Homodyne versus photon-counting quantum trajectories for dissipative   Kerr resonators with two-photon driving
  We investigate two different kinds of quantum trajectories for a nonlinear photon resonator subject to two-photon pumping, a configuration recently studied for the generation of photonic Schroedinger cat states. In the absence of feedback control and in the strong-driving limit, the steady-state density matrix is a statistical mixture of two states with equal weight. While along a single photon-counting trajectory the systems intermittently switches between an odd and an even cat state, we show that upon homodyne detection the situation is different. Indeed, homodyne quantum trajectories reveal switches between coherent states of opposite phase. 
Nicola Bartolo, Fabrizio Minganti, Jared Lolli, Cristiano Ciuti
quant-ph cond-mat.quant-gas