Many-Body Quantum Simulation with Hybrid Circuits – SIM-CIRCUIT

The metal-semiconductor hybrid circuits recently developed by Partner 1 and already labelled analog quantum simulators by other teams, constitute the solid back-bone at the heart of the present proposal. Expanding upon such devices, combined with Partner 3’s expertise on strongly coupled electromagnetic environments and on high frequency measurements, will give us access to a vast field of research yet virgin soil for experimental investigations. Specifically, we will implement a Kondo impurity with degenerate charge states of a metallic circuit node and/or engineer specific on-chip electromagnetic environments. In the context of interacting 1D conductors, this environment determines the strength and range of interactions. Partners 1 and 3 outstanding instrumental capabilities (high frequencies, record-low temperatures, precision thermometry, noise sensitivity) are also decisive in enabling the present proposal. For instance, reaching the universality regime requires very low temperatures (far below the high energy cutoff) combined with a precise on-chip thermometry of the electrons. We will tackle this many-body physics from a remarkably wide range of approaches, both experimental (electrical and heat transport, out-of-equilibrium, fluctuations, high frequency response…) and theoretical (conformal field theory, renormalization group, bosonization…).

Workpackage «Quantum criticality in Tomonaga-Luttinger liquids (TLL)«:
Two papers have been published on the universal renormalization flow of the electrical conductance in a TLL with an impurity. An excellent agreement, quantitative and without fit parameters as expected from a quantum simulator, is obtained with the new theoretical predictions extended by Edouard Boulat as well as with approximate numerical calculations (fRG). Beyond what was expected, experiments are underway to explore the renormalization of conductance in the presence of a temperature difference.

Workpackage «Tomonaga Luttinger liquid (TLL) physics beyond electrical conductance«:
A first article was published on the measurement of shot noise induced by a temperature difference, and on the observation of a new heat transport mechanism associated with this noise combined with the Coulomb interaction. The unplanned observation of the remote transmission of the quantum state of electrons in a regime where the flow of heat is completely blocked by the Coulomb interaction is the subject of a second article. The experimental works on the demonstration of fractional TLL charges and on the expected link between conductance renormalization and shot noise is in progress. Another experiment, initially not planned, on the demonstration of the anyonic statistics of the TLLs induced in the fractional quantum Hall effect regime will then be carried out.

Workpackage «Quantum contact point in series with one mode«:
We have designed and manufactured microwave resonators in noble metals (copper, silver and gold), from spiral inductors. The resonant frequency of 5.5 GHz, the characteristic impedance of 1 kO, and the internal quality factor of the order of 100 will allow both to observe the effect of such a resonator on the conductance and the properties of finite frequency transport of this type of resonator.

Remote transmission of the quantum state of electrons in a circuit:
This immaterial form of electronic teleportation involving Coulomb interaction was observed, for the first time, through a metallic island of micrometric size.

Observation of shot noise induced by a temperature difference:
While the electrical noise induced by the dc current flowing through a small quantum conductor is well known, the noise induced only by a temperature difference at its terminals (at a fixed average temperature and zero dc current) has only recently been observed. This result was achieved almost simultaneously, and published a bit earlier, by an Israeli team using a different approach.

Observation of a new mechanism for quantum heat transport in mesoscopic circuits:
An additional heat flux, induced by the combination of Coulomb interaction with the shot noise induced by a temperature difference, could be observed for the first time.

Articles published:
1. Electronic heat flow and thermal shot noise in quantum circuits, E. Sivre, H. Duprez, A. Anthore, A. Aassime, F. D. Parmentier, A. Cavanna, A. Ouerghi, U. Gennser & F. Pierre, Nature Communications 10, 5638 (2019)
2. Transmitting the quantum state of electrons across a metallic island with Coulomb interaction, H. Duprez, E. Sivre, A. Anthore, A. Aassime, A. Cavanna, U. Gennser, F. Pierre, Science 366, 1243–1247 (2019)
3. Universality at work - the local sine-Gordon model, lattice fermions, and quantum circuits, A. Anthore, D. M. Kennes, E. Boulat, S. Andergassen, F. Pierre, and V. Meden, Eur. Phys. J. Special Topics 229, 663-682 (2020)
4. Absence of a dissipative quantum phase transition in Josephson junctions, A. Murani, N. Bourlet, H. le Sueur, F. Portier, C. Altimiras, D. Esteve, H. Grabert, J. Stockburger, J. Ankerhold, and P. Joyez, Phys. Rev. X 10, 021003 (2020)

Materials with strongly-correlated electrons exhibit unconventional phenomena, with existing applications and remarkable potential. Important societal impacts are expected from a quantitative understanding of the underlying microscopic mechanisms, as it would pave the way to the quantum engineering of materials with novel properties. However, a major difficulty lies in the complexity of real-world strongly correlated materials. Moreover, even the simplified many-body Hamiltonians used to model these materials often cannot be solved completely. Experimental analog quantum simulation can provide a powerful workaround to the experimental and theoretical barriers. The project is to develop, exploit and analyse analog quantum simulators for the experimental exploration and theoretical understanding of a wide range of strongly-correlated electron and quantum critical physics, including phenomena with technological implications. For this purpose, novel quantum simulators based on solid-state circuits will be nano-engineered and tuned in-situ to exhibit a broad variety of continuous quantum phase transitions and to emulate the correlated physics of interacting one-dimensional systems.

We plan to nano-engineer tuneable circuits designed to allow for parameter-free, quantitative comparisons with state-of-the-art analytical and numerical predictions. In regimes still out-of-reach of theory, these devices will constitute genuine quantum simulators in the strongest sense. Achievements of the so-called quantum supremacy, such as aimed in this project, constitute the main justification of the research field dedicated to quantum simulation. In combination with theoretical developments, our goal is to advance the understanding of central models believed to underpin heavy fermions materials, high-Tc superconductors and interacting 1D conductors. We also expect to unveil novel unconventional behaviours in yet uncharted strongly correlated regimes, as illustrated with the unanticipated super-ballistic conductance (higher than the quantum limit for free electrons) recently revealed by Partners 1 and 2. In order to achieve the broadest understanding, this physics will be tackled through a wide range of approaches, by taking advantage of the consortium’s remarkable arsenal, both experimental (electrical and heat transport, fluctuations, high frequency response, ultra-low temperatures…) and theoretical (conformal field theory, renormalization group, bosonization…).

The project is structured into two broad objectives:
O1) Quantum criticality in generalized Kondo-type models. In this context, profoundly different kinds of quantum phase transitions develop, driven by a competition to screen the Kondo impurity.
O2) Strongly-correlated physics of 1D conductors (Tomonaga-Luttinger liquids and beyond) in dissipative mesoscopic circuits. The project is to investigate the 1D physics through circuit quantum simulation, and to simultaneously advance on the understanding of the quantum laws of transport in such composite circuits.