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arXiv:2306.00866 · Nano Letters

Demonstration of the Nonlocal Josephson Effect in Andreev Molecules

D. Z. Haxell, Marco Coraiola, Manuel Hinderling, Sofieke C. ten Kate, Deividas Sabonis, Aleksandr E. Svetogorov, Wolfgang Belzig, Erik Cheah, Filip Křížek, Rüdiger Schott, W. Wegscheider, Fabrizio Nichele

Published Aug 8, 2023• 29 citations
arXivHTMLPDF

Abstract

High Resolution Image Download MS PowerPoint Slide We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current–phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ 0 -junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.

DOI
10.1021/acs.nanolett.3c02066

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High Resolution Image Download MS PowerPoint Slide We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current–phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ 0 -junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.
A Josephson junction (JJ) is a key device for developing superconducting circuits, wherein a supercurrent in the JJ is controlled by the phase difference between the two superconducting electrodes. When two JJs sharing one superconducting electrode are coherently coupled and form the Andreev molecules, a supercurrent of one JJ is expected to be nonlocally controlled by the phase difference of another JJ. Here, we evaluate the supercurrent in one of the coupled two JJs as a function of local and nonlocal phase differences. Consequently, the results exhibit that the nonlocal phase control generates a finite supercurrent even when the local phase difference is zero. In addition, an offset of the local phase difference giving the JJ ground state depends on the nonlocal phase difference. These features demonstrate the anomalous Josephson effect realized by the nonlocal phase control. Our results provide a useful concept for engineering superconducting devices such as phase batteries and dissipationless rectifiers.
Fermion parity is a fundamental property of superconducting many-body states. Here, we show that the global fermion parity of a delocalized superconducting state can be detected locally by exploiting the nonlocal Josephson effect. Using a carbon nanotube-based Andreev molecule formed by two coupled quantum-dot Josephson junctions, we observe a pronounced nonlocal Josephson response and demonstrate the formation of delocalized Andreev molecular states extending across both junctions. We further show that changes in the molecular ground-state parity manifest as characteristic πππ-phase shifts in the nonlocal response. Supported by a minimal theoretical model, these results identify global fermion parity as an experimentally accessible degree of freedom in hybrid superconducting circuits that can be readily revealed through the nonlocal Josephson effect.
Gate-tunable Josephson junctions (JJs) are the backbone of superconducting classical and quantum computation. Typically, these systems exploit low-charge-concentration materials and present technological difficulties limiting their scalability. Surprisingly, electric field modulation of a supercurrent in metallic wires and JJs has been recently demonstrated. Here, we report the realization of titanium-based monolithic interferometers which allow tuning both JJs independently via voltage bias applied to capacitively coupled electrodes. Our experiments demonstrate full control of the amplitude of the switching current ( I s ) and of the superconducting phase across the single JJ in a wide range of temperatures. Astoundingly, by gate-biasing a single junction, the maximum achievable total I s is suppressed down to values much lower than the critical current of a single JJ. A theoretical model including gate-induced phase fluctuations on a single junction accounts for our experimental findings. This class of quantum interferometers could represent a breakthrough for several applications such as digital electronics, quantum computing, sensitive magnetometry, and single-photon detection.
Andreev molecule states arise from hybridization of Andreev bound states in different Josephson Junctions. Extensive theoretical and experimental research concentrates on direct coherent electron coupling between the junctions: this implies the distance between the junctions is of the order of superconducting coherence length, that is, short. We propose and discuss the possibility to create Andreev molecules at long (in principle, arbitrary long) distance between the junctions. In this case, the hybridized states are excited quasi-particle singlets and the coupling is provided by an embedding electric circuit. To achieve a strong hybridization, one aligns the energies of the Andreev bound states with associated phase differences. In fact, a recent experiment realizes such setup. With circuit theory we derive the hybridization level splitting and estimate the scale of the effect. Since the phenomenon encompasses excited states, we derive and solve the associated Lindblad equation under condition of persistent resonant excitation. By analyzing the resulting dissipative dynamics we identify relevant regimes where the hybridization and resonant excitation peaks are most pronounced. The low-frequency mutual inductance of the Josephson junctions is an important signature of the molecular state and associated non-local Josephson effect. We demonstrate the peak structures for both mutual and self-inductance, and compute them in various frequency regimes. In an interesting common case the embedding circuit includes an oscillator, which can be used both to enhance hybridization and for state readout with two-tone spectroscopy. We derive and solve Lindblad equations for the conditions of two-tone spectroscopy to demonstrate the the readout of molecular states.
We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.
We demonstrate microwave measurements of the Andreev-bound-state (ABS) spectrum in planar Josephson junctions (JJs) defined in Ge high-mobility two-dimensional hole gases contacted by superconducting platinum germanosilicide ( Pt Si Ge ). The JJs and readout circuitry are located on separate chips and inductively coupled via flip-chip bonding. For a device with 350-nm junction length, the spectroscopic signatures were consistent with the short-junction limit, with an induced superconducting gap Δ ∗ ≈ 48 μ eV and transmission τ ≈ 0.94 . The interaction between the highest-transmission ABS and the resonator was well described by a Jaynes-Cummings model with a vacuum Rabi splitting of approximately 6 MHz. A device with a junction length of 1 μ m showed an ABS spectrum consistent with a long-junction model. Time-resolved monitoring of the readout resonator in the dispersive regime revealed gate-voltage tunable-junction parity fluctuations on the time scale of seconds. Our work indicates a viable path toward hybrid quantum devices based on planar Ge . Published by the American Physical Society 2024