#### Single-electron sources

The controlled production of single and few particle excitations in electronics offers the possibility to probe the microscopic physics which underlies quantum transport and promises a variety of applications ranging from quantum computation to quantum metrology. The required level of control was recently achieved experimentally for single-electron sources provided by a mesoscopic capacitor [1] and Lorentzian voltage pulses [2]. As a theory group, our goal is to reach new insights into quantum transport by characterizing setups involving such sources and to propose feasible experiments which make their underlying principles detectable. Recent developments include the analysis of the mesoscopic capacitor in a two-dimensional topological insulator [3], where it can be used to produce entanglement as well as spin-polarized currents [4], and a source that allows for the control of the amplitude and phase of a single electron wavefunction using microwave excitations [5].

[1] *An On-Demand Coherent Single-Electron Source*, G. Fève *et al.* Science **316**, 1169 (2007)

[2] *Minimal-excitation states for electron quantum optics using levitons*, J. Dubois *et al.* Nature **502**, 659 (2013)

[3] *Emission of time-bin entangled particles into helical edge states*, P. P. Hofer and M. Büttiker, Phys. Rev. B **88**, 241308(R) (2013)

[4] *Proposal for an ac spin current source*, P. P. Hofer, H. Aramberri, C. Schenke, P. A. L. Delplace, EPL **107**, 27003 (2014)

[5] *An On-Demand Single-Electron Time-Bin Qubit Source, *J. R. Ott and M. Moskalets, *submitted *arXiv:1404.0185v1

#### Noise and fluctuations

In contrast to the electronic properties of most macroscopic objects, where measuring the current as a function of the applied voltage is in most cases sufficient for a complete characterization, the quantum regime of transport through nanostructures shows a richer phenomenology. Here, the investigation of not only the current, but also its fluctuations at different frequencies (noise) reveals important insights into the physics. Moreover, one can study the full probability distribution of charge transfers within a given time interval to obtain all cumulants of the current, also known as “full counting statistics” [1]. In a complementary approach, we are interested in the probability distribution of times passing between two or more successive electrons traversing the conductor, called the “waiting time distribution” [2]. It is most suitable to investigate transport properties on short to intermediate time scales and becomes especially important for the characterization of periodically driven quantum systems such as the single electron sources described above. Moreover, it reveals surprising insights into correlations between electrons in a phase-coherent conductor. We use scattering theory [3] as well as generalized master equations [4] to investigate noise and fluctuations in mesoscopic systems.

[1] *Full Counting Statistics of Andreev Tunneling*, V. F. Maisi, D. Kambly, C. Flindt, and J. P. Pekola, Phys. Rev. Lett. **112**, 036801 (2014)

[2]* Electron Waiting Times in Mesoscopic Conductors, *M. Albert, G. Haack, C. Flindt, and M. Büttiker, Phys. Rev. Lett. **108**, 186806 (2012)

[3]* Floquet Theory of Electron Waiting Times in Quantum-Coherent Conductors, *D. Dasenbrook, C. Flindt, and M. Büttiker, Phys. Rev. Lett. **112**, 146801 (2014)

[4]* Electron waiting times in non-Markovian quantum transport, *K. H. Thomas and C. Flindt, Phys. Rev. B **87**, 121405(R) (2013)

#### Quantum heat engines

Thermoelectric energy harvesting can help to recover waste heat back into useful electricity, e.g., in small electronic circuits. Unfortunately, thermoelectric materials typically offer a lower efficiency of heat to work conversion. Mesoscopic physics can help to overcome these limitations by providing highly efficient nanoscale heat engines. A particular realization of such nano heat engines is based on double quantum dots in a three-terminal geometry. The two dots are capacitively coupled so they can exchange only energy but no particles. This allows for a crossed flow of heat and charge without direct electrical contact between the hot and the cold bath. For quantum dots in the Coulomb-blockade regime, it was found that they can reach Carnot efficiency when operated adiabatically while they still reach half the Carnot efficiency when operated at maximum power [1]. We showed that heat engines based on chaotic cavities reach much larger currents [2]. However, their output power and efficiency drops as the number of open transport channels connecting the dots to their reservoirs is increased. We could demonstrate that the optimal energy harvester is based on resonant tunneling through either quantum dots [3]. It can yield a large output power while reaching decent efficiencies of about 20 percent of Carnot efficiency. In addition, the quantum dot heat engine can be scaled up to macroscopic dimension by strong parallelization in the form of a Swiss cheese sandwich heat engine. A similar proposal based on quantum wells is even twice as powerful but only about half as efficient [4]. We also considered other types of heat engines that involve bosonic degrees of freedom such as magnons (spin waves) [5] and microwave cavity photons [6], thereby establishing connections to spin caloritonics and circuit QED.

[1] *Optimal energy quanta to current conversion*, R. Sánchez and M. Büttiker, Phys. Rev. B **83**, 085428 (2011).

[2] *Rectification of thermal fluctuations in a chaotic cavity heat engine*, B. Sothmann, R. Sánchez, A. N. Jordan, and M. Büttiker,

Phys. Rev. B **85**, 205301 (2012).

[3] *Powerful and efficient energy harvester with resonant-tunneling quantum dots*, A. N. Jordan, B. Sothmann, R. Sánchez and M. Büttiker,

Phys. Rev. B **87**, 075312 (2012).

[4] *Powerful energy harvester based on resonant-tunneling quantum wells*, B. Sothmann, R. Sánchez, A. N. Jordan and M. Büttiker,

New J. Phys. **15**, 095021 (2013).

[5] *Magnon-driven quantum-dot heat engine*, B. Sothmann and M. Büttiker, Europhys. Lett. **99**, 27001 (2012).

[6] *Hybrid Microwave Cavity Heat Engine*, C. Bergenfeldt, P. Samuelsson, B. Sothmann, C. Flindt, and M. Büttiker, Phys. Rev. Lett. **112** 076803 (2014).