Spectrum of Andreev bound states in a molecule embedded inside a microwave-excited superconducting junction

Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena

Circuit QED techniques have been instrumental in manipulating and probing with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices in which the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments uses cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.

Direct Cavity Detection of Majorana Pairs

No experiment could directly test the particle-antiparticle duality of Majorana fermions, so far. However, this property represents a necessary ingredient towards the realization of topological quantum computing schemes. Here, we show how to complete this task by using microwave techniques. The direct coupling between a pair of overlapping Majorana bound states and the electric field from a microwave cavity is extremely difficult to detect due to the self-adjoint character of Majorana fermions which forbids direct energy exchanges with the cavity. We show theoretically how this problem can be circumvented by using photoassisted tunneling to fermionic reservoirs. The absence of a direct microwave transition inside the Majorana pair in spite of the light-Majorana coupling would represent a smoking gun for the Majorana self-adjoint character.

Enhancements of the Andreev conductance due to emission/absorption of bosonic quanta

We predict that the subgap spectrum and transport properties of the quantum dot embedded between superconducting and metallic reservoirs can be substantially enhanced by emission/absorption of external bosonic quanta. Upon tuning the gate voltage the in-gap Andreev states eventually interfere with each other. We explore the measurable signatures of such interference appearing in the differential conductance for both linear and nonlinear regimes.

Tunneling spectroscopy of Andreev energy levels in a quantum dot coupled to a superconductor

The coupling of a quantum dot with a BCS-type superconducting reservoir results in an intriguing system where low energy physics is governed by the interplay of two distinct phases, singlet and doublet. In this Letter we show that the spectrum of Andreev energy levels, which capture the properties of the two phases, can be detected in transport measurements with a quantum dot strongly coupled to a superconducting lead and weakly coupled to a normal metal lead. We observe phase transitions between BCS singlet and degenerate magnetic doublet states when the quantum dot chemical potential is tuned with an electrostatic gate, in good qualitative agreement with numerical renormalization group calculations.

Effect of microwaves on the current-phase relation of superconductor-normal-metal-superconductor josephson junctions

We investigate the current-phase relation (CPR) of long diffusive superconductor-normal-metal-superconductor (Nb/Ag/Nb) Josephson junctions in thermodynamic equilibrium and under microwave irradiation. While in equilibrium good agreement with the predictions of quasiclassical theory is found, we observe that the shape of the CPR can be strongly affected by microwave irradiation. Close to a Josephson-phase difference phi approximately pi, the supercurrent can be strongly suppressed when increasing the rf power. Our results can be understood in terms of microwave excitation of low-lying Andreev bound states across the minigap in the junction. In the frequency interval studied, this mechanism becomes important, when the minigap closes at phi approximately pi.

Josephson-current-induced conformational switching of a molecular quantum dot

We discuss the behavior of a two-level system coupled to a quantum dot contacted by superconducting source and drain electrodes, representing a simple model for the conformational degree of freedom of a molecular dot or a break junction. The Josephson current is shown to induce conformational changes, including a complete reversal. For small bias voltage, periodic conformational motions induced by Landau-Zener transitions between Andreev states are predicted.