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