Carles Altimiras

Heat flow in the Chern Insulator states of the Hofstadter butterfly is obtained in a graphene/hBN moir\'e for the first time.

Coulomb interactions deeply affect quantum transport in simple ballistic systems, but their impact on scaled up ballistic structures remains underexplored. Here, we theoretically consider a chain of small metallic dots with frozen charge dynamics connected by ballistic channels. We identify a neutral mode of transport that is specific to a chain with at least two islands and entwines local diffusion by neutral excitations with long-range correlations between the islands' charge states. We show, as an experimentally measurable signature of this many-body behavior, that the Wiedemann-Franz law is violated with a Lorenz ratio scaling as the square root of the chain's length.

Exotic quantum Hall systems hosting counterpropagating edge states can show seemingly nonuniversal transport regimes, usually depending on the size of the sample. We experimentally probe transport in a quantum Hall sample engineered to host a tunable number of counterpropagating edge states. The latter are coupled by Landauer reservoirs, which force charge equilibration over a tunable effective length. We show that charge transport is determined by the balance of up- and downstream channels, with a ballistic regime emerging for unequal numbers of channels. For equal numbers, we observe a transition to a critical diffusive regime, characterized by a diverging equilibration length. Our approach allows simulating the equilibration of hole-conjugate states and other exotic quantum Hall effects with fully controlled parameters using well-understood quantum Hall states.

We present an experimental test of Kubo formula performed on a nonlinear quantum conductor, a Superconductor-Insulator-Superconductor tunnel junction, driven far from equilibrium by a DC voltage bias. We implement the proposal of Lesovik & Loosen [G. B. Lesovik and R. Loosen, J. Exp. Theor. Phys. Lett. 65, 295 (1997)] and demonstrate experimentally that it is possible to extract both the emission and absorption noise of the conductor by measuring the power it exchanges with a linear detection circuit whose occupation is tuned close to vacuum levels. We then compare their difference to the real part of the admittance which is independently measured by coherent reflectometry, finding that Kubo formula holds within experimental accuracy. Last, we show theoretically that the spectral density of power exchanged between a quantum conductor and its linear detection circuit follows a Lesovik & Loosen like formula, even in the presence of strong detection back-action. This result applies as long as the conductor acts as a current source for the detection circuit and the detection circuit is not singular.

We show experimentally that a dc-biased Josephson junction in series with two microwave resonators emits entangled beams of microwaves leaking out of the resonators. In the absence of a stationary phase reference for characterizing the entanglement of the outgoing beams, we measure second-order coherence functions to prove the entanglement. The experimental results are found in quantitative agreement with theory, proving that the low-frequency noise of the dc bias is the main limitation for the coherence time of the entangled beams. This agreement allows us to evaluate the entropy of entanglement of the resonators, estimate the entanglement flux at their output, and to identify the improvements that could bring this device closer to a useful bright source of entangled microwaves for quantum-technological applications.

In their Comment [P. Hakonen and E. B. Sonin, preceding comment, Phys. Rev. X 11, 018001 (2021)], Hakonen and Sonin (HS) object to our conclusion on the absence of a dissipation-induced superconducting-to-insulating quantum phase transition (DQPT) in resistively shunted Josephson junctions (RSJJs) originally predicted by Schmid and Bulgadaev (SB). Their objections are based on the account they make of a theory explaining the DQPT in terms of Bloch bands which was developed in the 1980s and early 1990s. In this Reply, we point to several issues in the Comment which undermine the objections HS formulate against our work.

Half a century after its discovery, the Josephson junction has become the most important nonlinear quantum electronic component at our disposal. It has helped reshape the International System of Units around quantum effects and is used in scores of quantum devices. By itself, the use of Josephson junctions in volt metrology seems to imply an exquisite understanding of the component in every aspect. Yet, surprisingly, there have been long-standing subtle issues regarding the modeling of the interaction of a junction with its electromagnetic environment. Here, we find that a Josephson junction connected to a resistor does not become insulating beyond a given value of the resistance due to a dissipative quantum phase transition, as is commonly believed. Our work clarifies how this key quantum component behaves in the presence of a dissipative environment and provides a comprehensive and consistent picture, notably regarding the treatment of its phase.