## Wolfgang Niedenzu

*University of Innsbruck*

Wolfgang Niedenzu did his PhD with Helmut Ritsch at the University of Innsbruck, Austria, working on cold atoms in optical resonators. He then moved to the Weizmann Institute of Science in Rehovot, Israel, for a PostDoc in the group of Gershon Kurizki where he worked on topics in quantum thermodynamics. In April he returned to Innsbruck through an ESQ fellowship of the Austrian Academy of Sciences.

Heat engines were the basis of the industrial revolution and are still indispensable in our modern world. With the emergence of the field of quantum thermodynamics, there is growing interest in their microscopic counterparts. In particular, the question arose whether quantum engines exploiting non-thermal resources (shown in the figure [1]), e.g., squeezed-thermal baths or entangled baths, could surpass the Carnot efficiency bound and, if yes, what limits their efficiency? A better understanding of quantum engines is important in the context of quantum technologies and in view of current experiments on squeezed quantum engines [2].

According to the second law of thermodynamics, the Carnot bound is attained by cyclic heat engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. Yet, the maximum efficiency of quantum engines energised by non-thermal baths cannot be determined by the reversibility condition, which may yield an unachievable efficiency bound above 1. We identify the fraction of the exchanged energy between a quantum system and a bath that necessarily causes an entropy change and derive a new inequality for this change. This inequality relies on the concept of non-passive states. The definition of a non-passive state is that its energy can be unitarily reduced until the state becomes passive, thereby extracting work. Non-passive states may thus be thought of as being "quantum batteries".

Our derived inequality for the system entropy change reveals a general efficiency bound for quantum engines that operate between thermal and non-thermal baths. The found efficiency bound does not imply reversibility, unless the two baths are thermal. It cannot be solely deduced from the laws of thermodynamics but additionally requires the concept of non-passive states.

A key insight is that quantum non-thermal baths may act not only as a heat source but also provide work, whereby only the former is related to an entropy change of the engine's working medium. The Carnot bound does not apply on such hybrid engines. In order to use the energy imparted by the quantum non-thermal bath in the most efficient way possible, standard thermodynamic cycles must be modified to account for the non-passivity of the engine's working medium.

[1] W. Niedenzu, V. Mukherjee, A. Ghosh, A. G. Kofman and G. Kurizki, Nat. Commun. 9, 165 (2018).

[2] J. Klaers, S. Faelt, A. Imamoglu and E. Togan, Phys. Rev. X 7, 031044 (2017).

Fundamental science for quantum technologies , Quantum optics and non-classical light sources