  Semiconductor quantum dots, where electrons or holes are isolated via
electrostatic potentials generated by surface gates, are promising building
blocks for semiconductor-based quantum technology. Here, we investigate double
quantum dot (DQD) charge qubits in GaAs, capacitively coupled to high-impedance
SQUID array and Josephson junction array resonators. We tune the strength of
the electric dipole interaction between the qubit and the resonator in-situ
using surface gates. We characterize the qubit-resonator coupling strength,
qubit decoherence, and detuning noise affecting the charge qubit for different
electrostatic DQD configurations. We find that all quantities can be tuned
systematically over more than one order of magnitude, resulting in reproducible
decoherence rates $\Gamma_2/2\pi<~5$ MHz in the limit of high interdot
capacitance. Conversely, by reducing the interdot capacitance, we can increase
the DQD electric dipole strength, and therefore its coupling to the resonator.
By employing a Josephson junction array resonator with an impedance of $\sim4$
k$\Omega$ and a resonance frequency of $\omega_r/2\pi \sim 5.6$ GHz, we observe
a coupling strength of $g/2\pi \sim 630$ MHz, demonstrating the possibility to
achieve the ultrastrong coupling regime (USC) for electrons hosted in a
semiconductor DQD. These results are essential for further increasing the
coherence of quantum dot based qubits and investigating USC physics in
semiconducting QDs.
