Download Quantum Control in Semiconductor Quantum Dots

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
C11H5F5O2Fe
15 = 3 x 5 -- Realization of Shor Algorithm (1994)
by I. Chuang (2001), IBM Almaden
Time Constants (Nielsen & Chuang p.278)
system
nuclear spin
electron spin
ion trap (In+)
electron (Au)
electron (GaAs)
Quantum dot
Optical cavity
Microwave cavity
Coh. T
10+2
10-3
10-1
10-8
10-10
10-6
10-5
1
Op. T
10-3
10-7
10-14
10-14
10-13
10-9
10-14
10-4
No Op
10+5
10+4
10+13
10+6
10+3
10+3
10+9
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


H s (t )  J (t )S1  S2
Exciton in Semiconductor
E
e
 
V (re , rh )  
2
r
  0.05 mo
k
Eb = 6 meV
Exciton in Q-dot

 

Eb   e (re ) V (re , rh )  h (rh )
Eb = 20 meV
2
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   E
Combined laser pulses
Excited by a left polarized beam
Two-pulse combination
E (t )  Eo e
 (t /  )
o   
1      
2
e
 i 0 t
 E1e
 ( t /  1 ) 2  i1t  i
e
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