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Experimental and theoretical studies of semiconductor quantum bits 양자정보처리연구단 iQUIPS Doyeol Ahn Institute of Quantum Information Processing & Systems University of Seoul Collaborators iQUIPS H. K. Kim, S. H. Hong, B. C. Kim, Y. S. Choi: Dept. of Electronics & Computer Eng., Korea Univ. Dr. J. H. Oh, Dr. H. J. Lee, Dr. J. S. Hwang, Dr. M. H. Son, Y. H. Moon: iQUIPS, Univ. of Seoul S. Seong, Prof. T. H. Park: School of Chemical Eng., Seoul National Univ. S. K. Kwak, Prof. D. J. Ahn: Dept. of Chemical & Biochemical Eng., Korea Univ. Special Thanks to Program committee of AWAD 2005 Further Acknowledgements iQUIPS This work is supported by the Korean Ministry of Science and Technology through the Creative research Initiatives Program under Contract No. M10116000008-02F0000-00610. Motivation iQUIPS Solid state quantum bits: Decoherence control in charge qubit Spin vs Charge qubits Very short decoherence of compound semiconductor quantum dots Suppression of optical phonon processes in Si quantum dots Utilization of multi-valley interactions in Si Birth of New Information Technology iQUIPS Research Objectives (1998-2007) Understand and implement semiconductor quantum bits (spin vs. charge qubit) Understand decoherence processes (nonMarkovian domain) Fundamentals of Quantum Entanglement Quantum Information Theory What is quantum information processing? iQUIPS A research in quantum information processing is to understand how quantum mechanics can improve acquisition, transmission and processing of information. Who may be involved? Computer scientists Mathematicians Electrical engineers Chemists Physicists 양자 상태 vector를 source로 하는 경우 Qubit: a vector in Hilbert space "0" "0" ei 0 "1" "1" ei 1 Superposition C0 0 C1 1 2 |0> with prob. |C0| 2 |1> with prob. |C1| {|0>, |1>} = H2 Vectors in 2-D Hilbert space iQUIPS Tensor product 1 1 0 | 0 0 0 1 0 0 0 0 1 1 | 0 1 0 0 0 1 0 iQUIPS 1 0 0 | 1 0 1 0 1 0 0 0 0 0 0 1 | 1 1 1 0 1 Deutch Problem : quantum parallelism (1) iQUIPS Black x f (0) f (1) box f(x) : constant f (0) f (1) : balanced uˆ f : x y x y f x Se t uˆ f x y 1 2 1 0 1 2 0 1 x 0 f x 1 f x 1 0 f x 1 f x 2 0 1 if 1 0 if 1 f x 0 f ( x) 0 f ( x) 1 1 iQUIPS Example : f (0) 1, f (1) 0 0 1 uˆ f : 0 0 0 0 f 0 | 0 |1 0 0 1 0 uˆ f : 0 1 0 1 f 0 | 0 | 0 0 0 Deutch Problem : quantum parallelism (2) iQUIPS uˆ f x 1 0 1 x 1 f x 1 0 1 2 2 Set uˆ f : x 1 0 1 2 1 0 1 1 0 1 2 2 1 f 0 1 0 1 1 1 1 f 1 1 0 1 0 1 2 2 2 2 1 1 f 0 0 1 f 1 1 2 12 0 1 Output f(0)&f(1) can be calculated at the same time!!! Deutch Problem : quantum parallelism (3) û f uˆ f x 0 x f x on N qubits Set 1 2 iQUIPS 0 1 1 uˆ f 0 1 2 N 2 N 1 1 2 N 0 uˆ f N 2 x 0 2 N 1 1 N 2 1 2 Massive parallelism !!! (2N outputs in one query) x N 2 x 0 x 0 2 N 1 x f x 2 x 0 A Quantum Information Science and technology Roadmap iQUIPS Chrage qubit (NTT) Chrage qubit (iQUIPS) Cooper pair qubit (NEC) Cooper pair CNOT (NEC) Real operation in time domain Design and fabrication of hybrid circuits iQUIPS SOI quantum dot transistors and circuits have been successfully fabricated and tested. We are now in the stage of designing, fabricating, and testing those circuits. The more important factor is that we will need to see the quantum gate operation and we have to wait for the setup of dilution refrigerator in the third stage. (In collaboration with SNU ISRC) Fabrication and characterization of a vertical QDT for quantum gate operation iQUIPS