[Paper Review] Dynamical Stabilization of Multiplet Supercurrents in Multi-terminal Josephson Junctions

Ethan G. Arnault, Sara Idris+7 more|arXiv (Cornell University)|Jan 26, 2022

Quantum and electron transport phenomena40 references35 citations

TL;DR

This paper demonstrates that multiplet supercurrents—entangled states of four or more electrons—can be dynamically stabilized in three-terminal Josephson junctions through phase-locked oscillations under specific bias conditions (nV₁ = −mV₂), rather than relying on static entanglement. Using graphene-based junctions, analog circuits, and simulations, the authors show that these resonances emerge due to dynamical stabilization analogous to Kapitza's inverted pendulum, enabling robust, classically stable 2φ-harmonic supercurrents useful for topological qubit engineering.

ABSTRACT

The dynamical properties of multi-terminal Josephson junctions have recently attracted interest, driven by the promise of new insights into synthetic topological phases of matter and Floquet states. This effort has culminated in the discovery of Cooper multiplets, in which the splitting of a Cooper pair is enabled via a series of Andreev reflections that entangle four (or more) electrons. In this text, we show conclusively that multiplet resonances can also emerge as a consequence of the three terminal circuit model. The supercurrent appears due to the correlated phase dynamics at values that correspond to the multiplet condition $nV_1 = -mV_2$ of applied bias. The emergence of multiplet resonances is seen in i) a nanofabricated three-terminal graphene Josephson junction, ii) an analog three terminal Josephson junction circuit, and iii) a circuit simulation. The mechanism which stabilizes the state of the system under those conditions is purely dynamical, and a close analog to Kapitza's inverted pendulum problem. We describe parameter considerations that best optimize the detection of the multiplet lines both for design of future devices. Further, these supercurrents have a classically robust $\cos2\phi$ energy contribution, which can be used to engineer qubits based on higher harmonics.

Motivation & Objective

• To demonstrate that multiplet supercurrents in multi-terminal Josephson junctions can arise from dynamical phase stabilization rather than static entanglement.
• To identify and characterize the dynamical mechanism stabilizing these supercurrents under specific bias conditions (nV₁ = −mV₂).
• To validate the phenomenon experimentally in a three-terminal graphene Josephson junction, via an analog circuit, and through circuit simulations.
• To optimize device parameters for enhanced detection of multiplet resonances in future quantum devices.
• To explore the potential of the cos²φ energy contribution in these systems for engineering higher-harmonic qubits.

Proposed method

• Modeling the three-terminal junction as a network of shunted Josephson junctions with resistors and capacitors, using the RCSJ framework extended to two-dimensional phase dynamics.
• Deriving a system of coupled differential equations for the phase variables φL and φR, incorporating Josephson relations and Kirchhoff's laws.
• Applying the condition nV₁ = −mV₂ to identify dynamical stabilization points where supercurrents emerge.
• Conducting experiments on a nanofabricated, encapsulated graphene three-terminal Josephson junction at 30 mK.
• Constructing and testing an analog Josephson junction circuit to reproduce the dynamical behavior.
• Performing circuit simulations to validate the observed resonances and phase dynamics.

Experimental results

Research questions

• RQ1 Can multiplet supercurrents in multi-terminal Josephson junctions be stabilized through dynamical phase locking rather than static entanglement?
• RQ2 What specific bias conditions (nV₁ = −mV₂) lead to the emergence of these dynamical resonances?
• RQ3 How do variations in gate voltage and contact transparency affect the visibility of multiplet lines?
• RQ4 To what extent can the dynamical stabilization mechanism be replicated in analog circuits and simulations?
• RQ5 What is the role of the cos²φ energy contribution in enabling higher-harmonic qubit designs?

Key findings

• Multiplet resonances, identified as quartet lines (Q), emerge in a three-terminal graphene Josephson junction when the bias condition nV₁ = −mV₂ is satisfied, indicating dynamical stabilization.
• The quartet lines disappear near the Dirac point (VG = −2 V), where reduced contact transparency increases normal resistance (Rn) and suppresses coherent transport, consistent with the loss of nondissipative MAR.
• The observed resonances are not due to microscopic multi-contact Andreev processes but are instead a classical dynamical effect arising from phase-locked oscillations in the RCSJ model.
• The system exhibits a classically robust cos²φ energy contribution, which provides a stable platform for engineering qubits based on higher harmonics.
• The dynamical stabilization mechanism is analogous to Kapitza’s inverted pendulum, where phase oscillations stabilize a metastable state.
• Parameter tuning—particularly gate voltage and current bias—can optimize the visibility of multiplet lines, enabling design principles for future quantum devices.