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Single-shot read-out of one electron spin

Explore single-shot read-out of electron spin for quantum information processing in the 2004 Newton Institute Workshop. Learn about quantum dot systems, spin measurement principles, and overcoming challenges in single-spin detection.

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Single-shot read-out of one electron spin

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  1. 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. 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

  3. 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)

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

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

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

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

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

  9. 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

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

  11. 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

  12. 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)

  13. 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

  14. 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

  15. 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

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

  17. 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

  18. 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

  19. 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)

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

  21. 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

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

  23. 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)

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

  25. 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

  26. 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

  27. 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 = ??

  28. 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

  29. 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

  30. 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

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

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

  33. 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

  34. 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

  35. 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

  36. Tunnel process is stochastic out out DIQPC (nA) in Time(ms) Time(ms)

  37. G ~ (60 ms)-1 G ~ (230 ms)-1 Increase tunnelbarrier Histograms tunnel time DI QPC [a.u.]

  38. tread twait thold 0.5 1.0 More spin-down traces 2 DIQPC (nA) 1 0 0 1.5 Time (ms)

  39. Read-out characterization spin: outcome: 1-a “up”  a b “down”  1-b

  40. 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)

  41. Characterization: b = Pr [“up” if ] b1 = Pr [ flips before tunneling ] 1-b = (1-b1)(1-b2) + ab1 1/T1 1 = 1/T1+ G 1 + GT1 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)

  42. Finding the spin read-out regime

  43. gl = gd need glgd 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

  44. Alternative spin read-out schemes | = (| - |)+(| + |) = |S + |T0 Engel et al, PRL, to appear (cond-mat/0309023)See also: Ono et al, Science, 2002

  45. 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

  46. Strongly coupled dots -1167 dIQPC/dVPR B// = 6 Tesla Right gate (mV) 00 -933 Left gate (mV) -967 -1167 QPC gate (mV) -1000 -700

  47. -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 Gtp • Top: barrier to drain closed • Right: barrier to reservoir closed • Middle: both closed

  48. 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

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