A vertical QDT was successfully fabricated. The key processes are formation of vertical pillar and planarization by polyimide for contact isolation. The QDT also can include InAs quantum dots. 3.0x10 11 2.5x10 11 2.0x10 11 1.5x10 11 1.0x10 11 5.0x10 10 2 Current Density [A/cm ] top electrode circuit for the generation of local B pillar 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Applied Voltage [eV] -0.040 f-state Stacked QD 0.3 0.2 Single QD 0.1 -0.056 Energy (eV) dI/dV (S) dI/dV (S) AS 0.4 0.4 0.0 S 0.5 B = 0 T, T=20 mK 0.5 AS symmetric : S anti-symmetric : AS 0.3 0.2 0.1 d-state -0.058 S AS-Py -0.180 -0.181 -0.182 -0.183 -0.184 -0.185 AS-Px p-state -0.362 0.08 0.10 0.12 V (V) 0.14 0.08 0.09 0.10 V (V) S-Py S-Px AS 0.11 -0.364 s-state S -0.366 0 2 4 6 8 10 B (T) 12 14 16 18 iQUIPS Simple spin dynamics for 1-qubit (interaction picture) H B, B B0 zˆ B1 ( xˆ cos t yˆ sin t ) (0 / 2) z g ( x cos t y sin t ) | (t ) exp(i z t / 2) | (t ) | (t ) H | (t ) t i | (t ) 0 z g x | (t ) t 2 i | (t ) exp i 0 z g x t | (0) 2 = exp i nˆ / 2 | (0) ; single qubit rotation about nˆ axis when 0 nˆ zˆ and 0 nˆ xˆ t (0 )2 4 g 2 Fabrication of nano-electromagnet for quantum gate operation iQUIPS Nanometer size electromagnet is an important ingredient for the realization of qubits and quantum gates. An AC magnetic field around the quantum dot can rotate the spin of the electrons in the quantum dot. We successfully fabricated nano-electromagnet and demonstrated the operation by Faraday’s induction experiment. 12 <Vin> = 1.1 ~ 6 mV (100 nm spacing) <Vin> = 1.0 ~ 5 mV (11 m spacing) 10 <I2> (nA) 8 6 4 2 0 0 200 400 600 f (Hz) 800 1000 Realization of a charge qubit using stacked InAs selfassembled quantum dots #1 0.0 T=4K 8 -0.2 -0.4 -0.6 -0.8 6 AS 4 S 2 dI/dV (S) Isub 5 nm GaAs InAs QD 5 nm GaAs InAs QD 6 nm GaAs 0.6 m GaAs buffer (1018) n+ GaAs sub I (A) iQUIPS A charge qubit has been realized utilizing the symmetric/anti-symmetric quantum states of stacked InAs self-assembled quantum dots. Short period (> 30 psec) electrical pulses were applied on the source electrode and time-averaged decay current was measured as a function of pulse width. The decay current exhibits periodic oscillations as a function of the pulse width and this is a direct evidence of the manipulation of the quantum state in time domain. Our achievement was before the first electrical measurement of charge qubit by Fujisawa. 0 -1.0 -2 -0.9 -0.8 -0.7 -0.6 -0.5 V (V) iQUIPS Evolution of a quantum state | (t ) i H (t ) | (t ) t 6 | (t ) S k (t ) exp i k t / | k k 0 S o (0) 1 S k (0) 0 (k 1,2,3,4,5,6) Realization of a charge qubit using stacked InAs selfassembled quantum dots #2 0.00 -0.01 -0.02 100 0.04 Isub (pA) -0.8 -0.6 Veff (V) C -5 -10 0.5 A B D 0.0 -15 -0.5 -20 -1.0 0 100 200 300 400 500 t (psec) dIsub/d(t) (Arb. unit) 0 150 -0.02 0.06 0.04 0.02 0.00 -0.02 -0.04 -0.06 300 310 320 t (ps) 330 340 (c) 4 K 350 360 0.2 0.1 0.0 -0.1 -0.2 290 370 380 t (ps) 390 400 (d) 88 K Isub (pA) 1.0 140 0.00 0.08 0.04 0.00 -0.04 -0.08 -0.12 300 310 320 t (ps) 330 340 (e) Isub (pA) -1.0 130 t (ps) (b) 4 K -0.04 290 -1.6 120 4K 360 380 400 t (ps) 420 440 3 2 1 0 0 100 200 300 400 Frequency (GHz) 500 100 200 300 400 Frequency (GHz) 500 100 200 300 400 Frequency (GHz) 500 100 200 300 400 Frequency (GHz) 500 100 200 300 400 Frequency (GHz) 500 6 4 2 0 0 8 6 4 2 0 0 1.5 1.0 0.5 0.0 0 Amplitude (arb. unit) -1.2 0.02 110 Amplitude (arb. unit) -0.8 Isub (pA) (a) 4 K