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Universität Karlsruhe
Phys. Rev. Lett. 97, 076803 (2006)
• Some recent efforts to control a single electron spin
Single-shot read-out of an individual electron spin in a quantum dot
J. M. Elzerman, R. Hanson, et al. Nature 430, 431 (2004).
• … or two spins!
Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots
J. R. Petta, A. C. Johnson, et al. Science 309 2180 (2005)
• Spin decay mechanisms
– Magnetic noise (hyperfine coupling to nuclear spins)
– Electric noise (spin-orbit mediated)
• Environment charge fluctuations or phonons produce
noisy electric fields
• But electric fields do not couple to electron spin!
• Indirect spin decay: Spin-orbit (SO) coupling
Spin-orbit mediated decay
So, err… what is spin-orbit coupling?
“Coupling between the orbital and the spin degrees of freedom arising
from relativistic corrections to the Schrödinger equation”
Uh?
In semiconductor heterostructures:
A: Momentum dependent
‘magnetic field’ (Bext=0)
B: Quasiclassically: as the
electron moves a distance dr
in time dt the spin is rotated
by U, which doesn’t depend
on dt (‘geometric’)
C: Motion induced by random
external forces (phonons)
induces a diffusion of the
electron spin
Measurement, control, and decay of quantum-dots spins
W. A. Coish, V. N. Golovach, J. C. Egues, D. Loss. cond-mat/0606782
Detailed model for an electron in a quantum dot
Low energy
effective dynamics
• Three relaxation times T1 (one for each process)
• Different environments, different spectral
densities: it affects the relaxation rate
Piezoelectric phonons
Charge fluctuations
Spin relaxation rate resulting from each of the different processes
(in a symmetrical GaAs lateral quantum dot with 1 Kelvin unperturbed level spacing)
Crossover magnetic field: B**=15 mT
“A quantal system in an eigenstate, slowly transported round a circuit C by varying
parameters R(t) in its Hamiltonian H(R), will acquire a geometrical phase factor
exp{ig(C)} in addition to the familiar dynamical phase factor”
Quantal phase factors accompanying adiabatic changes
M. V. Berry, Proc. R. Soc. Lond. A 392, 45-57 (1984)
•
At B=0 the environment dephases the two pseudospin states: each one
acquires an opposite (and random) geometrical phase
•
Pure geometric dephasing
•
Pointer basis = normal to the heterostructure
• Even in a strongly quantum system at B=0, a noisy
electric environment can cause geometric spin
dephasing and relaxation through spin-orbit coupling