## Quantum Thermodynamics

Quantum Thermodynamics (QT) is concerned with the investigation of phenomena such as thermalization and equilibration, heat engines, and foundations of thermodynamics in the quantum regime.The study of thermodynamics in the quantum domain provides an amazing example for the cross-fertilization between different areas of physics, involving classical thermodynamics and solid state physics, as well as quantum information and quantum field theory. For recent reviews see [Goold, Huber, Riera, del Rio, Skrzypczyk, J. Phys. A: Math. Theor.

My current reseach interest within QT lies in fundamental and practical restrictions for thermodynamic processes in quantum optics. In particular, I am interested in learning about the usefulness (and restrictiveness) of Gaussian operations for tasks such as energy extraction, storage, and distribution.

**49**, 143001 (2016)], [Vinjanampathy, Anders, Contemp. Phys.**57**, 1 (2016)] and [Millen, Xuereb, New J. Phys.**18**, 011002 (2016)].My current reseach interest within QT lies in fundamental and practical restrictions for thermodynamic processes in quantum optics. In particular, I am interested in learning about the usefulness (and restrictiveness) of Gaussian operations for tasks such as energy extraction, storage, and distribution.

**Gaussian Quantum Thermodynamics**

In QT, energy is one of the primary resources, but not all energy may be freely extracted or converted to be used at leisure for tasks at hand. In particular, so-called passive states cannot yield any work in cyclic Hamiltonian processes. Viewing QT as a resource theory of work extraction it is hence tempting to view passive states as being freely available (and non-passive states as valuable). On the other hand, the unitaries needed to extract work from an arbitrary non-passive state may in practice be complicated and not feasibly realizable.

This motivates the notion of Gaussian passivity [Brown, Friis, Huber, New J. Phys.

**18**, 113028 (2016)], i.e., a quantum state’s property of containing work extractable by Gaussian operations, which are typically practically implementable in many quantum optical setups. Once work has been extracted, one would also like to put it to use, e.g., to prepare specific states for quantum computation or quantum metrology. It is hence expected that practical limitations applying to work extraction will be of relevance for quantum technologies. Following the full characterization of Gaussian passivity [Brown, Friis, Huber, New J. Phys.

**18**, 113028 (2016)], I hence wish to investigate practical limitations, in particular, the restriction to Gaussian operations, for other tasks in QT.

One such task is storing (previously extracted) work in a suitable battery. Here, quantum systems in thermal equilibrium with the environment come to mind, since they can be considered empty in the sense that they do not contain any extractable work. In [Friis, Huber, Quantum
2, 61 (2018)]. we investigate the usefulness and limitations when using Gaussian unitaries to charge such batteries. In particular, we derive the fundamental bounds on the charging precision and work fluctuations during the charging process, and compare these with the optimal and worst Gaussian operations. |

Energy Cost of CorrelationsAnother reseach interest within QT is the relationship of entanglement and correlations with thermodynamic quantities, that is, how energy can be converted into (quantum) correlations in the presence of background temperature (entropy). Interestingly, every amount of correlations implies extractable work [Perarnau-Llobet, Hovhannisyan, Huber, Skrzypczyk, Brunner, Acín, Phys. Rev. X 5, 041011 (2015)], and conversely, correlations come at the expense of energy [Huber, Perarnau-Llobet, Hovhannisyan, Skrzypczyk, Klöckl, Brunner, Acín, New J. Phys. 17, 065008 (2015)]. |

We have studied the optimal conversion between resources of thermodynamics and quantum information tasks for non-interacting systems [Bruschi, Perarnau-Llobet, Friis, Hovhannisyan, Huber, Phys. Rev. E

**91**, 032118 (2015)], and recently also for interacting systems [Friis, Huber, Perarnau-Llobet, Phys. Rev. E**93**, 042135 (2016)]. A presentation about this research can be found here.These thermodynamics considerations have many interesting applications, for instance, in quantum optics, or in analogue gravity systems, as explained below.

**Entanglement in Analogue Gravity Systems**

Can quantum effects in curved spacetimes be simulated in compact, laboratory-based experimental setups? Following the formal analogy between quantum field theory on curved spacetimes and classical fluid systems [Unruh, Phys. Rev. D 14, 870 (1976)], this question has captivated researchers for decades, see e.g. [Barceló, Liberati, and Visser, Living Rev. Relativity 8, 12 (2005)] for a recent review. A central aim in such studies is the observation of radiation that can be associated to quantum pair creation processes, e.g., to the Hawking-, Unruh- and the dynamical Casimir effect. All of these effects rely on similar mechanisms in quantum field theory, i.e., particle creation due to time-dependent gravitational fields and boundary conditions, or the presence of horizons.We investigate the possibility to generate quantum-correlated quasi-particles utilizing such analogue gravity systems. The quantumness of these correlations is a key aspect of analogue gravity effects and their presence allows for a clear separation between classical and quantum analogue gravity effects. |

However, experiments in analogue systems, such as Bose-Einstein condensates, and shallow water waves, are always conducted at non-ideal conditions, in particular, one is dealing with dispersive media at nonzero temperatures. In [Bruschi, Friis, Fuentes,Weinfurtner, New J. Phys.

A presentation can be downloaded here [pdf].

**15**, 113016 (2013)] we analyze the influence of the initial temperature on the entanglement generation in analogue gravity phenomena. We lay out all the necessary steps to calculate the entanglement generated between quasi-particle modes and we analytically derive an upper bound on the maximal temperature at which given modes can still be entangled. We further investigate a mechanism to enhance the quantum correlations. As a particular example we analyze the robustness of the entanglement creation against thermal noise in a sudden quench of an ideally homogeneous Bose-Einstein condensate, taking into account the super-sonic dispersion relations.A presentation can be downloaded here [pdf].