We study quantum trajectories of collective atomic spin states of N
effective two-level atoms driven with laser and cavity fields. We show that
interesting ``entangled-state cycles'' arise probabilistically when the (Raman)
transition rates between the two atomic levels are set equal. For odd (even)
N, there are (N+1)/2 (N/2) possible cycles. During each cycle the
N-qubit state switches, with each cavity photon emission, between the states
(∣N/2,m>±∣N/2,−m>)/2​, where ∣N/2,m> is a Dicke state in a rotated
collective basis. The quantum number m (>0), which distinguishes the
particular cycle, is determined by the photon counting record and varies
randomly from one trajectory to the next. For even N it is also possible,
under the same conditions, to prepare probabilistically (but in steady state)
the Dicke state ∣N/2,0>, i.e., an N-qubit state with N/2 excitations,
which is of particular interest in the context of multipartite entanglement.Comment: 10 pages, 9 figure