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A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.

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Electron scattering on both neutral (X) and charged (X − ) excitons in quantum wells is studied theoretically. A microscopic model is presented, taking into account both elastic and dissociating scattering. The model is based on calculating the exciton-electron direct and exchange interaction matrix elements, from which we derive the exciton scattering rates. We find that for an electron density of 10 9 cm −2 in a GaAs QW at T = 5K, the X − linewidth due to electron scattering is roughly twice as large as that of the neutral exciton. This reflects both the X − larger interaction matrix elements compared with those of X, and their different dependence on the transferred momentum. Calculated reflection spectra can then be obtained by considering the three electronic excitations of the system, namely, the heavy-hole and light-hole 1S neutral excitons, and the heavy-hole 1S charged exciton, with the appropriate oscillator strengths.

A dynamical nuclear polarization scheme is studied in gated double dots. We demonstrate that a small polarization (∼ 0.5%) is sufficient to enhance the singlet decay time by two orders of magnitude. This enhancement is attributed to an equilibration process between the nuclear reservoirs in the two dots accompanied by reduced fluctuations in the Overhauser fields, that are mediated by the electron-nuclear spin hyperfine interaction.