Negative temperature phenomena in two coupled qubit-ensembles

Abstract

Negative absolute temperature has wide range of applications, such as high-efficiency quantum heat engines, quantum refrigerators, and quantum simulation. In a recent paper [Phys. Rev. Lett. 120, 060403 (2018)], the authors proposed two spin ensembles coupled to the same reservoir collectively, one ensemble relaxes to negative temperature since two ensembles have unbalanced spin sizes. However, the coherent coupling mediated by the common environment is not considered. Here, we discuss negative temperature in a system where two qubit-ensembles are coupled to a same one-dimensional waveguide. In the limit of Markovian approximation, by investigating the coherent coupling and non-cross (cross) collective decay between two qubit-ensembles, we find that the duration of negative temperature state depends on the distance between two ensembles. The decrease of negative temperature duration is due to coherent coupling between two ensembles that will hybrid the unitary evolution of the system. Some optimal points produce the longest duration time of negative temperature, but it could not occur since the distance is out of the range of appropriate regions. The negative temperature sub-ensemble plays the role of a reservoir in quantum Otto heat engine, which is performed beyond the Otto limit.