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

80 Conclusion
Instancing the quantum wire, we showed that for parabolically confined nanostructures,
it is helpful to map the underlying one-electron model onto a bosonic
representation, which highlights the effects of spin-orbit coupling in confined systems
and shows many similarities to models of quantum optics. Following this
reasoning, in chapter 3, we discussed the effect of spin-orbit coupling in fewelectron
quantum dots. Starting from standard Fock–Darwin theory for oneelectron
dots and including the Rashba Hamiltonian, an approximate model is
derived by making an analogy with quantum optics. When the spin-orbit coupling
becomes weaker than the dot confinement, the effective model is shown to be
formally identical to the Jaynes–Cummings model (JCM) of atom-light interaction,
and its integrability provides valuable insight into the coupling between spin
and orbital degrees of freedom in the quantum dot. In comparison to the JCM of
quantum optics, here the roles of atomic pseudo-spin and quantised light field are
played by the spin and orbital angular momentum of the same electron.
The excitation spectrum of the dot exhibits anticrossings as a characteristic
signature of spin-orbit coupling, which goes along with a decomposition into twolevel
systems, any of which can be considered as a novel compound spin-angular
momentum qubit degree of freedom. We predict that the width of the anticrossing
is proportional to α √ n + 1 with the strength of the spin-orbit coupling α and the
index of crossing n. The measurement of this relation would be verification of our
effective model and opens a unique way to determine the spin-orbit parameter in
quantum dots.
By applying the constant-interaction model we have translated results from the
single to the few-electron dot case. In addition, an experimentally feasible proposal
for the observation of coherent oscillations in the electron transport through
the quantum dot is outlined. The oscillations within the new qubit degree of freedom
are spin-orbit driven by utilising that the strength of the spin-orbit coupling
can be changed non-adiabatically by applying a voltage pulse to the system. For
parameters corresponding to an InGaAs dot, a Rabi frequency of 2GHz and an
amplitude of current oscillations of up to 45% are calculated, both being within
accessible ranges of state-of-the-art experimental technique.
Due to the incorporation of the spin-orbit coupling into the dynamics of the
dot, the dominating spin relaxation mechanisms in quantum dots are suppressed.
In addition, it is shown that the hybridisation of spin and orbital wavefunction in
the eigenstates of the qubit does not increase the fragility of the system in the case
of dissipation to phonons. Due to the design of the qubit states, the coupling to
long wavelength acoustic phonons is shown to be strongly suppressed, leading to
a relaxation rate Γ ep ≤ 10 −4 ω 0 with dot energy ω 0 . Thus, the residual relaxation
time is expected to be sufficiently long to observe the coherent evolution of the
qubit in the time domain.