Quantum Information Processing with Semiconductor Quantum Dots. slides courtesy of Lieven Vandersypen, TU Delft

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1 Quantum Information Processing with Semiconductor Quantum Dots slides courtesy of Lieven Vandersypen, TU Delft

2 Can we access the quantum world at the level of single-particles? in a solid state environment? S L S R Kane, Nature 1998 Imamoglu et al, PRL 1999 Loss & DiVincenzo PRA 1998

3 Electrically controlled and measured quantum dots A small semiconducting (or metallic) island where electrons are confined, giving a discrete level spectrum SOURCE e ISLAND DRAIN GATE V sd V g I Coupled via tunnel barriers to source and drain reservoirs Coupled capacitively to gate electrode, to control # of electrons

4 Examples of quantum dots single molecule self-assembled QD lateral QD nanotube 1 nm 10 nm 100 nm 1µm metallic nanoparticle vertical QD nanowire

5 Electrostatically defined quantum dots Electrically measured (contact to 2DEG) Electrically controlled number of electrons Electrically controlled tunnel barriers

6 Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC02 (quant-ph/ ) Initialization 1-electron, low T, high B 0 H 0 ~ Σ ω i σ zi Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ Σ A i (t) cos(ω i t) σ xi exchange interaction EZ = gµbb H J ~ Σ J ij (t) σ i σ j Coherence long relaxation time T 1 long coherence time T 2 J(t)

7 Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC02 (quant-ph/ ) Initialization 1-electron, low T, high B 0 H 0 ~ Σ ω i σ zi Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ Σ A i (t) cos(ω i t) σ xi exchange interaction EZ = gµbb H J ~ Σ J ij (t) σ i σ j Coherence long relaxation time T 1 long coherence time T 2 J(t)

8 Transport through quantum dot - 50 Coulomb blockade Current dot [pa] µ N=3 µ N=2 µ L µ R µ N=1 Is this the last electron?? Gate Voltage [mv]

9 A quantum point contact (QPC) as a charge detector Field et al, PRL 1993 Conductance (e 2 /h) QPC gate voltage (V) QPC Current (na) Dot plunger voltage (V)

10 The last electron! Dot current [pa] N=2 N=1 N= Current QPC [pa] Gate Voltage [mv] Sprinzak et al 01

11 Few-electron double dot design Ciorga et al 99 I DOT T Elzerman et al., PRB 2003 Open design Field et al 93 Sprinzak et al 01 QPC-L I QPC I QPC QPC-R QPC for charge detection GaAs/AlGaAs wafers: L P L M P R R 200 nm NTT (T. Saku, Y. Hirayama) Sumitomo Electric Universität Regensburg (W. Wegscheider)

12 Few-electron double dot Measured via QPC J.M. Elzerman et al., PRB 67, R (2003) -1.1 diqpc/dv L 0 Tesla V L (V) 00 V L (V) V PR (V) V PR (V) Double dot can be emptied QPC can detect all charge transitions

13 Single electron tunneling through two dots in series Γ L Γ R ΓΓ L L Γ R Γ R µ S µ (N+1,N) µ (N,N+1) µ D µ D Vg1 Vg2

14 Few-electron double dot Transport through dots J. Elzerman et al., cond-mat/ Peak height < 1 pa V L (V) pa V PR (V) pa

15 Energy level spectroscopy at B = 0 10 di DOT /dv SD SOURCE T DRAIN (mv) V SD 0 N=1 B = 0 T V T (mv) E ~ 1.1meV E C ~ 2.5meV N=0 No transport Γ 200 nm M P R Ground state transport Q Ground and excited state transport

16 Single electron Zeeman splitting in B // V SD (mv) 2 2 ES 0 GS N=0-2 0T Hanson et al, PRL 91, (2003) Also: Potok et al, PRL 91, (2003) B=0 B> 0 gµbb g =0.44 V SD (mv) N=1 N=1 6T N=0 V T (mv) -675 N=0 10 T -995 V R (mv) E Z (mev) B // (T)

17 Initialization of a single electron spin Method 1: spin-selective tunneling Method 2: relaxation to ground state

18 Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC02 (quant-ph/ ) Initialization 1-electron, low T, high B 0 H 0 ~ Σ ω i σ zi Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ Σ A i (t) cos(ω i t) σ xi exchange interaction EZ = gµbb H J ~ Σ J ij (t) σ i σ j Coherence long relaxation time T 1 long coherence time T 2 J(t)

