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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. 2. 1. F. F. 6. 3. F. 12 C. 13 C. 7. 13 C. F.
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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
2 1 F F 6 3 F 12C 13C 7 13C F 12C 5 4 Fe F CO C5H5 CO A seven-spin NMR quantum computer Vandersypen et al., Nature414, 883 (2001) Vandersypen & Chuang, RMP, Oct 2004. 15 = 3 x 5
SL SR Quantum computing with electron spins Loss & DiVincenzo, PRA 1998Vandersypen et al., Proc. MQC02 (quant-ph/0207059) Initialization1 electron, low T, high B0 H0 ~ Swi szi Read-out convert spin to charge then measure charge Read-out convert spin to charge then measure charge ESRpulsed microwave magnetic field HRF ~ S Ai(t) cos(wi t) sxi SWAPexchange interaction HJ ~ S Jij (t) si ·sj Coherencemeasure coherence time in 2DEG:T2 > 100 ns (Kikkawa&Awschalom, 1998)
Electrical single-shot spin measurement Convert spin to charge, then measure charge Loss & DiVincenzo, PRA 1998
Outline (1) one-electron quantum dots… (3) …fast charge detection… (4) ….single spin measurement! (2) …two-level system… EZ = gmBB
Outline: we need… (1) one-electron double dots… (3) …fast charge detection… (4) ….single spin measurement! (2) …two-level system… EZ = gmBB
A quantum dot as a one-electron box • Electrically measured (contact to 2DEG) • Electrically controlled (gated tunnel barriers, dot potential)
A quantum point contact (QPC) as a charge detector Field et al, PRL 1993
01 00 12 11 10 (V) (V) 22 21 L L V V -1.02 (V) (V) V V PR PR -0.96 -0.15 -0.30 Few-electron double dotTransport through QPC J.M. Elzerman et al., PRB 67, R161308 (2003) dIQPC/dVL 0 Tesla -1.1 00 -0.9 0 -0.6 • Double dot can be emptied • QPC can detect all charge transitions
Outline: we need… (1) one-electron double dots… (3) …fast charge detection… (4) ….single spin measurement! (2) …two-level system… EZ = gmBB
T DRAIN SOURCE Q G 200 nm M R P Energy level spectroscopy at B = 0 10 dIDOT/dVSD VSD(mV) 0 N=1 N=0 Ground and excited state Ground state Notransport B = 0T -10 -653 -695 VT(mV) • E ~ 1.1meV • EC ~ 2.5meV
2 B=0 B> 0 ES VSD (mV) N=0 0 gmBB GS 0T -2 2 |g|=0.44 0.2 VSD (mV) DEZ (meV) N=1 N=1 N=0 N=0 0 0.1 6T 10T -2 0 VT(mV) VR (mV) -657 -675 -995 -1010 15 0 5 10 B// (T) Single electron Zeeman splitting in B// Hanson et al, PRL 91, 196802 (2003)Also: Potok et al, PRL 91, 016802 (2003)
T Q M R P Excited-state spectroscopy on a nearly-closed quantum dot Elzerman et al, APL 84, 4617, 2004Also: Johnson, cond-mat/04 DRAIN 0 t t IQPC -VP time RESERVOIR DIQPC time 200 nm G SOURCE EF G • Apply pulse train to gate P • Measure amplitude of pulse-response with lock-in amplifier Electron tunneling small pulse response
