04 Septembre – Thesis defense - Quentin Schaeverbeke

15 h University of Bordeaux

Photon emission and quantum transport in nanoplasmonic cavities.

The study of light--matter interaction has drawn through the years more and more interests. With improvement of the techniques used for building electromagnetic cavities, it is now possible to couple cavities with nanocircuits merging the fields of quantum optics and nanoelectronics. Not only that, but some experiments also reported the possibility to use a scanning tunneling microscope as a plasmonic cavity coupled with electronic transport.
In this thesis a theoretical framework is proposed, based on mesoscopic quantum electrodynamics, for studying the coupling between electronic transport in a molecular junction and the electromagnetic field of a cavity. This thesis focuses on the sequential tunneling regime for the electrons and use density matrix. This allows to derive the master equations as well as a computational scheme to compute electronic current as well as the photon statistic when it was not possible to obtain analytical results.
First, a single--level model for the molecule in the junction is studied. Indeed the electronic current induces a fluctuation of the charge on the molecule that couples with the electromagnetic field in the cavity. The investigations on this system are done in the experimentally relevant limit of large damping rate $kappa$ for the cavity mode and arbitrary strong light--matter coupling strength. This model shows the equivalence between the electron--photon coupling for a single level and the electron--phonon coupling that has long been studied in nanoelectronics known as the Franck--Condon principle. The current--voltage characteristics show steps, each separated by the energy of a photon, as the electron tunneling dissipate some energy in the cavity mode. In this work a formula has been derived for the electronic current taking into account the damping of the cavity. This allows to show that the width of the current's steps are controlled by $kappa$ rather than the temperature. The single-level junction shows interesting light--emission regimes. At large bias voltage this theory predicts strong photon bunching of the order $kappa/Gamma$ where $Gamma$ is the electronic tunneling rate. However, at the first inelastic threshold the theory predicts current--driven non--classical light emission from the single--level junction. Finally the investigation of the effect of a strong external drive of the cavity on the electronic current shows a quantization of the current that is linked to the Franck--Condon effect.
Finally the theory is applied to a double--level model for the molecular junction inspired by quantum optics. In this scenario, the cavity mode couples to the electronic transition between the two states of the molecule. The effect of the charge fluctuations for each single electronic level is neglected. Therefore the coupling is a dipolar coupling in this case. The focus is mainly on the weak coupling regime. The electronic current shows the Rabi splitting due to the hybridization of the cavity mode and the molecule. Electronic tunneling can occur into these hybridized states and is responsible for light emission in the cavity in a single tunneling process. Light anti bunching is seen in the weak coupling regime since our model predicts that only single photon emission is possible during a tunneling event in this case. Though the average coupling regime is only briefly treated, the strong coupling regime is shown to be similar to two independent single level.

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