Lecture 2: Double quantum dots
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1 Lecture 2: Double quantum dots Basics Pauli blockade Spin initialization and readout in double dots Spin relaxation in double quantum dots
2 Quick Review Quantum dot Single spin qubit 1 Qubit states: 450 nm E Zeeman 0 Long spin relaxation time, T 1 ~ 1 sec.
3 Review: Coulomb blockade and charging in a single dot R 1,C 1 R 2,C 2 N-1 N N+1 N+2 I V G Energy V SD Charging energy E 2 c =e /2C V G E F e 2 /C Kastner, RMP 64, 849 (1992) V G V G
4 Double dot charge stability diagram R 1,C 1 R M,C M R 2,C 2 S D Two limits: V G1 V G2 C M 0 C M /C (1,2) 1 (2,0) (2,1) (2,2) V (1,0) (1,1) 1) (1,2) V G1 V G1 (0,0) (0,1) (0,2) V G2 V G2 Double dot review article: van der Wiel et al., RMP 75, 1 (2003)
5 Double dot charge stability diagram R 1,C 1 R M,C M R 2,C 2 S D V G1 V G2 In between these limits: (1,1) (2,0) (2,1) (2,2) V G1 (1,0) (1,1) (1,2) V G1 (0,0) (1,0) (0,0) (0,1) (0,2) (0,1) triple points V G2 V G2 Double dot review article: van der Wiel et al., RMP 75, 1 (2003)
6 Experimental setup Parameters: T= K, Feature size < 100 nm, Frequency = 35 GHz
7 Double dot measurements Charge transport T M, N~20 e 2 G D (10-3 /h) G SL 0.5 m G D G SR -650 V L (m mv) -670 (M+1,N) (M,N) (M+1,N+1) (M,N+1) L R -660 V -640 R (mv) Charge sensing M, N=0, 1, V R (V) QPC sensing: Field et al., PRL 70, 1311 (1993) GSR R (e 2 /h) L (V) V L -1.1 (1,0) (0,0) 0) (1,1) (0,1) V R (V) -1.0 Petta et al., PRL 93, (2004) Elzerman et al., PRB 67, (2003) GD (10-3 e 2 /h) dg SR /dv VL (a.u.)
8 Charge -vs- spin qubits Charge physics: The one-electron regime (1,0) (0,1) -500 vs. V L (m mv) dg rs /dv L (a.u.) (1,0) (1,1) (1,2) (0,0) 0) (0,1) (0,2) V R (mv) -400 Spin physics: The two-electron regime -515 (0,2) (1,1) (1,1) (1,2) vs. V L (m mv) -530 (0,1) (0,2) -415 V R (mv) -400
9 Gate tunable interdot tunnel coupling 1.0 V T (V) V t V L (V) V t =-1.04 V V t M L (V) V dg S /dv L (au) (a.u.) d) d) V t =-1.01 V V R (V) V R (V) V t (V) (mv) M 1 N = 2 1- tanh = 2 +4t 2 DiCarlo et al., kt 2t (GHz) <kt Phys. Rev. Lett. 92, (2004)
10 Photon assisted tunneling in a one-electron double dot E A E A Energy E ħ ħ E B PAT in transport PAT in charge sensing f=24 GHz f=24 GHz L (V) V L I D (pa) L (V) V L G (10-3 e 2 S /h) V R (V) V R (V)
11 Charge qubit spectroscopy On resonance: = (hf) 2-4t 2 V t f<35 GHz V ac Energy 2t hf 1.0 f (GHz) off ev) 100 V t (V) t (GHz) M 0.5 Splitting ( (mv) See also: Oosterkamp et al., Nature 395, 873 (1998) f (GHz) 30
12 Charge relaxation and dephasing measurement 1.00 f=24 GHz ns T 2 * 400 ps max()/m ma ax(=5 ns) M m 0.75 ) M( =1 s N (mv) 12 db 6 db T 1 ~16 ns 0dB 2h/T* (s) (mv) Petta et al., PRL 93, (2004)
13 Charge qubit: Coherent oscillations Enhancement in T 2 at =0 Vion et al., Science (2002) Hayashi et al., PRL (2003), K. D. Petersson et al., PRL (2010)
14 Single spin qubits -vs- Singlet-triplet qubits Single spin qubit (Loss and DiVincenzo) 1 0 E Zeeman Encoded spin qubit- singlet-triplet qubit (J. Levy) Qubit encoded in two-electron spin states S T m S =0 Basis: S and T 0, m S =0 m S =0 Insensitive to field fluctuations decoherence free subspace T T m S =1 m S =-1 Work in magnetic field, T + and T - not relevant due to Zeeman energy
15 The two electron regime (1,1) (1,1) singlet-triplet splitting: j=4t 2 /U=0.4 ev<<kt T - T O T + S j<<kt with U~4 mev, t~20 ev (0,2) (0,2) singlet-triplet splitting: Theory: J~0.3 mev T - T O T + Expt:J~01to1meV Expt.: J~0.1 to 1 J~400 ev Kyriakidis et al., PRB 66, (2002) Ashoori et al., PRL 71, 613 (1993) S
16 Double dot finite bias spectroscopy R L,C L R M,C M R R,C R S D I I d V sd V L V R Finite bias triangles (1,0) (1,1) 1) I d (pa) V L (V) (0,0) (0,1) V R (V)