Zeeman splitting for N = 1 10 DEZ lock-in signal (arb.units) VP (mV) B = 10 T N = 0 N = 1 -1.150 -1.135 VM (V) f = 385 Hz 1 -1.13 VM (V) -1.15 Geff G
T0 T- T+ T0 VSD (mV) S S N=2 N=1 Gate voltage Expt: Hanson et al, cond-mat/0311414, Theory: Recher et al, PRL 85,1962, 2000 Bipolar spin filter 0 VSD (mV) 0 N=1 N=0 Gate voltage
Outline: we need… (1) one-electron double dots… (3) …fast charge detection… (4) ….single spin measurement! (2) …two-level system… EZ = gmBB
T Q M R P Fast charge detection DRAIN • VA = 0.8nV/Hz1/2 (white) • IA = 0.4 pA/Hz1/2 @ 40 kHz (~ f ) • CL = 1.5 nF • Operating BW: 40 kHz • Shot-noise limit: 40 MHz RESERVOIR IQPC G 200 nm SOURCE
T Q M R P Observation of individual tunnel events Vandersypen et al, APL, to appear (see cond-mat/0407121) DRAIN RESERVOIR IQPC G 200 nm SOURCE • VSD = 1 mV • IQPC ~ 30 nA • ∆IQPC ~ 0.3 nA • Shortest steps ~ 8 µs
Pulse-induced tunneling response to electron tunneling 0.8 response to pulse 0.4 DIQPC (nA) 0.0 -0.4 0 0.5 1.0 1.5 Time(ms)
Outline: we need… (1) one-electron double dots… (3) …fast charge detection… (4) ….single spin measurement! (2) …two-level system… EZ = gmBB
Spin read-out principle:convert spin to charge charge SPIN UP 0 -e time N = 1 charge SPIN DOWN 0 -e time N = 1 N = 0 N = 1 ~G-1
Spin read-out procedure inject & wait read-out spin empty QD empty QD Vpulse DIQPC Inspiration: Fujisawa et al., Nature 419, 279, 2002
Spin read-out results Elzerman et al., Nature 430, 431, 2004 inject & wait read-out spin empty QD empty QD Vpulse DIQPC 2 “SPIN UP” “SPIN DOWN” DIQPC (nA) 1 0 0 0 0.5 1.0 0.5 1.0 1.5 1.5 Time (ms) Time (ms)
Verification spin read-out Spin down fraction Waiting time (ms)
Measurement of T1 B = 8 T T1 ~ 0.85 ms B = 10 T T1 ~ 0.55 ms • Surprisingly long T1 • T1goes up at low B B = 14 T T1 ~ 0.12 ms Elzerman et al., Nature 430, 431, 2004
Single-shot read-out fidelity 1.0 spin: outcome: 0.8 0.93 “up” 0.6 a=0.07 a 1-b 65% 0.4 b=0.28 0.2 “down” 0.0 0.72 0.6 0.8 1.0 visibility = 1-a-b 0.65 Threshold (nA) • a = Pr[ escapes] • b = Pr[miss step] + Pr[relaxes] • Future improvements: • a: lower Tel • b: faster charge detection
SL SR Outlook Initialization1 electron, low T, high B0 H0 ~ Swi szi Read-out convert spin to charge then measure charge ESRpulsed microwave magnetic field HRF ~ S Ai(t) cos(wi t) sxi SWAPexchange interaction HJ ~ S Jij (t) si ·sj Coherencemeasure coherence time T1 is long; T2 = ??
