Electron spin dynamics in self-assembled quantum dots
A. Greilich, R. Oulton, E.A. Zhukov, I.A. Yugova, D.R. Yakovlev, and M. Bayer
Experimentelle Physik II, Universität Dortmund, D-44221 Dortmund, Germany
A. Shabaev and Al. L. Efros
Naval Research Laborator, Washington, DC 20375, USA
I.A. Merkulov
A.F. Ioffe Physico-Technical Institute, RAS, St. Petersburg, 194021 Russia
D. Reuter and A. Wieck
Angewandte Festkörperphysik, Ruhr-Universität Bochum, Germany
(a)
(b)
B=1 T
FR amplitude (arb. units)
150mW


120
80
60

40
20
5
1
0.6
0
200 400 600 800 1000 0
Time (ps)
5
10
15
Pulse area (arb.units)
FR amplitude (arb. units)
An electron spin in a single QD represents a qubit candidate that is much more attractive than other two-level
systems for solid state quantum information processing [1,2]. Recent studies have demonstrated long spin relaxation
lifetimes, T1, in the millisecond-range at cryogenic temperatures. [3] This has raised hopes that T2, which may last as
long as 2 T1, [4] could be similarly long, with encouraging indications to that effect found lately. [5] For fast spin
manipulation, rotations by Raman processes are envisaged whose cross sections can be enhanced by resonant
excitation of a charged exciton state. [6] In a first step, however, electron spin coherence must be established, as
addressed recently for GaAs/AlGaAs interface QDs. [7] Coherent spin control in QDs is, however, still a problem
under active discussion. [8]
Here the creation of electron spin coherence in n-modulation doped (In,Ga)As/GaAs quantum dots will be
addressed. [9] Each dot in the ensemble contains on average a single electron. The problem has been studied by
pump-probe Faraday rotation at T = 2K. The magnetic field B up to 7 T was aligned perpendicular to the structure
growth direction. A Ti-sapphire laser emitting pulses with a duration of ~1 ps was used, hitting the sample along the
growth direction. The laser was tuned to the QD ground state transition energy. For detecting the rotation angle of
the linearly polarized probe pulses, a homodyne technique based on phase-sensitive balanced detection was used.
The left panel Figure shows Faraday rotation signals at B = 1T for different pump powers. The corresponding
Faraday rotation amplitude is shown in the right panel as function of the pulse area. For pulses of constant duration,
but varying power, as used here, the pulse area is proportional to the square root of excitation power, and it is given
in arbitrary units. The Faraday rotation amplitude shows a non-monotonic behavior with increasing pulse area. It
increases first, and then drops after having passed a maximum. Thereafter it shows another strongly damped
oscillation. This behavior is very similar Rabi-oscillations of the exciton Bloch vector. [10] The FR amplitude
becomes maximum applying a -pulse as pump, for which the z-component of the Bloch vector, describing the
population, is fully inverted. It becomes minimum for a 2-pulse, for which the Bloch vector is turned by 360, and
so on. The damping of the Rabi oscillations most likely is due to ensemble inhomogeneities of QD properties. [11]
These results clearly demonstrate that intense short laser pulses can be used to generate electron spin coherence
along the growth direction of a quantum dot ensemble, which originally has no spin coherence along this direction,
due to the magnetic field oriented perpendicular to it.
[1] D. Loss and D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
[2] A. Imamoglu et al., Phys. Rev. Lett. 83, 4204 (1999).
[3] J.M. Elzerman et al., Nature 430, 431 (2004); M. Kroutvar et al.,
Nature 432, 81 (2004).
[4] W.A. Coish and D. Loss, Phys. Rev. B 70, 195340 (2004).
[5] J.R. Petta et al., Science 309, 2180 (2005).
[6] P. Chen et al., Phys. Rev. B 69, 075320 (2003).
[7] M. V. Gurudev Dutt et al., Phys. Rev. Lett. 94, 227403 (2005).
[8] A. Shabaev et al., Phys. Rev. B 68, 201305(R) (2003).
[9] A. Greilch et al., submitted for publication.
[10] see, for example, T. H. Stievater et al., Phys. Rev. Lett. 87,
133603 (2001); A. Zrenner et al., Nature 418, 612 (2002) and
references therein.
[11] P. Borri et al., Phys. Rev. B 66, 081306 (2002).