Quantum Information Processing with Semiconductor Quantum Dots slides courtesy of Lieven Vandersypen, TU Delft
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
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
Examples of quantum dots single molecule self-assembled QD lateral QD nanotube 1 nm 10 nm 100 nm 1µm metallic nanoparticle vertical QD nanowire
Electrostatically defined quantum dots Electrically measured (contact to 2DEG) Electrically controlled number of electrons Electrically controlled tunnel barriers
Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC02 (quant-ph/0207059) 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)
Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC02 (quant-ph/0207059) 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)
Transport through quantum dot - 50 Coulomb blockade Current dot [pa] 40 30 20 10 µ N=3 µ N=2 µ L µ R µ N=1 Is this the last electron?? 0-1350 -1400-1450 -1500-1550 -1600-1650 Gate Voltage [mv]
A quantum point contact (QPC) as a charge detector Field et al, PRL 1993 Conductance (e 2 /h) 2 0-0.80-0.85-0.90-0.95-1.00 QPC gate voltage (V) QPC Current (na) 2.0 1.5 1.0-1.17-1.20-1.23-1.26-1.29 Dot plunger voltage (V)
The last electron! 50 2000 40 1500 Dot current [pa] 30 20 10 N=2 N=1 N=0 1000 500 Current QPC [pa] 0 0-1350 -1400-1450 -1500-1550 -1600-1650 Gate Voltage [mv] Sprinzak et al 01
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)
Few-electron double dot Measured via QPC J.M. Elzerman et al., PRB 67, R161308 (2003) -1.1 diqpc/dv L 0 Tesla -1.02 01 00 V L (V) 00 V L (V) 12 22 11 21 10-0.9 0-0.6 V PR (V) -0.96 V PR (V) -0.15-0.30 Double dot can be emptied QPC can detect all charge transitions
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
Few-electron double dot Transport through dots J. Elzerman et al., cond-mat/0212489 Peak height -1.02 01 00 < 1 pa V L (V) 12 22 11 21 10 2 pa -0.96 V PR (V) -0.15-0.30 70 pa
Energy level spectroscopy at B = 0 10 di DOT /dv SD SOURCE T DRAIN (mv) V SD 0 N=1 B = 0 T -10-653 -695 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
Single electron Zeeman splitting in B // V SD (mv) 2 2 ES 0 GS N=0-2 0T Hanson et al, PRL 91, 196802 (2003) Also: Potok et al, PRL 91, 016802 (2003) B=0 B> 0 gµbb g =0.44 V SD (mv) 0-2 -657 N=1 N=1 6T N=0 V T (mv) -675 N=0 10 T -995 V R (mv) -1010 E Z (mev) 0.2 0.1 0 0 5 10 15 B // (T)
Initialization of a single electron spin Method 1: spin-selective tunneling Method 2: relaxation to ground state
Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC02 (quant-ph/0207059) 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)
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
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
Pulse-induced tunneling I QPC (na) 0.8 0.4 0.0 response to pulse response to electron tunneling -0.4 0 0.5 1.0 1.5 Time (ms)
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
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) 2 1 0 SPIN UP SPIN DOWN 0 0.5 1.0 Time (ms) 1.5 0 0.5 1.0 1.5 Time (ms)
Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC02 (quant-ph/0207059) 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)
ESR detection in a single dot ESR lifts Coulomb blockade Engel & Loss, PRL 2001
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
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
ESR spin state spectroscopy Dotcurent(fA) (mv) V R Dot current (fa) 500 400 300 200 100 0 RF at 460 MHz P~-16dBm RF off -150 0 Magnetic 500 field (mt) 150 RF frequency (MHz) 700 600 400 300 200 100 ESR signature: Sattelite peaks emerge at spin resonance condition ( g-factor ~ 0.35) I dot (fa) 400 300 100 200 0 Koppens et al., Nature 2006 0-150 -100-50 0 50 100 150 Magnetic field (mt)
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
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
Dotcurent(fA) Driven coherent oscillations -6 I dot (fa) RF Power (dbm) -12 210 110-18 0 400 600 800 1000 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
Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC02 (quant-ph/0207059) 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)
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
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