The application of dynamical decoupling pulses to a single qubit interacting with a linear harmonic oscillator bath with $1/f$ (more generally, strong low-frequency) spectral density is studied, and compared to the Ohmic case. Decoupling pulses that are slower than the fastest bath time scale are shown to drastically reduce the decoherence rate in the $1/f$ case. Contrary to conclusions drawn from previous studies, this shows that dynamical decoupling pulses do not always have to be ultrafast. Our results explain the recent experiment in which dephasing due to $1/f$ charge noise affecting a charge qubit in a small superconducting electrode was successfully suppressed using spin-echo-type gate-voltage pulses.

• Received 23 May 2003

DOI:https://doi.org/10.1103/PhysRevA.69.030302