  Hole qubits in germanium quantum dots are promising candidates for coherent
control and manipulation of the spin degree of freedom through electric dipole
spin resonance. We theoretically study the time dynamics of a single heavy-hole
qubit in a laser-driven planar germanium quantum dot confined laterally by a
harmonic potential in presence of linear and cubic Rashba spin-orbit couplings
and an out-of-plane magnetic field. We obtain an approximate analytical formula
of the Rabi frequency using a Schrieffer-Wolff transformation and establish a
connection of our model with the ESDR results obtained for this system. For
stronger beams, we employ different methods such as unitary transformation and
Floquet theory to study the time evolution numerically. We observe that high
radiation intensity is not suitable for the qubit rotation due to the presence
of high frequency noise superimposed on the Rabi oscillations. We display the
Floquet spectrum and highlight the quasienergy levels responsible for the Rabi
oscillations in the Floquet picture. We study the interplay of both the types
of Rashba couplings and show that the Rabi oscillations, which are brought
about by the linear Rashba coupling, vanish for typical values of the cubic
Rashba coupling in this system.