Amplitude (arb. unit) 100ps Isub (pA) Isub (pA) -0.4 0.01 Amplitude (arb. unit) Isub (pA) 0.02 Amplitude (arb. unit) iQUIPS 5 4 3 2 1 0 0 Direct measurement of tunneling rate through InAs self-assembled quantum dots #1 iQUIPS The tunneling rate through InAs self-assembled quantum dots was measured again by the electrical pump and probe measurement. Microwave (MW) signal was combined with the DC bias and was applied on the diode with InAs self-assembled quantum dots. Non-adiabacity factor of the decay current as a function of the frequency of the MW signal gives the direct estimate of the tunneling rate through the quantum dot. This experiment is another important achievement in timedomain transport measurements. D Drain S QD -1.1 Source 25 from 1 to 0 21 18 -1.3 15 -1.4 12 C A B C -1.5 -0.29 B -0.28 V(V) dI/dV (nS) I (nA) -1.2 20 dI/dV (nS) S D 15 10 A 9 -0.27 -0.29 -0.28 VDC (V) -0.27 Direct measurement of tunneling rate through InAs self-assembled quantum dots #2 iQUIPS High Frequency (50 MHz to 2 GHz) 1.0 0.6 dI/dV 0.8 Experiment Fit 0.4 0.2 0 4 8 12 16 1/f (ns) 20 24 28 DC -0.29 -0.28 VDC(V) -0.27 Evidence of double layer quantum dot formation in SOI QDT iQUIPS SOI QDT with a thin silicon layer showed, for the first time, evidences of double quantum dot formation each at the front and the back interface. This double layer formation can be used to automatically fabricate coupled Si quantum dot by fabricating a single quantum dot. VGS CGS1 CGS2 VDS CD1 CD2 Cm QD 1 QD 2 CS1 CS2 CBS1 CBS2 VBS 10 VGS(V) 0.60 VDS(mV) 0 0.55 -10 0.50 0.55 VGS(V) 0.60 -50 0 VDS(mV) 50 New proposal for Si quantum dot qubit and quantum gate iQUIPS The multi-valley quantum state transitions in a Si quantum dot is studied as a possible candidate for a quantum bit with a long decoherence time. Qubits are the multi-valley symmetric and anti-symmetric orbitals. Evolution of these orbitals is controlled by an external electric field, which turns on and off the inter-valley interactions. Such silicon quantum dot transistors were already fabricated for the test of the proposal. 0.1 E (valley 5,6) 5 E (valley 1,2) E (valley 3,4) 4 2 0.08 E (valley 1,2) E (valley 5,6) 1 3 D Energy (eV) 0.06 E E (valley 5,6) 5 0 E 3 0.04 Anti-symmetri c state C 0.02 Symmetric state 0 0 D. Ahn, J. Appl. Phys. 98, 033709 (2005) 100 200 300 Electric Field (kV/cm) 400 500 iQUIPS New proposal for Si quantum gate Inter-valley interactions Qubit: multi-valley symmetric and anti-symmetric states Control: external electric field Long decoherence time iQUIPS Electron state in a quantum dot F (r ) F (k ) exp( ik r ) k , F(k ) i Fi (k ) i i : expansion coefficient for the valley i (group Td ) iQUIPS i (k ) Fi (k ) Dkij,k nV (k k n) Fj (k n) Fi (k ) j kn Dkkij n DKiji , K j n D ij Ki , K j Ki ij Ki , K j D n Kj DKij i , K j I ij J ij n J ij n H l (i) V (r ) E Fl (r ) H l ' l ll ' (r , i) Fl ' (r ) 0 iQUIPS H ll' (r, i) Ill' exp[i(Kl Kl' ) r ](V(r )) i(Jll' ) exp[i(Kl K l' ) r ](V (r )) exp[i(Kl Kl' ) r ](V(r ))(iJ ll' ) iQUIPS ll' Kl ,K l' D 13 (K,0,0), (0,K, 0) D Ill' el el ' 12 (K,0, 0),( K,0,0 ) 0.3915, D 0.2171 1 1 Ill' (1 el el' ) (1 el el ' )cos(2 K ) 2 2 iQUIPS Jll' Ill' Kl el Ill' K K el (1 el el' ) sin( 2 K ) K iQUIPS 0.15 Energy |1> B (operation) E E~ o 0.1 |0> Energy (meV) Field E A (preparation) 0.05 0 0 100 200 300 Electric Field (kV/cm) 400 500 iQUIPS 0.1 E (valley 5,6) 5 E (valley 1,2) E (valley 3,4) 4 2 0.08 Anti-crossing Energies (Point D of figure 3) 