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The competition between quantum many-particle dynamics and continuous monitoring can lead to measurement-induced phase transitions (MIPTs). So far, MIPTs have been much explored in fermionic or spin systems. To examine the possibility of a MIPT in bosonic systems, we study the entanglement structure in continuously monitored free bosons with long-range couplings. When the measurement is local, we find that no MIPTs occur because the substantial entanglement generated by the long-range coupling overcome the entanglement destruction due to the measurement. In contrast, we show that the nonlocal measurement can efficiently suppress the entanglement generation, leading to a MIPT where the bipartite entanglement entropy exhibits the subvolume-to-area law transition as the measurement strength is increased. Possible experimental relevance to levitated nanoparticle arrays is also briefly discussed.
Yokomizo et al. (Thu,) studied this question.