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

C11H5F5O2Fe

Time Constants (Nielsen & Chuang p.278)

system Coh. T Op. T No Op

nuclear spin 10+2 10-3 10+5

electron spin 10-3 10-7 10+4

ion trap (In+) 10-1 10-14 10+13

electron (Au) 10-8 10-14 10+6

electron (GaAs) 10-10 10-13 10+3

Quantum dot 10-6 10-9 10+3

Optical cavity 10-5 10-14 10+9

Microwave cavity 1 10-4 10+4

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 105 – 106 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

21)()( SStJtH s

Exciton in Semiconductor

k

E

r

errV he

),(2

om 05.0

Eb = 6 meV

Exciton in Q-dot

Eb = 20 meV

2)(),()( hhheeeb rrrVrE

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

L.Sham, PRL 2001, PRB 2002

Ee - Eh = 1.6926

Eex = 1.6724

Tcoh = 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

E

Excited by a left polarized beam

1

)/(1

)/( 12

102

)(

o

itittito eeEeeEtE

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