z B0 fLarmor S 250 nm fres B1 B1 y B0 S’ IAC Single Electron Spin Resonance W W 250 μm x B1 = 1 mT fRabi~ 5 MHz
ESR induced current peak GL GR mS ISD mD Detection of Continuous Wave ESR Engel & Loss, PRL 86, 4648 (`01) GL, GR =10 MHz T2 =100 ns For 1.1 mT (~ -10dBm) Peak is only 300 fA 300 fA
0.8 I (pA) 0.0 -1.023 Electric field dominates signal! Photon Assisted TunnelingPumping -1.029 gate voltage (V) Electron transport under CW microwaves from -60dBm to -40dBm hf hf
Pulsed ESR scheme Apply microwaves Read out spin state electric field component no longer hinders ESR detection
ESR in a Si-FET channel M. Xiao et al.Nature 430, 435 (‘04)
00 Summary http://qt.tn.tudelft.nl/research/spinqubits Spin qubit ideas Vandersypen et al, Proc. MQC02,quant-ph/0207059 Engel et al. PRL (to appear) Tunable few-electron double dot Elzerman et al., PRB 67, R161308, 2003 DC or LOCK-IN SINGLE-SHOT Zeeman splitting Fast charge detection Hanson et al, PRL 91, 196802, 2003 Vandersypen et al, APL to appear, cond-mat/0407121 Bipolar spin filter Single-shot spin read-outT1 ~ 0.85 ms (8 T) Hanson et al, cond-mat/0311414 Excited states using QPC Elzerman et al, Nature 430, 431, 2004 Elzerman et al, APL 84, 4617, 2004
Ciorga ’99 QPC-R QPC-L Open design GaAs/AlGaAs heterostructure 2DEG 90 nm deep ns = 2.9 x 1011 cm-2 Tunable double dot design T IDOT IQPC IQPC Field ’93Sprinzak ’01 PR PL R L M QPC for charge detection
01 00 12 -1.02 11 10 (V) 22 21 L V -0.96 (V) V -0.15 -0.30 PR Few-electron double dotTransport through dots J.M. Elzerman et al., PRB 67, R161308 (2003) Peak height 1 pA 2 pA 70 pA
Tunnel process is stochastic out out DIQPC (nA) in Time(ms) Time(ms)
G ~ (60 ms)-1 G ~ (230 ms)-1 Increase tunnelbarrier Histograms tunnel time DI QPC [a.u.]
tread twait thold 0.5 1.0 More spin-down traces 2 DIQPC (nA) 1 0 0 1.5 Time (ms)
Read-out characterization spin: outcome: 1-a “up” a b “down” 1-b
2 1 DIQPC (nA) 0 0 0.5 1.0 1.5 Time (ms) Characterization: a = Pr [“down” if ] p(1- b - a) exp(- t / T1) +a Spin down fraction 1.0 0.8 a Waiting time (ms) 0.6 0.4 0.2 0.0 0.6 0.8 1.0 Threshold (nA)
Characterization: b = Pr [“up” if ] b1 = Pr [ flips before tunneling ] 1-b = (1-b1)(1-b2) + ab1 1/T1 1 = 1/T1+ G 1 + GT1 1.0 1-b2 0.8 b2= Pr [ miss step ] 0.6 a 1-b 0.4 1 DIQPC (nA) 0.2 0.0 0 0.6 0.8 1.0 Threshold (nA) Time (ms)
gl = gd need glgd N=2 Etriplet > Esinglet gl exchange enhanced (2 DEG, Englert et al, von Klitzing et al) (Tarucha et al, Loss et al) Alternative spin read-out schemes (2) EF Vandersypen et al, Proc. MQC02, see quant-ph/0207059
Alternative spin read-out schemes | = (| - |)+(| + |) = |S + |T0 Engel et al, PRL, to appear (cond-mat/0309023)See also: Ono et al, Science, 2002
Weakly coupled dots dIQPC/dVPR -1000 30 40 20 10 B// = 6 Tesla 00 31 21 11 42 01 32 Right gate (mV) 22 12 02 33 23 13 03 34 24 14 04 -867 Left gate (mV) -900 -1100 QPC gate (mV) -1108 -800
Strongly coupled dots -1167 dIQPC/dVPR B// = 6 Tesla Right gate (mV) 00 -933 Left gate (mV) -967 -1167 QPC gate (mV) -1000 -700
-0.96 0 100 1 2 dip height (%) 3 4 VR (V) 5 6 0 t (ms) 0 370 7 8 2 f = 4.17 kHz 5 4 6 3 7 -0.76 VM (V) -1.07 -1.40 Electron response reveals tunnel rate t = 15 ms 45 lock-in signal (arb.units) 90 180 300 -1.12 -1.13 VM (V) • Electron response (dip) disappears for high frequencies (small t) • Dip half-developed when Gtp • Top: barrier to drain closed • Right: barrier to reservoir closed • Middle: both closed
Singlet-triplet and Zeeman for N = 2 10 10 DEST VP (mV) VP (mV) N = 2 N = 1 N = 2 N = 1 f = 385 Hz f = 1.538 kHz 1 1 -1.160 -1.160 -1.175 -1.175 VM (V) VM (V) Geff G S S