Time-dependent quantum heat engines


The development of quantum technologies requires a deeper understanding of the energetics and thermodynamics of nonequilibrium quantum systems. Key problems for the construction of future quantum machines include optimization of the energetic cost of quantum protocols, efficient heat management, and the development of effective strategies for cooling. The common framework to deal with these problems is to consider open quantum systems weakly coupled to an infinitely large environment, so that any information which has been transferred to the environment is lost and cannot be retrieved by the system, thus excluding memory effects.

On the other hand, when dealing with small, nanoscale quantum systems the above assumptions easily break down, and one should develop methods and tools to address regimes beyond that framework, taking into account memory effects and system-environment quantum correlations.

We have addressed [1] the above questions in systems where the system-environment couplings are periodically modulated in time, and suitably engineered to perform thermodynamic tasks. In particular, asymmetric couplings to two heat baths can be used to extract heat from the cold reservoir and to realize an ideal heat rectifier, where the heat current can be blocked either in the forward or in the reverse configuration by simply tuning the frequency of the couplings modulation.

The developed formalism is ideally suited to apply optimal control and machine learning techniques to quantum thermal machines, beyond standard approaches for open quantum systems.

 




Isothermal heat engines


Starting with the Carnot engine, the ideal efficiency of a heat engine has been associated with quasistatic transformations and vanishingly small output power. We have exactly calculated [2] the thermodynamic properties of an isothermal heat engine, in which the working medium is a periodically driven underdamped harmonic oscillator, focusing instead on the opposite, antiadiabatic limit, where the period of a cycle is much shorter than the system’s timescales. We have shown that in that limit it is possible to approach the ideal energy conversion efficiency η = 1, with finite output power and vanishingly small relative power fluctuations. The simultaneous realization of all the three desiderata of a heat engine is possible thanks to the breaking of time-reversal symmetry. We have also shown that non-Markovian dynamics can further improve the power-efficiency trade-off.






References

[1] M. Carrega, L. M. Cangemi, G. De Filippis, V. Cataudella, G. Benenti and M. Sassetti, Engineering dynamical couplings for quantum thermodynamic tasks, preprint arXiv:2109.11510 [cond-mat.mes-hall].
[2]  L. M. Cangemi, M. Carrega, A. De Candia, V. Cataudella, G. De Filippis, M. Sassetti and G. Benenti, Optimal energy conversion through anti-adiabatic driving breaking time-reversal symmetry, Phys. Rev. Res. 3, 013237 (2021).