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Single Spin Detection J. Fernández-Rossier IUMA, Universidad de Alicante, Spain Manipulation and Measurement of the Quantum State of a single spin in a solid state environment 1023 atoms, 1025 spins Signal for only 1 Needle in a Hay Stack Talk available in: www.ua.es/jfrossier/personal Single Spin Detection CdTe nanocrystal + 1Mn PL S=5/2 2S+1=6 L. Besombes et al., PRL 93, 207403, (2004) The institute of Complex Adaptative Matter encourages (forces) scientist to explain their work to other scientist in pedestrian terms. I have learned more science through workshops organized by this institute and the personal contacts they generated than I have from all other professional activities combined. R. Laughlin, A Different Universe, (2005) Outline I. Motivation II. Basic Stuff III. Quantum Simulations IV. Conclusions Single Spin Detection RELATED WORK •J. Fernández-Rossier, C. Piermarocchi, P.C. Chen, L. J. Sham, and A. H. MacDonald, Theory of Laser induced ferromagnetism Phys. Rev. Lett. 93, 127201 (2004) •J. Fernández-Rossier, L. Brey Ferromagnetism mediated by few electrons in semimagnetic quantum dots Phys. Rev. Lett. 93, 1172001 (2004) •G. Chiappe, J. Fernández-Rossier, E. Anda, E. Louis Single-photon exchange interaction in a semiconductor microcavity Cond-mat/0407639 Talk available in: www.ua.es/jfrossier/personal I. Motivation II. Basic Concepts III. Quantum Simulations IV. Results and Conclusions Motivation I. Understanding QM from small... = .....to big alive dead Not only a philosophycal question 1 Atom “Shut up and calculate”. -- R. Feynman "I think it is safe to say that no one understands quantum mechanics." -- R. Feynman 104-106 Atoms 1023 Atoms: BULK Motivation II. The limits of miniaturization ‘Single electron’ transistor Going Nano Miniaturization: The limits Going Nano ‘Single atom’ magnet Going around THE LIMITS •Different Materials: •Molecular Electronics •Oxides •Different Ideas: •Spintronics •DNA •Quantum Computing •New Questions: •Smallest wire? •Smallest magnet? •Smallest diode? •Smallest transistor? •New challenges: •Single spin control •Single molecule transport •Nanocrystal formation Electronics: we ain´t seen nothing yet I. Motivation II. Basic Concepts III. Quantum Simulations IV. Conclusions Basic Concepts •Quantum computing for absolute beginners: •Quantum bit vs classical bit •Spin S=1/2 as a qbit •Quantum software and hardware •Diluted Magnetic Semiconductors •Quantum Dots What is a qbit? Classical information a y yes an no Will you marry me? Py 0 0 Pn 1 0 yes 1 0 0 0 0 no 0 0 1 Quantum information a 2 a a * P y n y y a a * a 2 C n y n C * Pn What is a qbit (II)? i a y yes an no cos e sin 2 2 A qbit is like a spin ½ What is a quantum computation? I. Prepare initial state a 1 2 b 1 2 c 1 2 d 1 2 II. Perform a well defined sequence of quantum operations (Quantum gates) U (t ) e iHt “Engineering” Hamiltonian. Universal Gates III. Read final state (single spin detection) Can something useful be done? Classical factorization algorithm Quantum factorization Algorithm (Shor ’90) Number of bits: N=2n Number of steps: n2 Example n=10 Qsteps: 100 Csteps: 10.000 Number of steps: n 2n QUANTUM SOFTWARE: A few algorithms and ideas Quantum Hardware: Proposals Sytem Qbit Nmax Who, where NMR Nuclei spin 7 Chuang (IBM) Ion traps Motional state 3 Colorado (JILA) SC Flux state 2 (Girvin,Devoret) Yale, Saclay P Donors E spin 1 Kane (Australia) Electrons in QD E spin 1 Di