Collective heat capacity for quantum thermometry and quantum engine enhancements

Abstract

The performances of quantum thermometry in thermal equilibrium together with the output power of certain class of quantum engines share a common characteristic: both are determined by the heat capacity of the probe or working medium. After noticing that the heat capacity of spin ensembles can be significantly modified by collective coupling with a thermal bath, we build on the above observation to investigate the respective impact of such collective effect on quantum thermometry and quantum engines. We find that the precision of the temperature estimation is largely increased at high temperatures, reaching even the Heisenberg scaling -inversely proportional to the number of spins. For Otto engines operating close to the Carnot efficiency, collective coupling always enhances the output power. Some tangible experimental implementations are suggested.

Roles of quantum coherences in thermal machines

“…These results were confirmed and extended for Otto engines operating close to the Carnot efficiency [74] by introducing collective heat capacity. In such regime, λ h /T h λ c /T c , where λ c and λ h are respectively the expansion and compression factors of the Otto cycle, with λ h > λ c .…”

“…Note that this manifest non-equivalence between continuous and cyclic collective engine is not in contradiction with the result of equivalence proved in [69] since the model of cyclic engine considered in [74,76] does not correspond to vanishing actions, regime where the equivalence holds.…”

“…Firstly, ensemble of qubits or spins interacting collectively with a thermal bath can reach equilibrium much faster than through individual coupling of each qubit with the bath. This fast equilibration can be used to reduce the duration of the isochoric strokes and therefore increase the power of cyclic engines [73,74]. Note that such fast equilibration is a direct consequence of the collective coupling with the bath which inherently generates coherences in the ensemble (see more details below).…”

“…Again, in the most favourable situation when ω/k B |T 0 | 1 and for high temperature of the hot bath (k B T h / ωλ h 1), the work extracted per cycle by the collective engine is multiplied by (ns + 1)/(s + 1) with respect to the independent engine, coinciding with what just seen in the above paragraph. Taking into account the collective fast equilibration [73,74] mentioned in the beginning of this section, the duration of the collective isochoric strokes can be divided by n, resulting in an output power multiplied by n. With this further improvement, the collective engine is always (for any bath temperature) performing as well as or better than the independent engine, see Fig. 2.…”

“…The continuous counterpart of the cyclic engines [74,76] described in the previous section is analysed in [82] using spins s = 1/2. The external driving consists in a periodic energy modulations of each spins, H WM = ω(t) 2 n k=1 σ k z .…”