17 Singlet-triplet spin blockade in dc transport Ono et al., Science 297, 1313 (2002).
18 Singlet-triplet spin blockade in dc transport (0,2) (1,1) transport is allowed L R (1,1) 1) (0,2) transport tis spin blocked V L V L V L V L Johnson, Petta, Marcus (2005). See also Ono et al., Science 297, 1313 (2002). V R V R
19 Singlet-triplet spin blockade in charge sensing R Int (0,0) (0,1) (1,0) L V L V L V L V L V R V R
20 Loss & DiVincenzo Proposal Phys. Rev. A 57, 120 (1998) Prepare spin in ground state Spin to charge conversion T * 1, T 2, T 2 ESR for single spin rotations Exchange interaction Standard semiconductor fabrication
21 Spin singlet state initialization (1,1) (1,2) V L (mv) (0,1) V R (mv) (0,2) T P T P S e J kt 105 S
22 Loss & DiVincenzo Proposal Phys. Rev. A 57, 120 (1998) Prepare spin in ground state Spin to charge conversion T * 1, T 2, T 2 ESR for single spin rotations Exchange interaction Standard semiconductor fabrication
23 Spin state measurement (spin-to-charge conversion) (1,1) (1,2) V L (mv) (0,1) V R (mv) (0,2) (1,1) (0,2) G QPC T Singlet measurement Energy T - T O T + S S
24 Spin state measurement (spin-to-charge conversion) (1,1) (1,2) V L (mv) (0,1) V R (mv) (0,2) G QPC (1,1) (0,2) T Triplet measurement Energy T - T O T + S S
25 Loss & DiVincenzo Proposal Phys. Rev. A 57, 120 (1998) Prepare spin in ground state Spin to charge conversion T * 1, T 2, T 2 ESR for single spin rotations Exchange interaction Standard semiconductor fabrication
26 Spin Relaxation and Dephasing: The Two-Electron System Johnson, Petta, Taylor, Yacoby, Lukin, Hanson, Gossard, Marcus, Nature 435, 925 (2005).
27 Pulsed-Gate Measurement of Spin Relaxation (1,1) 1) (1,2) (0,1) (0,2) Johnson, Petta, Taylor, Yacoby, Lukin, Hanson, Gossard, Marcus, Nature 435, 925 (2005).
28 Pulsed-Gate Measurement of Spin Relaxation (1,1) 1) (1,2) (0,1) (0,2) Johnson, Petta, Taylor, Yacoby, Lukin, Hanson, Gossard, Marcus, Nature 435, 925 (2005).
29 Pulsed-Gate Measurement of Spin Relaxation (1,1) 1) (1,2) (0,1)
30 Pulsed-Gate Measurement of Spin Relaxation (1,1) 1) (1,2) (0,1) (0,2) Johnson, Petta, Taylor, Yacoby, Lukin, Hanson, Gossard, Marcus, Nature 435, 925 (2005).
31 Spin relaxation: Getting stuck in (1,1) In measurement triangle dark: transition to (0,2) occurs light: transition to (0,2) blockaded
32 Enhanced, energy-dependent relaxation at zero field
33 Effective nuclear field from hyperfine interaction Large ensemble with random spin orientations, slow internal dynamics... Quasistatic effective field k B nuc b 0 r k 2 Ik I k rms B nuc b 0 I 0 (I 0 1) / N GaAs: b 0 =3.47 T, I 0 =3/2 Our device: N~ B nuc ~2-6 mt, t nuc ~3-10 ns
34 B Nuclear B Nuclear B Zeeman B Total B Total B Zeeman T 1, T 2 short T 1 long; T 2 short
35 Measuring the nuclear field: Energy dependence of tunnel rates Deviation above 1 ms Additional decay mechanism? t(b) t(0) B B nuc 2 1 B nuc = mt t nuc ~10 ns = T 2?
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