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

Control of spins by lightControl of spins by light

Part IPart I

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

Analytical effective H of two localized spins:

Effective magnetic field :

Heisenberg coupling:

Spin-spin couplingSpin-spin coupling

ORKKY

2 Si in GaAs

R=2aB (~20 nm)

Bonding

Anti-bonding

1 Ry*=5 meV

R-dependenceR-dependence

Free excitonsLong range

Excitons bounddonors. Short range

Rare earth impurities

Yb3+ in InP

•Long decoherence for spin

•Coupling with exciton by s-f exchange

Deep impuritiesDeep impurities

R dependence InP:YbR dependence InP:Yb

Deep confinement

Triplet channel

Singlet channel

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.

Control of atoms in Control of atoms in organic quantum wiresorganic quantum wires

Part IIPart II

• 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

Polarization Self-trappingPolarization Self-trapping

= 10-3t0

= 210-

3t0

= 510-

4t0

= 10-3t0

= 210-

3t0

= 510-

4t0

ForceForce

With light

Without light

Lattice deformationLattice deformation

= 210-

3t0

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

Control of currents in Control of currents in quantum ringsquantum rings

PART IIIPART III

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