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Optical quantum controlOptical quantum control in semiconductors nano-systems in semiconductors nano-systems
Carlo Piermarocchi
Department of Physics and AstronomyMichigan State University, East Lansing, Michigan
Support by Colloquium at Oakland UniversityMarch 17th 2005
I. Spins in semiconductors (Guillermo Quinteiro)
II. Atoms in organic quantum wires (Michael Katkov)
III. Currents in quantum rings (Yuriy Pershin, Mark Dykman)
SystemsSystems
Quantum control of two donors
Ψ =α(t) +β(t) +γ(t) +δ(t)
D +
s1
D +
s2
Neutral donors
GaAs:Si
0 1 2CH=H +H (t,σ ,σ ,...)•Control Hamiltonian
Optical RKKY Optical RKKY Conductio
n band
Valence band
EGap (GaAs)
Si Si
Itinerant excitons mediate the interaction
C. Piermarocchi,P.Chen,L.J.Sham,G.D.Steel, Phys. Rev. Lett. (2002)
1 2effH J s s
m*e=0.07m, m*h=0.5m, =300 Å
Quantum WellQuantum Well
2 X
κM δ
Exponential decay of the interaction
X Pδ E ω
Beyond ORKKYBeyond 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.
Solution for the 2 spins using
Solution for spin A + exciton
TA
Solution for spin B + exciton
TB
A B
Spin-spin couplingSpin-spin coupling
ORKKY
2 Si in GaAs
R=2aB (~20 nm)
Bonding
Anti-bonding
1 Ry*=5 meV
Rare earth impurities
Yb3+ in InP
•Long decoherence for spin
•Coupling with exciton by s-f exchange
Deep impuritiesDeep impurities
ExperimentsExperiments
2700 2720 2740 2760 2780 2800 2820
10
20
Energy (meV)
Po
sitio
n (μm
)
2724 27262700 2702
PL
Int
ensi
ty
Energy (meV)
1.41.1meV
meV
Excitons bound to single Te pairs in ZnSe. Deep isoelectronic (non magnetic)
Average separation between pairs: 1 micron
Single-impurity pair spectroscopy
A. Muller, P. Bianucci, C. Piermarocchi, M. Fornari, I. C. Robin, R. André and C. K. Shih (submitted, 2004).
Light-spin thermodynamics Light-spin thermodynamics
ZnSe:Mn
[ ]ORKKY i jij
H J s s
Can we induce a PM/FM transition using coherent
light?
J Fernandez-Rossier, C Piermarocchi, P Chen, LJ Sham, and AH MacDonald, Phys. Rev. Lett. (2004)
Light-induced Light-induced ferromagnetismferromagnetism
( 1)[ ]
3B c ORKKY
S SkT J
Mean Field approach
Conclusions (I)Conclusions (I)
• Light can induce spin-spin interaction in doped semiconductors.
• Strength and sign of the interaction are controllable.
• Light-induced phase transitions.
• 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
Coherent control of atomic chainsCoherent control of atomic chains
CC CC
C
C
R
R
RR
CC CC
C
C
R
R
RR
…
POLYDIACETYLENEPOLYDIACETYLENE
Excitons localized in the unit cells
Eg
un un+1
B†n+1Bn
un-1
HHAMILTONIANAMILTONIAN
Su-Schrieffer-Heeger for excitons
Intensity of the field and laser energy are control parameters f I
2
2 † †0 1 1, 1 1
1- -
2 2n
n n n n n n n n
pH C u u t B B B B
M
1, 0 1n n n nt t u u
† †( ) -2 n n g L n nCH B B E h B B
Control Hamiltonian
Light-dressed ground stateLight-dressed ground state
Optical detuningg LE
Optical polarization2n n nnB
2
0 1, 1
11
2L L n nC n n n nH H t
2 21n n
1 1 2 20 1 0 1 ... 0 1L n n
ENERGY
Nonlinear equation for the polarizationNonlinear equation for the polarization
23
0 2 22 0
1
n n
n n
n
tn
Nonlinear attractive interaction:polarization self trapping due to phonon coupling
Nonlinear repulsive interaction:saturation effects
External field: Determines the total polarization in the field
Conclusions (II)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
Quantum RingsQuantum Rings
A. Lorke, R. J. Luyken, A. O. Govorov, and J. P. Kotthaus, Phys. Rev. Lett. 84, 2223 (2000).
Self-assembled InAs quantum rings on GaAs surface, R ≈10nm
A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, Nature. 413, 822 (2001).
Quantum ring fabricated on AlGaAs-GaAs heterostructures
Circularly polarized light controls currents in a quantum ring
Polarized radiationPolarized radiation
22
* 22nE nm R
2 *2n
ei n
R m
2 2
12 2,..., ( )
2 C Ni i
H U tmR
dE
…
Transition from the ground state to an excited state characterized by a strong current
1,
2,
1,
2,
0 0( ) cos( ) sin( )t E t E t E i j
.
Excitation dynamicsExcitation dynamics ,iH D
1 1
2 2D
L L L L L L
Excitation pulse sequence
Evolution of level population in a 3-electron quantum ring
m n L
Liouville equation
Current in the ringCurrent in the ring
Pulse sequence
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.
Continuous wave excitation
Conclusions (III)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