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.
Demonstrating the topological protection of Andreev states in Josephson junctions is an experimental challenge. In particular the telltale 4π periodicity expected for the current phase relation has ...remained elusive, because of fast parity breaking processes. It was predicted that low temperature ac susceptibility measurements could reveal the topological protection of quantum spin Hall edge states by probing their low energy Andreev spectrum at finite frequency. We have performed such a microwave probing of a phase-biased Josephson junction built around a bismuth nanowire, a predicted second order topological insulator, and which was previously shown to host one-dimensional ballistic edge states. We find absorption peaks at the Andreev level crossings, whose temperature and frequency dependencies point to protected topological crossings with an accuracy limited by the electronic temperature of our experiment.
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.
The technique of longitudinal neutron polarization analysis on a multi‐detector neutron spectrometer (so‐called `xyz'‐polarization analysis) is presented. This technique allows the simultaneous and ...unambiguous determination of the nuclear, magnetic and nuclear spin‐incoherent scattering cross sections as a function of both momentum transfer and energy transfer. The implementation of xyz‐polarization analysis on the recently upgraded D7 spectrometer at the Institut Laue–Langevin in Grenoble is described. Several examples of neutron polarization analysis studies of disordered systems on D7 are given, illustrating the valuable information which can be retrieved from the analysis of neutron diffraction patterns between the Bragg peaks.
We have probed the superconducting proximity effect through long high-quality monocrystalline Ag nanowires, by realizing Josephson junctions of different lengths, with different superconducting ...materials. Thanks to the high number of junctions probed, both the contact resistance and electron diffusion constant could be determined, enabling a comparison of the measured switching current to theoretical prediction, over the entire regime from short to long diffusive junctions. Although the length dependence of the switching current is as expected, the amplitude of the RNIc product is smaller than predicted by theory. We also address the magnetic field dependence of the switching current. The quasi-Gaussian decay of the switching current with field expected in a long narrow junction is observed for all superconducting contacts we used except for aluminum. We present the striking nonmonotonous effect of field on the switching current of junctions with aluminum contacts when probed in a four-wire configuration and analyze it in terms of improved quasiparticle thermalization by a magnetic field.
Bistable dynamical systems are widely employed to robustly encode classical bits of information. However, they owe their robustness to inherent losses, making them unsuitable to encode quantum ...information. Surprisingly, there exists a loss mechanism, known as two-photon dissipation, that provides stability without inducing decoherence. An oscillator exchanging pairs of photons with its environment is expected to reach macroscopic bit-flip times between dynamical states containing only a handful of photons. However, previous implementations have observed bit-flip times saturating in the millisecond range. In this experiment, we design a superconducting resonator endowed with two-photon dissipation, and free of all suspected sources of instabilities and inessential ancillary systems. We attain bit-flip times exceeding 100 s in between states containing about 40 photons. Although a full quantum model is necessary to explain our data, the preparation of coherent superposition states remains inaccessible. This experiment demonstrates that macroscopic bit-flip times are attainable with mesoscopic photon numbers in a two-photon dissipative oscillator.
In order to point out experimentally accessible signatures of spin-orbit interaction, we investigate numerically the Andreev spectrum of a multichannel mesoscopic quantum wire (N) with high ...spin-orbit interaction coupled to superconducting electrodes (S), contrasting topological and nontopological behaviors. In the nontopological case (square lattice with Rashba interactions), we find that the Kramers degeneracy of Andreev levels is lifted by a phase difference between the S reservoirs except at multiples of π, when the normal quantum wires can host several conduction channels. The level crossings at these points invariant by time-reversal symmetry are not lifted by disorder. Whereas the dc Josephson current is insensitive to these level crossings, the high-frequency admittance (susceptibility) at finite temperature reveals these level crossings and the lifting of their degeneracy at π by a small Zeeman field. We have also investigated the hexagonal lattice with intrinsic spin-orbit interaction in the range of parameters where it is a two-dimensional topological insulator with one-dimensional helical edges protected against disorder. Nontopological superconducting contacts can induce topological superconductivity in this system characterized by zero-energy level crossing of Andreev levels. Both Josephson current and finite-frequency admittance carry then very specific signatures at low temperature of this disorder-protected Andreev level crossing at π and zero energy.
One of the best known causes of dissipation in ac-driven quantum systems stems from photon absorption causing transitions between levels. Dissipation can also be caused by the retarded response to ...the time-dependent excitation, and in general gives insight into the system's relaxation times and mechanisms. Here we address the dissipation in a mesoscopic normal wire with superconducting contacts, that sustains a dissipationless supercurrent at zero frequency and that may therefore naively be expected to remain dissipationless at a frequency lower than the superconducting gap. We probe the high-frequency linear response of such a normal metal/superconductor (NS) ring to a time-dependent flux by coupling it to a highly sensitive multimode microwave resonator. Far from being the simple, dissipationless derivative of the supercurrent-versus-phase relation, the ring's ac susceptibility also displays a dissipative component whose phase dependence is a signature of the dynamical processes occurring within the Andreev spectrum. We show how dissipation is driven by the competition between two mechanisms. The first is the relaxation of the Andreev level distribution function, while the second corresponds to microwave-induced transitions within the spectrum. Depending on the relative strength of those contributions, dissipation can be maximal at π, a phase at which the proximity-induced minigap closes, or can be maximal near π/2, a phase at which the dc supercurrent is maximal. We also find that the dissipative response paradoxically increases at low temperature and can even exceed the normal-state conductance. The results are successfully confronted with theoretical predictions of the Kubo linear response and time-dependent Usadel equations, derived from the Bogoliubov–de Gennes Hamiltonian describing the SNS junction. These experiments thus demonstrate the power of the ac susceptibility measurement of individual hybrid mesoscopic systems in probing in a controlled way the quantum dynamics of Andreev bound states. By spanning different physical regimes, our experiments provide unique access to inelastic scattering and spectroscopy of an isolated quantum coherent system, and reveal the associated relaxation times. This technique should be a tool of choice to investigate topological superconductivity and detect the topological protection of edge states.
A favored interpretation of the gamma <--> alpha phase transition in cerium postulates the transformation of the localized 4f state in gamma-Ce to a weakly correlated itinerant 4f band in alpha-Ce. ...However, results of high-energy neutron inelastic scattering measurements, presented here, show clearly that the magnetic susceptibility response from alpha-Ce follows the Ce3+ form factor despite the large, 30-fold, increase in its spectral width relative to that in gamma-Ce. This observation provides, for the first time, indisputable evidence for the localized character of the 4f state in the alpha phase. The present findings appear consistent with recent calculations combining dynamical mean-field theory with the local density approximation that indicate a strongly correlated 4f state in alpha-Ce. The localized 4f state is also fundamental to the Kondo volume collapse theories for the gamma <--> alpha phase transition in cerium.
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