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

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

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

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

Time Constants (Nielsen & Chuang p.278) systemCoh. TOp. TNo Op nuclear spin electron spin ion trap (In+) electron (Au) electron (GaAs) Quantum dot Optical cavity Microwave cavity

Quantum Dots Charge (current) Spin Exciton

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.

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

C. Pryor, PRL 1998

Charged quantum dots, Nielson & Chuang, p.344

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

Exciton in Semiconductor k E E b = 6 meV

Exciton in Q-dot E b = 20 meV

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

L.Sham, PRL 2001, PRB 2002

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

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

Excited by a left polarized beam

Two-pulse combination

Fidelity Test

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)

M. Bayer, Science 2001

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