Theory of optical quantum control of spins in semiconductors

Carlo PiermarocchiDepartment of Physics and AstronomyMichigan State University, East Lansing, Michigan

Workshop on Non equilibrium Dynamics in Interacting Systems. MPI Dresden, April 27th 2006.

(1) Optical RKKY

(2) Polaritons and spins in a microcavity

(3) Coherent photo-induced ferromagnetism

(4) Role of bound states

(1)

Laser pulses con be used to control single spins

D +

s1

D +

s2

Neutral donors

GaAs:Si

The theory works for:

Shallow donors and acceptors

Charged quantum dots

Magnetic impurities

Optical RKKY: Itinerant excitons mediate a spin interaction

Conduction band

Valence band

EGap (GaAs)

Si Si

C. Piermarocchi, P.Chen, L.J.Sham, G.D.Steel, Phys. Rev. Lett. 89 167402 (2002)

Effective spin Hamiltonian in second order perturbation theory

The effective interaction is ferromagnetic and decreases exponentially as a function of the spin distance

Quantum wellm*e=0.07m m*h=0.5m ξ=300 Å

(2)The range of the spin coupling can be increased using cavity QED

Mirrors

QW in a microcavity

Cavity photon and exciton in strong coupling

Vacuum Rabi splitting causes spin anisotropy

h: Jz=±3/2e: Jz=±1/2

Upper Polariton Jz=±1

Jz=±2Dark states Jz=±2

Jz=±1 ΩR

Lower Polariton Jz=±1

QW QW+Cavity

A spin flip necessarily implies polariton-dark states mixing, inhibited by the vacuum Rabi splitting

The polariton mediated Ising component has a very long range

0 20 40 60 80R aB*

10-1

10-2

10-3

10-4

10-5

Jffe@

yR

* D

0.25 0.5 0.75 1R mm

2 100

2 101

2 102

2 103

2 104

T@

spD

G. Quinteiro Rosen, J Fernández Rossier, and C Piermarocchi, cond-mat/0603472

(3)

Optical RKKY can induce ferromagnetism

Can we induce a PM/FM transition using off-resonant excitation?

ZnSe:MnJ Fernández-Rossier, C Piermarocchi, P Chen, LJ Sham, and AH MacDonald, Phys. Rev. Lett. 93 127201(2004)

The Curie temperature is of the order of 1K

(4)The role of bound states can be studied analytically

We seek a solution in terms of T matrix equation.

Solution for spin A + exciton

TA

Solution for spin B + exciton

TB

Solution for the 2 spins using

C. Piermarocchi and G. F. Quinteiro, Phys. Rev B 70 235210 (2004)

Exact analytical solution of the effective H of two localized spins

Effective magnetic field (Inverse Faraday Effect):

Heisenberg coupling:

Assuming Jkk’=J vk vk’

Both ferro and anti-ferro coupling can be obtained

ORKKY

2 Si in GaAs

R=2aB (~20 nm)

Bonding

Anti-bonding

1 Ry*=5 meV

Spin coupling by bound excitons has a shorter range

Free excitonsLong range

Excitons bounddonors. Short range

Deep impurities have a long decoherence time

Rare earth impurities

Yb3+ in InP

Coupling with exciton by s-f exchange

Bound exciton resonance is well separated from free exciton

Triplet channel

Singlet channel

InP:Yb

Deep confinement

Experiments on single-impurity exciton spectroscopy

2700 2720 2740 2760 2780 2800 2820

10

20

Energy (meV)

Pos

ition

(µm

)

2724 27262700 2702

PL

Inte

nsity

Energy (meV)

1.41.1meV

meV

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. Andréand C. K. Shih Phys. Rev. B 73 081306 (Rapid Communication) 2006

Light can induce spin-spin interaction in doped semiconductors

The polariton mediated spin coupling has a very long range

Coherent photo-induced ferromagnetism

Conclusions

Strength and sign of the interaction are controllable

Po Chung Chen Tsing-Hua Taipei

Duncan SteelU MichiganAllan MacDonald

U Texas AustinGuillermo Quinteiro Rosen Michigan State

Joaquin Fernandez RossierAlicante, Spain

Lu Sham UCSan Diego

Ken ShihU Texas Austin