Spin-orbit coupling and electron-phonon scattering - Fachbereich ...

3.3 Effects of relaxation 71
page 55) fulfil the conditions
1. initialisation time (panel Fig. 3.2b) t i ∼ Γ −1
R > Γ−1 L ,
2. pulse time (panel Fig. 3.2c) t p < Ω −1 ,
3. read-out time (panel Fig. 3.2d) t o ∼ Γ −1
R .
The time to initialise the dot in state Ψ − is limited by the time it takes to get rid
of an electron which by chance occupies the state Ψ + . Requiring Γ L > Γ R leads to
a preferential filling of the dot from the left lead. In addition, the pulse time needs
to be smaller than the inverse Rabi frequency to observe oscillation behaviour. The
read-out time is given by Γ −1
R . Thus, the period for one cycle is T cycle = 2Γ −1
R +t p
and the transferred charge is 2eP(t p ). The factor 2e corresponds to the fact that if
P(t p ) = 1 then two electrons are transferred per cycle on average; every electron
which undergoes the oscillation is accompanied by an additional electron simply
tunnelling through the dot via state Ψ + . Thus, the current can be estimated as
I(t p ) = 2eP(t p)
+t ≈ eΓ R P(t p ), for Γ R ≪ Ω. (3.47)
p
2Γ −1
R
By measuring the current as a function of the pulse length t p one can map the
oscillation in the occupation probability onto a transport quantity.
3.3 Effects of relaxation
Phase coherence is essential for the observation of probability oscillations which
is outlined above. However, in every real physical system decoherence is always
present due to coupling to the environment. Even if the system is prepared in the
ground state the phase will be randomised after times longer than the dephasing
time. Our scheme for the observation of coherent oscillations requires the systems
to remain in an excited state for a rather long time. Thus, any relaxation from the
excited state to the ground state will lead to dephasing and destroy the CO signal.
The relevant mechanisms for relaxation and dephasing of spin states in QDs
are still being investigated [37]. A lower bound for the relaxation time of 50µs
has been measured at 20mK in a one-electron GaAs dot with an in-plane field of
7.5T [131]. This time is orders of magnitude larger than in a 2D system. Notably,
the measurement was limited by the signal-to-noise ratio and thus, the real value
of the relaxation time may even be larger, substantiating the proposal to consider
the spin state of quantum dots as a possible physical realisation of a quantum
computing architecture [122].
The theoretical understanding of spin-flip transitions in QDs is important in
order that one can estimate spin coherence times which need to be sufficiently long