Negative temperature phenomena in two coupled qubit-ensembles

Negative absolute temperature has a wide range of applications, such as high-efficiency quantum heat engines, quantum refrigerators, and quantum simulation. In a recent paper (2018 Phys. Rev. Lett. 120 060403), the authors proposed two spin ensembles coupled to the same reservoir collectively; one ensemble relaxes to negative temperature since the 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 the same 1D 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 the negative temperature state depends on the distance between the two ensembles. The decrease in negative temperature duration is due to the coherent coupling between the two ensembles that will hybridize the unitary evolution of the system. Some optimal points produce the longest duration of negative temperature, but this could not occur since the distance is out of the range of the appropriate regions. The negative temperature subensemble plays the role of a reservoir in the quantum Otto heat engine, which takes place beyond the Otto limit.