0.092 E (valley 1,2) E (valley 5,6) 1 3 D 0.0918 E E (valley 5,6) 5 0 Energy (eV) Energy (eV) 0.06 E 3 0.04 Anti-symmetric state E anti-symmetric 5 0.0916 E: prepartion and read-out E symmetric 5 F: operation E anti-symmetric 3 C 0.0914 E symmetric 3 0.02 0.0912 Symmetric state 126 128 130 Electric Field (kV/cm) 0 0 100 200 300 Electric Field (kV/cm) 400 500 132 134 iQUIPS S , A 1 1 S , A (r ) S , A S , A (r ) 2 1 1 2 1 † 2 T12 dr1 dr2 a * (r1 ) H T (r1 , r2 ) b (r2 )( a ) b iQUIPS Vif dr1 dr2 1 * (r1 ) 2 * (r2 ) 21 2 * (r1 )1 * (r2 )12 Vsc (r1 r2 )1 (r1 ) 2 (r2 ) 21 12 1 when electrons in dot 1 and dot 2 have same parity 21 1 and 12 0 when electrons 1 dot 1 and 2 have opposite parities, which are preserved 21 0 and 12 1 when electrons 1 dot 1 and 2 have opposite parities, which are both changed iQUIPS 25 20 20 15 15 10 10 Coulomb Energy ( eV) 25 5 5 0 0 0 100 200 300 Electric Field (kV/cm) 400 500 iQUIPS E11 0 Hˆ 0 0 0 E10 EC 0 0 Ec E 01 0 0 0 0 E 00 Uˆ exp(iHˆ t) exp(3it) | 1111| cos 1t i sin 2 t|1010 | | 0101| 2 exp(it) | 0000 | cos 3 t 1 i sin 2 t| 1001 | | 0110 | , 2 iQUIPS Swap Operation |10 (cos1t i sin 2t ) |10 (1 cos3 t i sin 2 t) | 01 2 2 for t /(2 3 ) (4 13) 1 | 10 | 01 |10 | 01 cos 2 2 iQUIPS Electron-phonon interactions in a Si dot 2 W 2 q 1 1 2 iq r 2 E ( N ) | f | e | i | ( E f Ei q ) ac q 2Vq 2 2 f q iQUIPS 10 1 Decoherence time (sec) 0.1 0.01 100 mK 0.001 0.0001 150 mK 10 10 10 -5 -6 -7 0 50 100 Energy ( 10 150 -6 eV) 200 250 Possibility of quantum gate formation by molecular transistors iQUIPS Multi-qubit can be realized from specially designed molecules since the abundance of quantum states in molecules can be utilized for quantum computation. However, direct electrical contact to individual molecules is still a difficult task even though a few pioneering works exist with limited reliability. We developed a way of contacting molecules by capturing Au nanoparticles in nano-gap electrodes covered with self-assembled mono-layer (SAM). We used AC dielectrophoresis technique for the capture and a reliable and reproducible capture was successfully done. 0 .4 DS V B G = 0 .2 V 0 .2 0 .0 V B G = - 0 .2 V - 0 .2 - 0 .1 0 - 0 .0 5 0 .0 0 0 .0 5 0 .1 0 V D S(V ) 30 T = 4.2 K 25 ID(pA) I (n A ) V DS = 14 mV V BG = 112 mV 20 15 10 5 0 -0.3 V DS = 2 mV -0.2 -0.1 0.0 VBG(V) 0.1 0.2 0.3 Possibility of quantum gate formation by DNA molecules iQUIPS Thiol-modified double strand DNA molecules were shown to be selfassembled in the nano-gap with the help of Au nanoparticle. This opens up a reliable fabrication of QDT with DNA molecules. 400 300 600 Thiol modified DNA+20 nm gold nanoparticles Temperature=300 K 500 200 300 0 -100 200 -200 100 -300 0 -2 -1 0 V (V) 1 2 dI/dV (nS) 400 100 I (nA) Doping of DNA molecules iQUIPS DNA molecules are found to be doped with Au atoms. Doped DNA exhibits conductivity which is a strong function of the doping density. 40 30 Temperature = 300 K Number of Base Pairs = ~2000 20 I(nA) 10 0 -10 Au Doped DNA Undoped DNA -20 -30 -3 -2 -1 0 V(V) 1 2 3 What are grand challenges in quantum information processing? iQUIPS To manufacture, manipulate and characterize arbitrary entangled systems. To develop the fundamental theory of quantum entanglement. To control decoherence and prove the scalability of quantum information processing. To develop application of the few qubit quantum information processor. To master quantum coherences and understand the quantum-classical boundary. iQUIPS