Fig. 2: Interference protocol.
An initial π/2-pulse on the Cooper-pair box generates a charge superposition in the endcap electrodes, so that the charged nanoparticle feels a superposition of a spatially shifted and an unshifted harmonic potential. The time evolution (4) gives rise to two wave packets traveling on separate position and momentum trajectories. The corresponding classical trajectories are shown here. To verify this motional superposition state, the wave packets must be reunited. This can be achieved by applying two π-pulses, each interchanging the potentials felt by the two branches, in such a way that the trajectories finally coincide in position and momentum. (a) In the simplest case all pulses are separated by one sixth of the harmonic oscillation period and the particle is initially at rest. The π/2-pulse then leaves one branch unaffected (red dashed line), while the other one is accelerated (blue line). The first π-pulse accelerates the resting branch and decelerates the moving one to a standstill at the time of the second π-pulse. After that, the blue trajectory remains at rest while the red one is decelerated until it reaches the blue one with zero velocity. (b) Even for arbitrary pulse times τ the separation Δτ between the π-pulses can be chosen such that the corresponding paths in phase space coalesce for all initial states at 2τ + Δτ. (c) The scheme works for time durations much shorter than the oscillation period, which makes it particularly suitable for limited coherence times. In this short time limit the accelerations are essentially constant and Δτ = 2τ.
