Condensed-matter simuLatiOn in circuit quantUm electroDynamics – CLOUD

Physical situations where localized quantum states are strongly coupled to a continuum of electronic excitations are ubiquitous in condensed matter. They all show the same characteristic behavior: a cloud of electronic excitations screens localized degrees of freedom, thus forming a so-called many-body system. The Kondo effect, which describes the coupling between a single magnetic impurity and a continuum of electrons, is considered as the “hydrogen atom” of quantum impurity problems. As such, its complete understanding would pave the way to the explanation of the properties of the myriad of materials where strong interactions are the norm: heavy-fermions compounds, exotic superconductors and strongly correlated systems... However despite numerous theoretical and experimental efforts, the Kondo problem has not yet surrendered all his mysteries. Most strikingly, the famous Kondo cloud remains rather a theoretical concept than an experimentally characterized reality. Its spatial structure, its dynamical buildup, its nonlinear response, the quantum correlations and the nature of the entanglement between the electrons inside the cloud remain open questions. In addition Kondo physics experiments have mainly focused on electronic transport measurements, which gave very little information about the dynamical quantum properties of the cloud.

The CLOUD project addresses this matter in a new and innovative manner. Instead of using usual magnetic quantum impurity systems and their coupling to an electronic continuum, we have developed an analog quantum simulator to mimic their behaviors in an unprecedented level of tunability and versatility. It is based on a superconducting Josephson quantum bit (qubit) ultra-strongly coupled to many modes of a Josephson junction array. The superconducting qubit plays the role of the impurity and the array modes support a microwave photonic continuum, the equivalent to the electronic continuum. Because of the ultra-strong coupling between the qubit and the many modes, this novel experimental platform reaches a new paradigm in circuit-QED: the Multi-Mode Ultra-Strong Coupling (MMUSC). Therefore this system constitutes a concrete quantum simulator for the Kondo physics (or equivalently the spin-boson physics in the strong dissipative regime). A first generation of such a quantum simulator has just been demonstrated in my team. For the next generation, I envision a quantum simulator with a qubit simultaneously coupled to up to twenty modes.

Recently we demonstrated theoretically that the photonic Kondo cloud is described as a many-body Schrödinger cat. This result sheds a new light on the Kondo cloud nature and paves the way to new kinds of experiments. Indeed microwave spectroscopy measurements, experimental determination of the quantum correlations between microwave photons of the different modes and the time evolution of these correlations will all together reveal the quantum properties of the microwave photonic cloud.

The CLOUD project will take advantage of a new and powerful technology I recently implemented: meta-materials made of thousands of Josephson junctions. When engineered to show high impedance, they provide a very low-loss and tunable photonic continuum. In their low impedance version, they provide a non-linear medium perfectly suited to develop a new generation of quantum-limited amplifiers, needed to probe the quantum correlations inside the photonic cloud. Combining these two experimental achievements and the development of multi-mode heterodyne measurements will enable us to perform original experiments in order to unveil the many-body nature of the Schrödinger cat describing the Kondo cloud. In addition to a better understanding of the Kondo cloud properties, the CLOUD project will realize, in an original way, the quantum simulation of a highly complex many-body system.