19 Spin read-out principle: convert spin to charge charge SPIN UP N = 1 0 -e time charge 0 SPIN DOWN N = 1 N = 0 N = 1 -e Γ -1 time

20 Observation of individual tunnel events Vandersypen et al, APL 85, 4394, 2004 Also: Schlesser et al, 2004 RESERVOIR Γ T I QPC DRAIN Q 200 nm M P R SOURCE V SD = 1 mv I QPC ~ 30 na I QPC ~ 0.3 na Shortest steps ~ 8 µs

21 Pulse-induced tunneling I QPC (na) response to pulse response to electron tunneling Time (ms)

22 Spin read-out procedure V pulse empty QD inject & wait read-out spin empty QD I QPC Inspiration: Fujisawa et al., Nature 419, 279, 2002

23 V pulse empty QD Spin read-out results Elzerman et al., Nature 430, 431, 2004 inject & wait read-out spin empty QD I QPC I QPC (na) SPIN UP SPIN DOWN Time (ms) Time (ms)

24 Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC02 (quant-ph/ ) Initialization 1-electron, low T, high B 0 H 0 ~ Σ ω i σ zi Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ Σ A i (t) cos(ω i t) σ xi exchange interaction EZ = gµbb H J ~ Σ J ij (t) σ i σ j Coherence long relaxation time T 1 long coherence time T 2 J(t)

25 ESR detection in a single dot ESR lifts Coulomb blockade Engel & Loss, PRL 2001

26 Double dot in spin blockade for ESR detection E z ~µev<<kt!! ~mev T(0,2) S(0,2) Advantage: interdot transition instead of dot-lead transition Insensitive to temperature can use B < 100 mt, f < 500 MHz Insensitive to electric fields ESR flips spin, lifts spin blockade Combine Engel & Loss (PRL 2001) ESR detection with Ono & Tarucha (Science 2002) spin blockade

27 ESR device design B DC B AC Gates ~ 30 nm thick gold Dielectric ~ 100nm calixerene Stripline ~ 400nm thick gold Expected AC current ~ 1mA Expected AC field ~ 1mT Maximize B 1, minimize E 1 Ω Ω 250 µm

28 ESR spin state spectroscopy Dotcurent(fA) (mv) V R Dot current (fa) RF at 460 MHz P~-16dBm RF off Magnetic 500 field (mt) 150 RF frequency (MHz) ESR signature: Sattelite peaks emerge at spin resonance condition ( g-factor ~ 0.35) I dot (fa) Koppens et al., Nature Magnetic field (mt)

29 V(mV) R Coherent manipulation: pulse scheme Spin blockade Coulomb blockade Spin manipulation Projection S(0,2) V(mV) 6 RF signal 0 Gate pulse Initialization Manipulation Read-out time Initialization in mixture of and Measurement switched off (by pulsing to Coulomb blockade) during manipulation Read-out: projection on {,} vs. {,} basis

30 Dotcurent(fA) Coherent rotations of single electron spin! Koppens et al. Nature 2006 Oscillations visible up to 1µs Decay non exponential slow nuclear dynamics (non-markovian bath) Agreement with simple Hamiltonian taking into account different resonance conditions both dots

31 Dotcurent(fA) Driven coherent oscillations -6 I dot (fa) RF Power (dbm) Burst time (ns) Oscillation frequency ~ B AC π/2 pulse in 25ns max B 1 = B AC /2 = 1.9 mt B N,z = 1.3 mt clear signature of Rabi oscillations estimated fidelity ~73% Koppens et al. Nature 2006

32 Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC02 (quant-ph/ ) Initialization 1-electron, low T, high B 0 H 0 ~ Σ ω i σ zi Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ Σ A i (t) cos(ω i t) σ xi exchange interaction H J ~ Σ J ij (t) σ i σ j Coherence long relaxation time T 1 long coherence time T 2 EZ = gµbb J(t)

33 Coherent exchange of two spins Petta et al., Science 2005 free evolution under exchange Hamiltonian swap 1/2 in as little as 180 ps three oscillations visible, independent of J

34 Spin qubits in quantum dots - present status Initialization 1 electron, low T, high B 0 H 0 ~ Σ ω i σ zi S L S R Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ Σ A i (t) cos(ω i t) σ xi exchange interaction EZ = gµbb Coherence H J ~ Σ J ij (t) σ i σ j measure coherence time J(t) T 1 ~ 1 ms; T 2 > 1 µs