A quantum dot as a one-electron box • Electrically measured (contact to 2 DEG) • Electrically controlled (gated tunnel barriers, dot potential) 7

A quantum point contact (QPC) as a charge detector Field et al, PRL 1993 8

Few-electron double dot Transport through QPC J. M. Elzerman et al. , PRB 67, R 161308 (2003) d. IQPC/d. VL 0 Tesla -1. 1 VL (V) 00 VL (V) 01 -1. 02 12 11 22 -0. 9 00 10 21 -0. 96 0 V PR (V) -0. 6 -0. 15 V PR (V) • Double dot can be emptied • QPC can detect all charge transitions -0. 30 9

Outline: we need… (1) one-electron double dots… (3) …fast charge detection… (2) …two-level system… EZ = gm. BB (4) …. single spin measurement! 10

Energy level spectroscopy at B = 0 VSD (m. V) 10 d. IDOT/d. VSD SOURCE T Q G 0 N=1 -10 B -653 200 nm N=0 No transport = 0 T VT (m. V) DRAIN M P R Ground state Ground and excited state -695 • E ~ 1. 1 me. V • EC ~ 2. 5 me. V 11

Single electron Zeeman splitting in B// Hanson et al, PRL 91, 196802 (2003) Also: Potok et al, PRL 91, 016802 (2003) VSD (m. V) 2 ES 0 -2 B=0 N=0 GS B> 0 gm. BB 0 T 2 |g|=0. 44 EZ (me. V) VSD (m. V) 0. 2 0 N=1 N=0 0. 1 6 T -2 -657 VT (m. V) 10 T -675 -995 VR (m. V) -1010 0 0 5 10 B// (T) 1512

Excited-state spectroscopy on a nearly-closed quantum dot IQPC RESERVOIR 200 nm DRAIN t t -VP Q MP R 0 SOURCE • Apply pulse train to gate P • Measure amplitude of pulseresponse with lock-in amplifier time IQPC T Elzerman et al, APL 84, 4617, 2004 Also: Johnson, cond-mat/04 time EF G G Electron tunneling small pulse response 13

Zeeman splitting for N = 1 B = 10 T -1. 135 VM (V) N=1 -1. 150 1 Geff EZ VP (m. V) lock-in signal (arb. units) 10 f = 385 Hz -1. 13 VM (V) N=0 -1. 15 G 14

VSD (m. V) Bipolar spin filter 0 0 N=1 N=0 T- T 0 T+ T 0 S S VSD (m. V) Gate voltage N=2 N=1 Gate voltage Expt: Hanson et al, cond-mat/0311414, Theory: Recher et al, PRL 85, 1962, 2000 15

Outline: we need… (1) one-electron double dots… (3) …fast charge detection… (2) …two-level system… EZ = gm. BB (4) …. single spin measurement! 16

RESERVOIR Fast charge detection T DRAIN IQPC 200 nm • IA = 0. 4 p. A/Hz 1/2 @ 40 k. Hz (~ f ) Q G M P R • VA = 0. 8 n. V/Hz 1/2 (white) • CL = 1. 5 n. F • Operating BW: 40 k. Hz SOURCE • Shot-noise limit: 40 MHz 17

Observation of individual tunnel events RESERVOIR Vandersypen et al, APL, to appear (see cond-mat/0407121) T DRAIN IQPC Q G 200 nm M P R SOURCE • VSD = 1 m. V • IQPC ~ 30 n. A • ∆IQPC ~ 0. 3 n. A • Shortest steps ~ 8 µs 18

Pulse-induced tunneling response to electron tunneling IQPC (n. A) 0. 8 response to pulse 0. 4 0. 0 -0. 4 0 0. 5 1. 0 Time (ms) 1. 5 19

Outline: we need… (1) one-electron double dots… (3) …fast charge detection… (2) …two-level system… EZ = gm. BB (4) …. single spin measurement! 20

Spin read-out principle: convert spin to charge SPIN UP 0 -e time N=1 charge SPIN DOWN 0 -e N=1 N=0 N=1 ~G-1 time 21

IQPC Vpulse Spin read-out procedure empty QD inject & wait read-out spin empty QD 22 Inspiration: Fujisawa et al. , Nature 419, 279, 2002

Spin read-out results empty QD IQPC (n. A) IQPC Vpulse Elzerman et al. , Nature 430, 431, 2004 inject & wait 2 read-out spin “SPIN UP” empty QD “SPIN DOWN” 1 0 0 0. 5 1. 0 Time (ms) 1. 5 23

Spin down fraction Verification spin read-out Waiting time (ms) 24

Measurement of T 1 B=8 T T 1 ~ 0. 85 ms B = 10 T T 1 ~ 0. 55 ms • • Surprisingly long T 1 goes up at low B B = 14 T T 1 ~ 0. 12 ms Elzerman et al. , Nature 430, 431, 2004 25

Single-shot read-out fidelity 1. 0 spin: 0. 8 0. 6 0. 4 a 65% 1 -b 0. 2 0. 0 outcome: 0. 93 a=0 28. 0 b= . 07 “up” “down” 0. 72 0. 6 0. 8 1. 0 Threshold (n. A) • a Pr[ escapes] • b Pr[miss step] + Pr[ relaxes] visibility = 1 -a-b 0. 65 Future improvements: • a: lower Tel • b: faster charge detection 26

Outlook Initialization 1 electron, low T, high B 0 H 0 ~ S wi szi Read-out convert spin to charge SL SR then measure charge ESR pulsed microwave magnetic field HRF ~ S Ai(t) cos(wi t) sxi SWAP exchange interaction HJ ~ S Jij (t) si · sj Coherence measure coherence time T 1 is long; T 2 = ? ? 27

