1. 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 Needle in a Hay Stack Talk available in: www.ua.es/jfrossier/personal 10 23 atoms, 10 25 spins Signal for only 1

2. CdTe nanocrystal + 1Mn L. Besombes et al., PRL 93, 207403, (2004) PL S=5/2 2S+1=6 Single Spin Detection

3. Outline I. Motivation II. Basic Stuff III. Quantum Simulations IV. Conclusions 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)

4. 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

5. I. Motivation II. Basic Concepts III. Quantum Simulations IV. Results and Conclusions

6. = Motivation I. Understanding QM from small...

7. .....to big

8. “Shut up and calculate”. -- R. Feynman Not only a philosophycal question 10 4- 10 6 Atoms 1 Atom 10 23 Atoms: BULK "I think it is safe to say that no one understands quantum mechanics." -- R. Feynman

9. Motivation II. The limits of miniaturization Going Nano ‘Single electron’ transistor

10. Miniaturization: The limits ‘Single atom’ magnet Going Nano

11. 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

12. I. Motivation II. Basic Concepts III. Quantum Simulations IV. Conclusions

13. 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

14. What is a qbit? Will you marry me? Quantum information Classical information

15. What is a qbit (II)? A qbit is like a spin ½

16. What is a quantum computation? I. Prepare initial state II.Perform a well defined sequence of quantum operations (Quantum gates) III. Read final state (single spin detection) “Engineering” Hamiltonian. Universal Gates

17. Can something useful be done? Number of steps: n 2 n Classical factorization algorithm Quantum factorization Algorithm (Shor ’90) Number of bits: N=2 n Number of steps: n 2 Example n=10 Qsteps: 100 Csteps: 10.000 QUANTUM SOFTWARE: A few algorithms and ideas

18. Quantum Hardware: Proposals SytemQbit N max Who, where NMRNuclei spin7Chuang (IBM) Ion traps Motional state 3Colorado (JILA) SCFlux state2 (Girvin,Devoret) Yale, Saclay P DonorsE spin1Kane (Australia) Electrons in QD E spin1Di Vincenzo (IBM), Delft Exciton in QDEh spin2Sham (UCSD), D. Steel Not inyet

19. Diluted Magnetic Semiconductors

20. Charge doping of Semiconductors Pure ZnTe N- ZnTe (Zn,Ga)Te p- ZnTe Zn (Te,N) CHARGE DOPING Metal

21. Spin doping: diluted Magnetic Semiconductors (DMS) (Zn,Mn)Te SPIN DOPING Zn: Ar: 3d 10 4s 2 Mn: Ar: 3d 5 4s 2 Conduction Band Mainly s orbitals of Zn Valence Band Mainly p orbitals of Te Mn d levels

22. S=5/2 S=3/2 Why S=5/2 ? S=1/2 S=5/2. LOWEST Coulomb Repulsion (Hunds Rule) Magnetic Moment SPIN S=5/2 Real Space Cartoon Ground State Excited States Mn SPIN ROTATIONAL INVARIANCE S=5/2. 2S+1=6 DEGENARATE STATES  5/2  3/2  1/2

23. How to manipulate the spins ?

24. Electrons, holes, Mn and their interactions Spin of the CB electron and VB hole SPIN FLIP SPIN attractionSPIN repulsion SPIN ORBIT MATTERS A LOT CARRIER WAVE FUNCTION ENGINEERING

25. Single quantum spectroscopy? CdSe nanocrystal: TEM 5nm Absorption Emission CONFINEMENT

26. I. Motivation II. Basic Concepts III. Quantum Simulations IV. Conclusions

27. S=5/2 qbits in semiconductor nanocrystals? Absorption Emission Spin evolution L. Besombes et al., PRL 93, 207403, (2004) PL S=5/2 2S+1=6 dummy 1 SPIN 5/2 = 2 QBITS

28. Method : 1)Calculation of one-body wave functions (for a given dot) 2)Evaluation of many body exciton- Mn spin Hamiltonian 3)Exact diagonalization of GSM 4)Exact diagonalization of XSM 5)Linear reponse theory Ground State Manifold (GSM) Exciton States Manifold (XSM) 4x6 N 6N6N +1+2 1 4 N Mn GSM Qbits 162 2365 32167 4 1296 10

29. HAMILTONIAN Ground State Manifold (GSM) 4  6 N e h Exciton States Manifold (XSM) 6N6N SPIN ORBIT INTERACTION Heisenberg Ising

30. +1+2 1 4 Absorption Spin orbit and OPTICAL SELECTION RULES How can light affect spin?

31. Valence band Spin orbit: Ising coupling SHAPE MATTERS: Quenching the Hole-Mn spin flip

32. GSM and XSM spectrum E(meV) 1 Mn NG=6 NX=24 2 Mn NG=36 NX=244 3Mn NG=216 NX=864 E(meV) Magnetic Field (0,0,5)

33. Photoluminescence (PL) Theory Spontaneous Emission from X to G Energy conservation Optical Selection rules SPIN BLOCKADE PL SPECTRUM Occupation of excited state Thermal like occupation Energy (meV) PL, theory PL, experiment PL: results

34. OPTICAL SPIN BLOCKADE Franck Condon= Spin Blockade Standard optical selection rule GSM XSM Photon QUANTUM MEASUREMENT

35. PL, experiment N=3. Narrowing and shift 0T 2T 4T 6T 8T 10T P. S. Dorozhkin, Phys. Rev. B 68, 195313 (2003)

36. Bell States in DMS? HIGLY ENTANGLED Intriguing question: can the detection of a linearly polarized photon yield a Bell state? Lowest energy state Of XSM GSM

37. 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