Diagnosing dynamical phase transitions in Spin-1 Bose-Einstein condensate using classical and quantum information

Non-equilibrium dynamics has been used to probe quantum many-body physics and to perform state engineering which finds broad applications in various aspects of quantum technologies. Dynamical phase transitions (DPT), which signal different dynamical structures of a quantum system by tuning control parameters, provides a powerful tool to classify many-body dynamics in closed quantum systems. In this work, we identify an order parameter to diagnose the DPT in quench dynamics of a Spin-1 Bose-Einstein condensate for classical initial states (coherent spin states) which is motivated by a mean-field picture of the double-well structure in the phase space. Beyond the classical regime, a quantum probe based on the quantum Fisher information (QFI) is shown to be able to capture such a DPT for a broader type of initial states including both coherent spin states and Fock states. The classical Fisher information (CFI), as is more realistic to be measured in Spin-1 Bose-Einstein condensate nowadays, is also shown to mimic the role of QFI to some degrees and is useful in diagnosing such a DPT. Both the CFI and the QFI make a smooth connection between DPTs and quantum sensing.