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arXiv:2305.06596 · Science Advances

Phase engineering of anomalous Josephson effect derived from Andreev molecules

Sadashige Matsuo, Takaya Imoto, Tomohiro Yokoyama, Yosuke Sato, Tyler Lindemann, Sergei Gronin, G. C. Gardner, Michael J. Manfra, Seigo Tarucha

Published Dec 13, 2023• 28 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1126/sciadv.adj3698

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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.
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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 propose a Josephson diode mechanism in which nonreciprocity arises not from a conventional asymmetric Andreev spectrum but from nonequilibrium occupation of the current-carrying states engineered by attached reservoirs. We realize this mechanism in a double-quantum-dot junction, where a phase-textured nonlocal reservoir acts as a quantum Zeno selector: rapid dissipation freezes out the bright state directly coupled to the jump operator LLL, while preserving an orthogonal dark Andreev channel whose supercurrent remains comparable to that of the lossless junction. In the infinite-gap limit, the steady-state current factorizes as Iss=IAPγI_{\rm ss}=I_A P_γIss​=IA​Pγ​, so that even when the Andreev current IAI_AIA​ is strictly reciprocal, the phase asymmetry of PγP_γPγ​ alone can produce a Josephson diode effect through reservoir engineering. We further show that local Coulomb repulsion can drive the system toward a nearly ideal diode regime via a dark-pair resonance. Using Keldysh-Lindblad calculations, we demonstrate that our results remain robust for realistic junctions with a finite superconducting gap and dissipation.
An extended Josephson junction consists of two superconducting electrodes separated by an insulator and is therefore also a microwave cavity. The superconducting phase difference across the junction determines the amplitude as well as the spatial distribution of the supercurrent. Both external magnetic fields and resonant intracavity fields produce a spatial modification of the superconducting phase along the junction. The interplay between these two effects leads to interference in the critical current of the junction and allows us to continuously tune the coupling strength between the first cavity mode and the Josephson phase from 1 to $\ensuremath{-}0.68$. This enables static and dynamic control of the junction in the ultrastrong-coupling regime.