have been made in realizing different classes of multipartite entanglement in different artificially-engineered quantum systems. Greenberger-Horne-Zeilinger state, A well-known multipartite entanglement that shares the correlation on the creation and annihilation excited on all the particles, has already been generated at a scale up to 12 qubits in superconducting systems  [@PRL.122.110501], 18 qubits in photonic systems  [@PRL.120.260502], and 20 qubits in ions systems  [@PRX.8.021012]. The exponentially low efficiency in simultaneously detecting many particles restricts the achievable scale. An interesting way to enhance the collective correlation is to create twin Fock entanglement state in a Bose-Einstein condensate (BEC) system through quantum phase transitions  [@science_BEC]. W state is another representative multipartite entanglement that shares the correlation of the creation excited in one particle and annihilation in all other particles. The requirement of detecting only one excitation for W state is free from the exponential inefficiency of coincidence measurement, therefore can be more easily achieved at large scale, especially in atomic ensembles [@science_40atoms; @nature_680atoms; @nature_3000atoms; @NC_million-atoms].

The achieved large-scale entanglement states, however, have to be prepared and detected in the systems that are maintained at extremely low temperature and well isolated with environment to eliminate decoherence effects. The decoherence and noise induced by the 