Coherent dynamics of a Josephson charge qubit

We have fabricated a Josephson charge qubit by capacitively coupling a single-Cooper-pair box (SCB) to an electrometer based upon a single-electron transistor (SET) configured for radio-frequency readout (rf-SET). Charge quantization of $2e$ is observed and microwave spectroscopy is used to extract the Josephson and charging energies of the box. We perform coherent manipulation of the SCB by using very fast dc pulses and observe quantum oscillations in time of the charge that persist to $\simeq 10\mathrm{ns}.$ The observed contrast of the oscillations is high and agrees with that expected from the finite $E_J{/E}_C$ ratio and finite rise time of the dc pulses. In addition, we are able to demonstrate nearly $100\%$ initial charge state polarization. We also present a method to determine the relaxation time $T_1$ when it is shorter than the measurement time $T_{\mathrm{meas}}.$