1. Quantum Control in Semiconductor Quantum Dots Yan-Ten Lu Physics, NCKU

2. Basic Requirements 1. Representation of qubits 2. Controllable unitary evolution 3. Preparation of initial qubit states 4. Measurement of final qubit states

3. Representation of qubits Single photon Cavity QED Trapped ions Nuclear spins Solid state devices

4. 15 = 3 x 5 -- Realization of Shor Algorithm (1994) by I. Chuang (2001), IBM Almaden C 11 H 5 F 5 O 2 Fe

5. Time Constants (Nielsen & Chuang p.278) systemCoh. TOp. TNo Op nuclear spin10+210-310+5 electron spin10-310-710+4 ion trap (In+)10-110-1410+13 electron (Au)10-810-1410+6 electron (GaAs)10-1010-1310+3 Quantum dot10-610-910+3 Optical cavity10-510-1410+9 Microwave cavity110-410+4

6. Quantum Dots Charge (current) Spin Exciton

7. What is a quantum dot? In a semiconductor quantum dot, the electronic levels have a density of states characteristic of a single atom. Yet, the dots is a mesoscopic system, the quantization of electronic levels is realized within a system of 10 5 – 10 6 atoms.

8. InAs/GaAs, S.P. Gua, et. al. APL 1997

10. C. Pryor, PRL 1998

11. Charged quantum dots, Nielson & Chuang, p.344

12. Spin of a quantum dot Loss & DiVinceenzo, PRA, 1998

13. Exciton in Semiconductor k E E b = 6 meV

14. Exciton in Q-dot E b = 20 meV

15. Energy levels of multiple excitons, A. Barenco, PRB, 1995

16. L.Sham, PRL 2001, PRB 2002

17. E e - E h = 1.6926 E ex = 1.6724 T coh = 30 ps H. Ando, PRL 2001

18. Time Scale Consideration Pusle duration of operation laser beam must be less than coherence time Pulse duration of laser beam must be long enough to ensure Combined laser pulses

19. Excited by a left polarized beam

20. Two-pulse combination

21. Fidelity Test

24. What We can do ? More detail study of fidelity dependence on the shape of laser pulse. Applied to system of coupled quantum dots (1-d and 2-d)

25. M. Bayer, Science 2001

26. K.R. Brown, et. al. PRA 2001