Quantum fluctuations in a single electron box

Recent experiments have demonstrated that the number n of additional electrons on a small metallic island is a staircase function of a continuous external charge n_x for temperatures T small compared to the single electron charging energy U. We show that the finite conductance g of the tunnel barrier connecting the island to the external gate gives rise to quantum fluctuations in n which lead to a smearing of the staircase even at zero temperature. In the experimentally relevant case of wide junctions and in the limit of small conductance g≪1 the slope ∂<n>/∂n_x at the turning point between two plateaus saturates at a finite value of order 1/g as T→0 instead of diverging like U/T as predicted with thermal fluctuations only. The experimentally observed broadening however is still much larger which is probably due to extrinsic effects.