Hybrid light-matter states in topological superconductors coupled to cavity photons

We consider a one-dimensional topological superconductor hosting Majorana bound states at its ends coupled to a single mode cavity. In the strong light-matter coupling regime, electronic and photonic degrees of freedom hybridize resulting in the formation of polaritons. We find the polariton spectrum by calculating the cavity photon spectral function of the coupled electron-photon system. In the topological phase the lower in energy polariton modes are formed by the bulk-Majorana transitions coupled to cavity photons and are also sensitive to the Majorana parity. In the trivial phase the lower polariton modes emerge due to the coupling of the bulk-bulk transitions across the gap to photons. Our work demonstrates the formation of polaritons in topological superconductors coupled to photons that contain information on the features of the Majorana bound states.Comment: 9 pages, 5 figures; references adde

Microwave detection of gliding Majorana zero modes in nanowires

We study a topological superconducting nanowire that hosts gliding Majorana zero modes in the presence of a microwave cavity field. We show that the cavity decay rate depends on both the parity encoded by the Majorana zero modes and their motion, in the absence of any direct overlap of their wavefunctions. That is because the extended bulk states that overlap with both Majorana states, facilitate their momentum-resolved microwave spectroscopy, with the gliding acting as to modify the interference pattern via a momentum boost. Moreover, we demonstrate that these non-local effects are robust against moderate disorder in the chemical potential, and confirm the numerical calculations with an analytical low-energy model. Our approach offers an alternative to tunneling spectroscopy to probe non-local features associated with the Majorana zero modes in nanowires.Comment: 6 + 9 pages, 7 figure

Zero-energy Andreev bound states from quantum dots in proximitized Rashba nanowires

We study an analytical model of a Rashba nanowire that is partially covered by and coupled to a thin superconducting layer, where the uncovered region of the nanowire forms a quantum dot. We find that, even if there is no topological superconducting phase possible, there is a trivial Andreev bound state that becomes pinned exponentially close to zero energy as a function of magnetic field strength when the length of the quantum dot is tuned with respect to its spin-orbit length such that a resonance condition of Fabry-Perot type is satisfied. In this case, we find that the Andreev bound state remains pinned near zero energy for Zeeman energies that exceed the characteristic spacing between Andreev bound state levels but that are smaller than the spin-orbit energy of the quantum dot. Importantly, as the pinning of the Andreev bound state depends only on properties of the quantum dot, we conclude that this behavior is unrelated to topological superconductivity. To support our analytical model, we also perform a numerical simulation of a hybrid system while explicitly incorporating a thin superconducting layer, showing that all qualitative features of our analytical model are also present in the numerical results.Comment: Accepted for publication in Phys. Rev.

Pinning of Andreev bound states to zero energy in two-dimensional superconductor-semiconductor Rashba heterostructures

We consider a two-dimensional electron gas with Rashba spin-orbit interaction (SOI) partially covered by an s-wave superconductor, where the uncovered region remains normal but is exposed to an effective Zeeman field applied perpendicular to the plane. We find analytically and numerically Andreev bound states (ABSs) formed in the normal region and show that, due to SOI and by tuning the parameters of the system deeply into the topologically trivial phase, one can reach a regime where the energy of the lowest ABS becomes pinned close to zero as a function of Zeeman field. The energy of such an ABS is shown to decay as an inverse power-law in Zeeman field. We also consider a superconductor-semiconductor heterostructure with a superconducting vortex at the center and in the presence of strong SOI, and find again ABSs that can get pinned close to zero energy in the non-topological phase.Comment: 6 pages, 5 figure

Dynamic current susceptibility as a probe of Majorana bound states in nanowire-based Josephson junctions

We theoretically study a Josephson junction based on a semiconducting nanowire subject to a time-dependent flux bias. We establish a general density matrix approach for the dynamical response of the Majorana junction and calculate the resulting flux-dependent susceptibility using both microscopic and effective low-energy descriptions for the nanowire. We find that the diagonal component of the susceptibility, associated with the dynamics of the Majorana states populations, dominates over the standard Kubo contribution for a wide range of experimentally relevant parameters. The diagonal term, thus far unexplored in the context of Majorana physics, allows to probe accurately the presence of Majorana bound states in the junction.Comment: 5 pages, 3 figures, 15 pages of supplemental materia

Transport quantique dans une nanostructure corrélée, couplée à une cavité micro-ondes

In this thesis, we study theoretically various physical properties of nanostructures that are coupledto microwave cavities. Cavity quantum electrodynamics (QED) with a quantum dot has been proven to be a powerful experimental technique that allows to study the latter by photonic measurements in addition to electronic transport measurements. In this thesis, we propose to use the cavity microwave field to extract additional information on the properties of quantum conductors: optical transmission coefficient gives direct access to electronic susceptibilities of these quantum conductors. We apply this general framework to different mesoscopic systems coupled to a superconducting microwave cavity, such as a tunnel junction, a quantum dot coupled to the leads, a topological wire and a superconducting ring. Cavity QED can be used to probe the finite frequency admittance of the quantum dot coupled to the microwave cavity via photonic measurements. Concerning the topological wire, we found that the cavity allows for determining the topological phase transition, the emergence of Majorana fermions, and also the parity of the ground state. For the superconducting ring, we propose to study the Josephson effect and the transition from the latter to the fractional Josephson effect, which is associated with the emergence of the Majorana fermions in the system, via the optical response of the cavity. The proposed framework allows to probe a broad range of nanostructures, including quantum dots and topological superconductors, in a non-invasive manner. Furthermore, it gives new information on the properties of these quantum conductors, which was not available in transport experiments.Dans cette thèse, nous étudions d’un point de vue théorique les propriétés physiques de nanostructures couplées à des cavités micro-ondes. L’électrodynamique quantique (QED) en cavité en présence d’une boîte quantique s’est révélée être une technique expérimentale puissante, permettant d'étudier cette dernière par des mesures photoniques en plus des mesures de transport électronique conventionnelles. Dans cette thèse, nous proposons d'utiliser le champ micro-ondes de la cavité afin d’extraire des informations supplémentaires sur les propriétés des conducteurs quantiques : le coefficient de transmission optique est directement lié à la susceptibilité électronique de ces conducteurs quantiques. Nous appliquons ce cadre général à différents systèmes mésoscopiques couplés à une cavité supraconductrice micro-ondes comme  une jonction tunnel, une boîte quantique couplée à des réservoirs, un fil topologique et un anneau supraconducteur. La QED en cavité peut être utilisée pour sonder, par l'intermédiaire de mesures photoniques, la dépendance en fréquence de l’admittance du puits quantique couplé à la cavité micro-ondes. En ce qui concerne le fil topologique, nous avons montré que la cavité permet de caractériser la transition de phase topologique, l'émergence de fermions de Majorana, ainsi que la parité de l'état fondamental. Pour l'anneau supraconducteur, nous étudions par l'intermédiaire de la réponse optique de la cavité l’effet Josephson et le passage à l'effet Josephson fractionnaire, qui est associé à l'apparition de fermions de Majorana dans le système. Le cadre théorique proposé dans cette permet de sonder de manière non-invasive un large éventail de nanostructures, des boîtes quantiques aux supraconducteurs topologiques. En outre, il donne de nouvelles informations sur les propriétés de ces conducteurs quantiques, informations non accessibles via des expériences de transport