How exchange symmetry impacts performance of collective quantum heat engines

Recently, multilevel collectively coupled quantum machines like heat engines and refrigerators have been shown to admit performance enhancements in analogy to superradiance. Thus far, investigations of the performance of collective quantum machines have largely restricted the dynamics to particles with bosonic exchange symmetry, especially for large numbers of particles. However, collections of indistiguishable but not fundamentally identical particles may assume quantum states of more general exchange symmetry or combinations thereof, raising the question of whether collective advantages can be observed for dynamics that allow the full Hilbert space to be explored. Here, we compare a collection of single-particle three-level masers with their collectively coupled counterpart, while admitting more general forms of exchange symmetry. We study ergotropy and emitted power as the figures of merit and show which of the known results applicable to a single three-level engine carry over to an engine made up of a collectively coupled ensemble. We do this using results from representation theory to characterise the full basis of the Hilbert space and provide general tools for the description of the dynamics of such systems. We find that collective work extraction can extend beyond the temperature window of three-level lasing, whereas in the lasing regime, individual may outperform collective operation. In addition, the optimal parameter regime for work-like energy output varies for different symmetry types. Our results show a rich picture in which bosonic symmetry is not always optimal and sometimes individual particles may even perform best.