Spikes and jumps in quantum trajectories

We consider a quantum system whose unitary dynamics is subjected to continuous measurements. For the case where the observer records the outcome of measurements, the dynamics of the state of the system is described by a nonlinear stochastic ordinary differential equation and is referred to as a quantum trajectory.  The stochastic term appearing can be diffusive or Poissonian depending on the physical set up.  In the strong measurement regime, the noise grows larger and the quantum trajectories converge to a pure jump process (between fixed quantum states) but surprisingly one that is decorated by a secondary spike process. In the talk I will first describe earlier work on the spiking phenomena for the case with diffusive noise and then talk about our recent results for the case with Poissonian noise.