Lecture 2: Double quantum dots

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Transcription:

Lecture 2: Double quantum dots Basics Pauli blockade Spin initialization and readout in double dots Spin relaxation in double quantum dots

Quick Review Quantum dot Single spin qubit 1 Qubit states: 450 nm E Zeeman 0 Long spin relaxation time, T 1 ~ 1 sec.

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

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)

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)

Experimental setup Parameters: T= 0.030030 K, Feature size < 100 nm, Frequency = 35 GHz

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, 2 150 100 50 0-1.05-1.00 V R (V) 0.24-1.0 0.20 016 0.16 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) 20 0 5 0 --5-10- -1.1 V R (V) -1.0 Petta et al., PRL 93, 186802 (2004) Elzerman et al., PRB 67, 161308 (2003) GD (10-3 e 2 /h) dg SR /dv VL (a.u.)

Charge -vs- spin qubits Charge physics: The one-electron regime (1,0) (0,1) -500 vs. V L (m mv) -5 0 5 dg rs /dv L (a.u.) (1,0) (1,1) (1,2) (0,0) 0) (0,1) (0,2) -550-450 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

Gate tunable interdot tunnel coupling 1.0 V T (V) -1.11 111-1.08 V t -1.04-1.12-1.01 V L (V) V t =-1.04 V V t M 0.5 0.0-1.13 L (V) V -1.14-10 0 dg S /dv L (au) (a.u.) d) d) V t =-1.01 V -1.10-1.09 V R (V) -1.09 109-1.08 108 V R (V) V t (V) -1.08-1.04-1.01-1 0 1 (mv) M 1 N = 2 1- tanh = 2 +4t 2 DiCarlo et al., kt 2t (GHz) <kt 7.2 16.9 Phys. Rev. Lett. 92, 226801 (2004)

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 -1.1313 f=24 GHz 2 5-1.08 f=24 GHz 2 1 1 0 L (V) V L -1.14 1 2-5 I D (pa) L (V) V L -1.09 1 2 0-10 G (10-3 e 2 S /h) -1.085 V R (V) -1.075-1.080 V R (V) -1.072

Charge qubit spectroscopy On resonance: = (hf) 2-4t 2 V t f<35 GHz V ac Energy 2t hf 1.0 f (GHz) off 10 20 30 ev) 100 V t (V) -1.08-1.04-1.02-1.01 2t (GHz) 24 2.4 6.2 9.2 13.2 M 0.5 Splitting ( 50 0.0 0 0 (mv) -1.0 0 1.0 See also: Oosterkamp et al., Nature 395, 873 (1998) 10 20 f (GHz) 30

Charge relaxation and dephasing measurement 1.00 f=24 GHz 04 0.4 5ns T 2 * 400 ps 1.0 2 1 max()/m ma ax(=5 ns) M m 0.75 ) M( 0.2 0 =1 s N 0.5 0.4 0.8 (mv) 12 db 6 db T 1 ~16 ns 0dB 2h/T* 2 0.50 001 0.01 01 0.1 (s) 1 10 0.0-2.0 20-1.5-1.0-0.5 (mv) Petta et al., PRL 93, 186802 (2004)

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)

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 0 1 2 1 2 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

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, 035320 (2002) Ashoori et al., PRL 71, 613 (1993) S

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) 0 4 8 V L (V) -1.105-1.1 100 (0,0) (0,1) -1.035-1.030 V R (V)

Singlet-triplet spin blockade in dc transport Ono et al., Science 297, 1313 (2002).

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

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

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

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

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

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

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

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

Spin Relaxation and Dephasing: The Two-Electron System Johnson, Petta, Taylor, Yacoby, Lukin, Hanson, Gossard, Marcus, Nature 435, 925 (2005).

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).

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).

Pulsed-Gate Measurement of Spin Relaxation (1,1) 1) (1,2) (0,1)

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).

Spin relaxation: Getting stuck in (1,1) In measurement triangle dark: transition to (0,2) occurs light: transition to (0,2) blockaded

Enhanced, energy-dependent relaxation at zero field

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~10 6-10 7 B nuc ~2-6 mt, t nuc ~3-10 ns

B Nuclear B Nuclear B Zeeman B Total B Total B Zeeman T 1, T 2 short T 1 long; T 2 short

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 =2.8 0.2 mt t nuc ~10 ns = T 2?

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