Spin Squeezing under Non-Markovian Channels by Hierarchy Equation Method

We study spin squeezing under non-Markovian channels, and consider an ensemble of $N$ independent spin-1/2 particles with exchange symmetry. Each spin interacts with its own bath, and the baths are independent and identical. For this kind of open system, the spin squeezing under decoherence can be investigated from the dynamics of the local expectations, and the multi-qubit dynamics can be reduced into the two-qubit one. The reduced dynamics is obtained by the hierarchy equation method, which is a exact without rotating-wave and Born-Markov approximation. The numerical results show that the spin squeezing displays multiple sudden vanishing and revival with lower bath temperature, and it can also vanish asymptotically.