Relaxation in quantum dots due to evanescent-wave Johnson noise from a metallic backgate

We present our study of decoherence in charge (spin) qubits due to evanescent-wave Johnson noise (EWJN) in a laterally coupled double quantum dot (single quantum dot). The high density of evanescent modes in the vicinity of metallic gates causes energy relaxation and a loss of phase coherence of electrons trapped in quantum dots. We derive expressions for the resultant energy relaxation rates of charge and spin qubits in a variety of dot geometries, and EWJN is shown to be a dominant source of decoherence for spin qubits held at low magnetic fields. Previous studies in this field approximated the charge or spin qubit as a point dipole. Ignoring the finite size of the quantum dot in this way leads to a spurious divergence in the relaxation rate as the qubit approaches the metal. Our approach goes beyond the dipole approximation and remedies this unphysical divergence by taking into account the finite size of the quantum dot. Additionally, we derive an enhancement of EWJN that occurs outside a thin metallic film, relative to the field surrounding a conducting half-space.