Limitation of the modulation method to smooth wire guide roughness

It was recently demonstrated that wire guide roughness can be suppressed by modulating the wire currents so that the atoms experience a time-averaged potential without roughness. We theoretically study the limitations of this technique. At low modulation frequency, we show that the longitudinal potential modulation produces a heating of the cloud and we compute the heating rate. We also give a quantum derivation of the rough conservative potential associated with the micro-motion of the atoms. At large modulation frequency, we compute the loss rate due to non adiabatic spin flip and show it presents resonnances at multiple modulation frequencies. These studies show that the modulation technique works for a wide range of experimental parameters. We also give conditions to realise radio-frequency evaporative cooling in such a modulated trap.