Arbitrary phase shift of a semiconductor quantum dot charge qubit on a short time scale

We present an experimental technique to better control the phase of an electron charge qubit, formed by a GaAs double quantum dot. A standard non-adiabatic gate pulse is used to generate the qubit rotation around the x-axis of the Bloch sphere. To gain good control of the z-rotation (the phase) on a short time scale, a fast 130 ps tipping pulse is superimposed on the non-adiabatic pulse. The two-axis gate operation is exhibited in the composite pulse excited qubit evolution spectrum. We demonstrate that the dynamic phase can be varied continuously from 0 to $6\pi$ by varying the amplitude of the tipping pulse. The understanding of the spectrum is validated through simulation of the von Neumann equation. (letter)