laboratoire pierre aigrain
électronique et photonique quantiques
laboratoire pierre aigrain

Hybrid Quantum Circuits

Quantum transport in hybrid electronic systems

Shot noise measurements in carbon nanotube based devices

Measuring shot noise in carbon nanotubes became therefore rapidly an important goal in the community after the early transport experiments. However, due to the sensitivity of nanotubes to extrinsic noise sources, shot noise had remained hardly explored until recently. The originality of our work has been to combine state-of-the-art carbon nanotube device fabrication techniques with noise measurements at moderate frequencies (about 1MHz). Doing so allowed to cope with the effect of the extrinsic fluctuating charge noise sources.

When they are well coupled to metallic electrodes, carbon nanotubes exhibit an electronic Fabry Perot interferometer behavior. One can control the transport with the help of a gate electrode capacitively connected to the circuit. Thanks to this tunability, the HQC team observed the quantum noise suppression for transmissions through the nanotube device tuned to unity. This provided another example of a noiseless fermionic source, after quantum point contacts.

In a subsequent experiment, we studied the noise properties of a single Kondo impurity made out of a single wall carbon nanotube. The Kondo effect is a key phenomenon in condensed matter physics because it is a paradigm for strongly correlated electronic systems. The possibility to design artificial magnetic impurities in nanoscale conductors has opened an avenue to the study of the Kondo effect in unusual situations as compared to the original one where magnetic impurities are diluted in a metallic matrix. In particular, out of equilibrium situations can be studied. In this work, we found an intriguing enhancement of the noise, in contradiction with the non-interacting theory. This enhancement is quantitatively reproduced by an interacting theory which we developped using the slave boson technique. In addition, an invariant of the noise for the Kondo effect was determined. It should provide a particularly useful test bench for the theory of the Kondo in out of equilibrium situations, which is one of the most important challenges in the theory of condensed matter in many-body systems.

Orbitally phase coherent spintronics

Spin valves implement to some extent the analog of a polarizer/analyzer experiment in optics. This analogy is at the heart of the principle of the celebrated proposal by Datta and Das for a spin field effect transistor and can be transposed to any type of spintronics device. One of the goals of our research is to study how such an analogy can be used to find means to control the electronic spin. The optical analogies are also particularly illuminating for understanding transport in mesoscopic conductors in which the phase of the electronic function is well defined.

Essentially thanks to their low number of conducting channels, single wall carbon nanotubes offer the possibility to study the interplay between spin dependent transport in the traditional sense (i.e. with ferromagnetic contacts) and orbitally phase coherent transport. This property can be indirectly exploited in two-terminal devices but is particularly striking in multi-terminal (more than two) devices.

For temperatures below 10K, these devices behave as triple quantum dots connected to four reservoirs-two normal and two ferromagnetic. In order to control the electronic transport via the local electric field, we have implemented lateral gates to tune independently the two outer dots. In cases where we can neglect electron-electron interactions, this type of device can be viewed as a series of electronic Fabry-Perot interferometers.

Towards quantum entanglement with electronic states

Quantum optics has been an important source of inspiration for many recent experiments in nanoscale electric circuits. One of the basic goals is the generation of entangled electronic states in solid state systems. Superconductors have been suggested as a natural source of spin

entanglement, due to the singlet pairing state of Cooper pairs. One important building block required for the implementation of entanglement experiments using superconductors is a Cooper-pair beam splitter which should split the singlet state into two different electronic orbitals. The basic mechanism for converting Cooper pairs into quasiparticles is the Andreev reflection in which an originally quantum coherent electron pair in the singlet spin state is produced at an interface between a superconductor and a normal conductor. Conventional Andreev reflections are local and cannot readily be used to create bipartite states. Many theoretical proposals for circumventing this fact have been around for the last decade. It has been suggested to make use of electron-electron interactions, spin filtering or anomalous scattering in graphene to promote Cooper-pair splitting, i.e., the crossed Andreev reflection process. In this work, the HQC team (thesis of Lorenz Herrmann), in collaboration with colleagues at SPEC Saclay, at the university of Madrid and the university of Regensburg has used Coulomb interactions as well as size quantization in order to favor the crossed Andreev reflection processes in carbon nanotubes, realizing experimentally for the first time, simultaneously with a team in Basel, an efficient Cooper pair splitter. The devices studied are double quantum dots which can be viewed as artificial molecules connected to one superconducting reservoir and two normal reservoirs. Thanks to their tunability, they allow to change in situ the probability of emitting spit Cooper pairs. These findings open an avenue for more complex quantum optics like experiments with electronics sates which should allow, among other things, to test the coherence of the emitted split Cooper pairs.