Optical quantum control
in semiconductors nano-systems
Carlo Piermarocchi
Department of Physics and Astronomy
Michigan State University, East Lansing, Michigan
Support by
Colloquium at Oakland University
March 17th 2005
Systems
I.
Spins in semiconductors
(Guillermo Quinteiro)
II. Atoms in organic quantum wires
(Michael Katkov)
III. Currents in quantum rings
(Yuriy Pershin, Mark Dykman)
Part I
Control of spins by light
Quantum control of two donors
Neutral donors
GaAs:Si
Ψ =α(t)  +β(t)  +γ(t)  +δ(t) 
•Control Hamiltonian
H=H0 +HC (t,σ1 ,σ2,...)
Optical RKKY
Conduction
band
Si
Si
Itinerant excitons
mediate the interaction
EGap (GaAs)
Valence
band
C. Piermarocchi,P.Chen,L.J.Sham,G.D.Steel,
Phys. Rev. Lett. (2002)
H  Jeff s1  s2
Quantum Well
m*e=0.07m,
m*h=0.5m,
=300 Å
δ  EX  ωP
Exponential decay of the interaction
κ
2MX δ
Beyond ORKKY
• Can we have anti-ferromagnetic coupling?
• What is the effect of multiple scattering?
• What if the exciton is bound to the impurity?
Beyond second order in the exciton-spin coupling
C. Piermarocchi and G. F. Quinteiro, Phys. Rev B (2004)
We seek a solution in
terms of T matrix
equation.
g
g
A
Solution for spin
A + exciton
TA
B
Solution for spin
B + exciton
TB
Solution for the 2 spins using
Analytical effective H of two localized spins:
Effective magnetic field :
Heisenberg coupling:
Spin-spin coupling
2 Si in GaAs
Anti-bonding
R=2aB (~20 nm)
1 Ry*=5 meV
ORKKY
Bonding
R-dependence
Excitons bound
donors. Short range
Free excitons
Long range
Deep impurities
Rare earth impurities
Yb3+ in InP
•Long decoherence for spin
•Coupling with exciton by s-f exchange
R dependence InP:Yb
Triplet channel
Singlet channel
Deep confinement
Experiments
Energy (meV)
2724
2702
PL Intensity
Position (μm)
2700
1.4
meV
2726
1.1
meV
Single-impurity pair spectroscopy
20
10
2700
2720
2740
2760
Energy (meV)
2780
2800
Excitons bound to single Te pairs in ZnSe.
Deep isoelectronic (non magnetic)
Average separation between pairs: 1 micron
A. Muller, P. Bianucci, C. Piermarocchi, M. Fornari, I. C. Robin, R. André
and C. K. Shih (submitted, 2004).
2820
Light-spin thermodynamics
H  JORKKY [] si s j
ij
Can we induce a PM/FM
transition using coherent
light?
ZnSe:Mn
J Fernandez-Rossier, C Piermarocchi, P Chen, LJ Sham, and
AH MacDonald, Phys. Rev. Lett. (2004)
Light-induced ferromagnetism
Mean Field approach
S (S  1)
kBTc 
JORKKY []
3
Conclusions (I)
• Light can induce spin-spin interaction in
doped semiconductors.
• Strength and sign of the interaction are
controllable.
• Light-induced phase transitions.
Part II
Control of atoms in organic
quantum wires
Coherent control of atomic chains
• Polymer chain under strong non-resonant ac field
• Coherent optical polarization coupled to phonons
• Force on the “light-dressed” atoms
• Control of local lattice deformations
POLYDIACETYLENE
R
R
C
C
C
C
R
C
C
R
…
R
C
C
R
C
C
C
C
R
R
Excitons localized in the unit cells
B†n+1Bn
un-1
un
un+1
Eg
HAMILTONIAN
Su-Schrieffer-Heeger for excitons
p n2
1
2
H0  
  C un 1 - un  - tn 1,n Bn†1Bn  Bn†Bn 1
2M
2

tn 1,n  t0   un 1  un 
Control Hamiltonian
 †
HC   (Bn  Bn )   E g - hL Bn†Bn
2

  f  I

Intensity of the field and laser energy
are control parameters

Light-dressed ground state
L  1 0  1 1   2 0  2 1   ...  n 0  n 1
2
n  n
2
1
ENERGY
 L H0  HC  L

n
2
1
  tn 1,n n 1 n   n    1  n 
2

  Bn  2n n
  E g  L
Optical polarization
Optical detuning

Nonlinear equation for the polarization

2 n 

3
n

t0  2 n 






0

2
n
2

n 
1  n


Nonlinear attractive interaction:
polarization self trapping due to
phonon coupling
Nonlinear repulsive interaction:
saturation effects
External field:
Determines the total polarization in the field
Polarization Self-trapping
 = 510-4t0
 = 10-3t0
 = 210-3t0
Force
 = 510-4t0
 = 10-3t0
 = 210-3t0
Lattice deformation
 = 210-3t0
Without light
With light
Conclusions (II)
• Lattice deformation induced by the light
• Soliton-like solutions with a characteristic
saturation
• The force acting on the lattice can be finely
controlled through the field parameters
Katkov/Piermarocchi cond-mat/0410593
PART III
Control of currents in
quantum rings
Quantum Rings
Self-assembled InAs quantum
rings on GaAs surface, R ≈10nm
A. Lorke, R. J. Luyken, A. O. Govorov,
and J. P. Kotthaus, Phys. Rev. Lett. 84,
2223 (2000).
Quantum ring fabricated
on AlGaAs-GaAs
heterostructures
A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K.
Ensslin, W. Wegscheider, and M. Bichler,
Nature. 413, 822 (2001).
Polarized radiation
…
Circularly polarized light controls
currents in a quantum ring
Transition from the ground state to an
excited state characterized by a strong
current
2
H 
  UC 1 ,...,N   dE(t )
2mR 2 i i 2
2
En 
2
2m* R 2
n2
in 
e
n
2 R 2 m*
E(t )  iE0 cos(t )  jE0 sin(t )
 2,   
1 ,   
 2,   
1 ,   
Excitation dynamics
 
i
 H ,    D 
1
1


D     L  L  L L    L L 
2
2

 
Excitation pulse sequence
Liouville equation
L  g  .m n
Evolution of level population in
a 3-electron quantum ring
Current in the ring
Pulse sequence
Continuous wave excitation
Relaxation mechanisms:
• photon emission, tr ~ 0.1 ms.
• phonon emission,
tr ~ 10 ns .
For GaAs quantum ring of R = 10 nm, N =11
B0≈ 3 mT.
Conclusions (III)
• Trains of circularly-polarized pulses can control
the angular momentum of N electrons in a ring
• High angular momentum gives strong localized
current
• Externally-controlled source of local magnetic
field for single-spin quantum logic
Pershin/Piermarocchi cond-mat/0502001