Single Electron Spin Resonance z B 0 f. Larmor fres y W W S B 1 250 μm x 250 nm S’ B 1 B 0 B 1 = 1 m. T f. Rabi~ 5 MHz IAC 28

Detection of Continuous Wave ESR Engel & Loss, PRL 86, 4648 (`01) ESR induced current peak GL m. S GR m. D ISD GL, GR =10 MHz T 2 =100 ns 300 f. A For 1. 1 m. T (~ -10 d. Bm) Peak is only 300 f. A 29

Electron transport under CW microwaves 0. 8 hf from -60 d. Bm to -40 d. Bm I (p. A) hf 0. 0 -1. 029 Photon Assisted Tunneling Pumping gate voltage (V) -1. 023 Electric field dominates signal! 30

Pulsed ESR scheme Apply microwaves Read out spin state electric field component no longer hinders ESR detection 31

ESR in a Si-FET channel M. Xiao et al. Nature 430, 435 (‘ 04) 32

Summary http: //qt. tn. tudelft. nl/research/spinqubits Spin qubit ideas Vandersypen et al, Proc. MQC 02, quant-ph/0207059 Engel et al. PRL (to appear) 00 Tunable few-electron double dot Elzerman et al. , PRB 67, R 161308, 2003 DC or LOCK-IN Zeeman splitting Hanson et al, PRL 91, 196802, 2003 Bipolar spin filter Hanson et al, cond-mat/0311414 Excited states using QPC Elzerman et al, APL 84, 4617, 2004 SINGLE-SHOT Fast charge detection Vandersypen et al, APL to appear, cond-mat/0407121 Single-shot spin read-out T 1 ~ 0. 85 ms (8 T) Elzerman et al, Nature 430, 431, 2004 33

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Tunable double dot design T Ciorga ’ 99 IDOT Open design Field ’ 93 Sprinzak ’ 01 QPC-L QPC-R IQPC L QPC for charge detection PL M PR R Ga. As/Al. Ga. As heterostructure 2 DEG 90 nm deep ns = 2. 9 x 1011 cm-2 35

Few-electron double dot Transport through dots J. M. Elzerman et al. , PRB 67, R 161308 (2003) Peak height 01 VL (V) -1. 02 00 1 p. A 12 11 22 10 2 p. A 21 -0. 96 -0. 15 V PR (V) -0. 30 70 p. A 36

IQPC (n. A) Tunnel process is stochastic out in out Time (ms) 37

Histograms tunnel time G ~ (230 ms)-1 I QPC [a. u. ] G ~ (60 ms)-1 Increase tunnel barrier 38

More spin-down traces IQPC (n. A) twait tread 2 1 thold 0 0 0. 5 1. 0 1. 5 Time (ms) 39

Read-out characterization spin: outcome: 1 -a a b 1 -b “up” “down” 40

Spin down fraction Characterization: a = Pr [“down” if ] p (1 - b - a) exp(- t / T 1) + a 1. 0 0. 8 a Waiting time (ms) 0. 6 IQPC (n. A) 0. 4 2 0. 2 1 0. 0 0. 6 0 0. 8 Threshold (n. A) 0 0. 5 1. 0 1. 5 Time (ms) 41

Characterization: b = Pr [“up” if ] b 1 = Pr [ flips before tunneling ] 1/T 1 1 = 1/T 1 + G T 1 IQPC (n. A) b 2 = Pr [ miss step ] 1 -b (1 -b 1)(1 -b 2) + ab 1 1. 0 0. 6 0. 4 1 1 -b 2 0. 8 a 1 -b 0. 2 0. 0 0 0. 6 Time (ms) 0. 8 1. 0 Threshold (n. A) 42

Finding the spin read-out regime 43

Alternative spin read-out schemes (2) EF gl = gd need gl gd N=2 gl exchange enhanced Etriplet > Esinglet (2 DEG, Englert et al, von Klitzing et al) (Tarucha et al, Loss et al) Vandersypen et al, Proc. MQC 02, see quant-ph/0207059 44

Alternative spin read-out schemes | = (| - | ) + (| + | ) = |S + | T 0 Engel et al, PRL, to appear (cond-mat/0309023) See also: Ono et al, Science, 200245

-1000 Weakly coupled dots 30 20 31 10 21 42 B// = 6 Tesla 00 11 01 32 22 12 02 33 23 13 03 34 24 14 04 -867 Right gate (m. V) 40 d. IQPC/d. VPR -900 -1108 Left gate (m. V) QPC gate (m. V) -1100 -800 46

-1167 Strongly coupled dots d. IQPC/d. VPR Right gate (m. V) B// = 6 Tesla -933 00 -967 -1000 Left gate (m. V) QPC gate (m. V) -1167 -700 47

100 -0. 96 45 90 180 300 -1. 12 0 t VM (V) (ms) 370 -1. 13 • Electron response (dip) disappears for high frequencies (small t) • Dip half-developed when Gt p 0 0 1 2 VR (V) t = 15 ms dip height (%) lock-in signal (arb. units) Electron response reveals tunnel rate 3 4 5 6 7 8 5 -0. 76 f = 4. 17 k. Hz 7 6 -1. 07 VM (V) 4 2 3 -1. 40 • Top: barrier to drain closed • Right: barrier to reservoir closed • Middle: both closed 48

Singlet-triplet and Zeeman for N = 2 1 10 EST N=2 N=1 f = 385 Hz -1. 160 VP (m. V) 10 1 -1. 175 VM (V) G N=2 N=1 f = 1. 538 k. Hz -1. 160 VM (V) -1. 175 Geff S S 49