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 1 nm 1 nm 1m 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. MQC2 (quant-ph/2759) Initialization 1-electron, low T, high B H ~ i zi Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ A i (t) cos( i t) xi exchange interaction EZ = gbb H J ~ J ij (t) i 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. MQC2 (quant-ph/2759) Initialization 1-electron, low T, high B H ~ i zi Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ A i (t) cos( i t) xi exchange interaction EZ = gbb H J ~ J ij (t) i j Coherence long relaxation time T 1 long coherence time T 2 J(t) Transport through quantum dot - Coulomb blockade 5 4 N=3 L N=2 R Current dot [pa] 3 2 1 N=1 Is this the last electron?? -135-14 -145-15 -155-16 -165 Gate Voltage [mv]
A quantum point contact (QPC) as a charge detector Field et al, PRL 1993 Conductance (e 2 /h) 2 -.8 -.85 -.9 -.95-1. QPC gate voltage (V) QPC Current (na) 2. 1.5 1. -1.17-1.2-1.23-1.26-1.29 Dot plunger voltage (V) The last electron! 5 2 4 15 Dot current [pa] 3 2 1 N=2 N=1 N= 1 5 Current QPC [pa] -135-14 -145-15 -155-16 -165 Gate Voltage [mv] Sprinzak et al 1
Few-electron double dot design Ciorga et al 99 I DOT T Elzerman et al., PRB 23 Open design Field et al 93 Sprinzak et al 1 QPC-L I QPC I QPC QPC-R QPC for charge detection GaAs/AlGaAs wafers: L P L M P R R 2 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, R16138 (23) -1.1 V L (V) diqpc/dv L Tesla -1.2 V L (V) 12 22 11 21 1 1 -.9 -.6 V PR (V) -.96 V PR (V) -.15 -.3 Double dot can be emptied QPC can detect all charge transitions
Single electron tunneling through two dots in series L R L L R R S (N+1,N) (N,N+1) D D Vg1 Vg2 Few-electron double dot Transport through dots J. Elzerman et al., cond-mat/212489 Peak height -1.2 1 1 pa V L (V) 12 22 11 21 1 2 pa -.96 V PR (V) -.15 -.3 7 pa
Energy level spectroscopy at B = 1 di DOT /dv SD SOURCE T DRAIN (mv) V SD N=1 B = T -1-653 -695 V T (mv) E ~ 1.1meV E C ~ 2.5meV N= No transport 2 nm M P R Ground state transport Q Ground and excited state transport Single electron Zeeman splitting in B // V SD (mv) 2-2 2 ES GS N= T Hanson et al, PRL 91, 19682 (23) Also: Potok et al, PRL 91, 1682 (23) B= B> gbb g =.44 V SD (mv) -2-657 N=1 N=1 6T N= V T (mv) -675 N= 1 T -995 V R (mv) -11 E Z (mev).2.1 5 1 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. MQC2 (quant-ph/2759) Initialization 1-electron, low T, high B H ~ i zi Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ A i (t) cos( i t) xi exchange interaction EZ = gbb H J ~ J ij (t) i 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 -e time charge SPIN DOWN -e N = 1 N = N = 1-1 time Observation of individual tunnel events Vandersypen et al, APL 85, 4394, 24 Also: Schlesser et al, 24 RESERVOIR T I QPC DRAIN Q 2 nm M P R SOURCE V SD = 1 mv I QPC ~ 3 na I QPC ~.3 na Shortest steps ~ 8 μs
Pulse-induced tunneling I QPC (na).8.4. response to pulse response to electron tunneling -.4.5 1. 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, 22
V pulse empty QD Spin read-out results Elzerman et al., Nature 43, 431, 24 inject & wait read-out spin empty QD I QPC (na) I QPC 2 1 SPIN UP SPIN DOWN.5 1. Time (ms) 1.5.5 1. 1.5 Time (ms) Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC2 (quant-ph/2759) Initialization 1-electron, low T, high B H ~ i zi Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ A i (t) cos( i t) xi exchange interaction EZ = gbb H J ~ J ij (t) i 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 21 Double dot in spin blockade for ESR detection E z ~µev<<kt!! ~mev T(,2) S(,2) Advantage: interdot transition instead of dot-lead transition Insensitive to temperature can use B < 1 mt, f < 5 MHz Insensitive to electric fields ESR flips spin, lifts spin blockade Combine Engel & Loss (PRL 21) ESR detection with Ono & Tarucha (Science 22) spin blockade
Dotcurent(fA) (mv) V R ESR device design B DC B AC Gates ~ 3 nm thick gold Dielectric ~ 1nm calixerene Stripline ~ 4nm thick gold Expected AC current ~ 1mA Expected AC field ~ 1mT Maximize B 1, minimize E 1 25 μm ESR spin state spectroscopy Dot current (fa) 5 4 3 2 1 RF at 46 MHz P~-16dBm RF off -15 Magnetic 5 field (mt) 15 RF frequency (MHz) 7 6 4 3 2 1 ESR signature: Sattelite peaks emerge at spin resonance condition ( g-factor ~.35) I dot (fa) 4 3 1 2 Koppens et al., Nature 26-15 -1-5 5 1 15 Magnetic field (mt)
Dotcurent(fA) V(mV) R Coherent manipulation: pulse scheme Spin blockade Coulomb blockade Spin manipulation Projection S(,2) V(mV) 6 RF signal 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 Coherent rotations of single electron spin! Koppens et al. Nature 26 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 21 11-18 4 6 8 1 Burst time (ns) Oscillation frequency ~ B AC /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 26 Spin qubits in quantum dots S L SR Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC2 (quant-ph/2759) Initialization 1-electron, low T, high B H ~ i zi Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ A i (t) cos( i t) xi exchange interaction H J ~ J ij (t) i j Coherence long relaxation time T 1 long coherence time T 2 EZ = gbb J(t)
Coherent exchange of two spins Petta et al., Science 25 free evolution under exchange Hamiltonian swap 1/2 in as little as 18 ps three oscillations visible, independent of J Spin qubits in quantum dots - present status Initialization 1 electron, low T, high B H ~ i zi S L S R Read-out convert spin to charge then measure charge ESR SWAP pulsed microwave magnetic field H RF ~ A i (t) cos( i t) xi exchange interaction EZ = gbb Coherence H J ~ J ij (t) i j measure coherence time J(t) T 1 ~ 1 ms; T 2 > 1 s