SPEAKER: Etienne Jussiau, Universite' Grenoble Alpes, Center for Coherence and Quantum Optics

TITLE: Transmission properties of a discrete level strongly coupled to a continuum with a band structure

ABSTRACT: It is quite widely believed that small efficient machines will play a crucial role in the future of energetics due to the increased control over the parameters of a device at the nanoscale. As such, there is currently growing interest in the study of heat to work. conversion at the nanoscale. Of particular interest is the regime of strong system-reservoir coupling: we might be able to use it in designing lower resistance electronic devices and more powerful nanoscale heat engines and refrigerators. This regime is however very challenging to tackle theoretically as the border between the system and the reservoir fades away. This results in devices with physical properties that could not be guessed from either the system or the reservoir’s properties. In this work, we consider a single discrete level coupled to a reservoir featuring a continuum of states. This system has an exact solution such that all aspects of the coupling to the reservoir can be taken into account. We are particularly interested in the influence the reservoir’s band structure. An unexpected phenomenon arises for reservoirs with band gaps: discrete bound states appear in the gaps when the system-reservoir coupling is strong enough. These states will partially trap any particle placed in the discrete level so it never fully decays into the continuum and thus give rise to non-Markovian dynamics. We investigate the changes in the continuum states which accompany the appearance of a bound state. These changes can be observed via the transmission function of the system, which is crucial in determining the thermoelectric transport properties of the system. We highlight the relation between bound states and perfectly transmitting states (continuum states that flow through the level without reflection): it seems that a bound state appears when a perfectly transmitting state is pushed out of the continuum due to level repulsion. This has important consequences for the thermoelectric properties of the discrete level. However, we then give examples of band structures that provide a different viewpoint on perfectly transmitting states. We show that, under certain conditions, additional pairs of perfectly transmitting states can be created. The discrete level's transmission function then resembles that of a multi-level system. Such phenomenon even occurs when the discrete level's energy is outside the reservoir's band.