Vincenzo (IBM), Delft 2 Sham (UCSD), D. Steel Exciton in QD Eh spin Not in yet Diluted Magnetic Semiconductors Charge doping of Semiconductors Pure ZnTe N- ZnTe (Zn,Ga)Te CHARGE DOPING p- ZnTe Zn (Te,N) Metal Spin doping: diluted Magnetic Semiconductors (DMS) (Zn,Mn)Te Zn: Ar: 3d10 4s2 Mn: Ar: 3d5 4s2 Conduction Band Mainly s orbitals of Zn Valence Band Mainly p orbitals of Te Mn d levels SPIN DOPING Why S=5/2 ? S=5/2 Ground State S=3/2 Excited States S=1/2 Real Space Cartoon S=5/2. LOWEST Coulomb Repulsion (Hunds Rule) Magnetic Moment SPIN S=5/2 Mn SPIN ROTATIONAL INVARIANCE S=5/2. 2S+1=6 DEGENARATE STATES 5/2 3/2 1/2 How to manipulate the spins ? Electrons, holes, Mn and their interactions H e J e Se M I r rI I SPIN attraction SPIN FLIP H h J h S h M I r rI SO S h L I Se Sh Spin of the CB electron and VB hole SPIN ORBIT MATTERS A LOT CARRIER WAVE FUNCTION ENGINEERING SPIN repulsion Single quantum spectroscopy? CdSe nanocrystal: TEM CONFINEMENT Absorption Emission 5nm I. Motivation II. Basic Concepts III. Quantum Simulations IV. Conclusions S=5/2 qbits in semiconductor nanocrystals? PL S=5/2 2S+1=6 1 0 11 0 0 0 1 L. Besombes et al., PRL 93, 207403, (2004) Absorption Spin evolution Emission 1 SPIN 5/2 = 2 QBITS dummy dummy 4x6N 4 -1 -1 +1 ( ) +2 ( ) 1 Exciton States Manifold (XSM) 6N Ground State Manifold (GSM) Method : 1) Calculation of one-body wave functions (for a given dot) 2) Evaluation of many body excitonMn spin Hamiltonian 3) Exact diagonalization of GSM 4) Exact diagonalization of XSM 5) Linear reponse theory NMn 1 2 3 4 GSM Qbits 6 2 36 5 216 7 1296 10 HAMILTONIAN Ground State Manifold (GSM) H 0 J I , I ' M I M I ' g B B M I I ,I ' I (S1 ,..., S N ) S1 ... S N H 0 G EG G 6N Exciton States Manifold (XSM) e H1 H J e M I Se ( xI ) Heisenberg I VB H J h M I S h ( xI ) Ising CB 4 6N h H 0 H1 X I EX X SPIN ORBIT INTERACTION M I S h ( xI ) M z I S z ( xI ) Spin orbit and OPTICAL SELECTION RULES H lightmatter er E 4 -1 -1 +1 ( ) +2 ( ) How can light affect spin? 1 HH 1 x iy HH 2 x iy Absorption s e x iy HH 2 e s x iy x iy e Valence band Spin orbit: Ising coupling SHAPE MATTERS: Quenching the Hole-Mn spin flip M I S h ( xI ) M I z S z ( xI ) GSM and XSM spectrum H 0 H1 X EX X H 0 H1 X EX X Magnetic Field (0,0,5) 1 Mn NG=6 NX=24 2 Mn NG=36 NX=244 3Mn NG=216 NX=864 E(meV) E(meV) Photoluminescence (PL) Theory PL: results PL, theory PL, experiment Spontaneous Emission from X to G 2 X X p G E X EG 2 ( ) G Optical Selection rules SPIN BLOCKADE Energy conservation ( ) PL SPECTRUM e E X / k BT PL( ) P( E X )X X ZX X X Energy (meV) Occupation of excited state Thermal like occupation OPTICAL SPIN BLOCKADE 2 X pG X p G E X EG 2 G 2 G ( S1 ,..., S _ N ) S ( S1 ,..., S _ N ) 2 g pX 2 Franck Condon= Spin Blockade GSM X Standard optical selection rule Photon QUANTUM MEASUREMENT XSM N=3. Narrowing and shift PL, experiment 0T 2T 4T 6T 8T 10T ( ) ( ) P. S. Dorozhkin, Phys. Rev. B 68, 195313 (2003) Bell States in DMS? HIGLY ENTANGLED h e h e Lowest energy state Of XSM GSM Intriguing question: can the detection of a linearly polarized photon yield a Bell state? CONCLUSIONS (and future work) • • • • • • Single spin detection possible due to Chemical Engineering (nanocrystals) Advanced material processing and electronics (multilayers, photodetectors) Laser technology, low temperatures DEEP UNDERSTANDING of the ELECTRONIC STRUCTURE (Solid state physics and chemistry) S=5/2 qbits. • Detection ok (at least N=2) • Time resolved control ok • 2 qbit operations ok