[Paper Review] Radio-frequency-driven motion of single Cooper pairs across the superconducting single-electron transistor with dissipative environment

A. B. Zorin, S. V. Lotkhov+2 more|arXiv (Cornell University)|May 10, 2001

Physics of Superconductivity and Magnetism3 citations

TL;DR

This paper demonstrates gate-driven, unidirectional transport of single Cooper pairs across a superconducting single-electron transistor by introducing a dissipative environment via an on-chip Cr resistor (R ≈ 40 kΩ). The rf-gated voltage bias induces phase-locked, resonant tunneling at frequency f, resulting in distinct current plateaus at I ≈ 2ef, confirming coherent, single-pair transfer with high fidelity under dissipative conditions.

ABSTRACT

We report on the effect of the frequency-locked transfer of single Cooper pairs in a superconducting single-electron Al transistor embedded in a dissipative environment (on-chip Cr resistor of R = 40 kOhm). The transistor was dc voltage biased, and the harmonic signal of frequency f of several MHz was applied to the gate. Due to the substantial rate of relaxation, the unidirectional transfer of single pairs occurred in each junction once per clock cycle and the current plateaus at I = 2ef were developed in the transistor's I-V curves. The mechanisms (supercurrent, Landau-Zener tunneling, quasiparticle tunneling, etc.) deteriorating the phase-locking regime are discussed.

Motivation & Objective

• To achieve controlled, unidirectional motion of single Cooper pairs in a superconducting single-electron transistor under voltage bias.
• To overcome the limitations of reversible, elastic Cooper pair tunneling by introducing finite damping via a dissipative resistor.
• To realize a phase-locked, resonant tunneling regime enabling quantized current plateaus at I ≈ 2ef.
• To identify and mitigate mechanisms degrading phase-locking, such as Landau-Zener transitions and quasiparticle tunneling.
• To assess the feasibility of such devices for fundamental metrology and quantum standards.

Proposed method

• A superconducting Al single-electron transistor with a gate and two Josephson junctions was fabricated, incorporating a series on-chip Cr resistor (R ≈ 40 kΩ) to provide dissipative environment.
• The system was dc voltage biased and driven by a harmonic rf signal at frequency f applied to the gate, inducing periodic modulation of the island charge.
• The dissipative environment suppresses supercurrent and enhances unidirectional tunneling by breaking symmetry in the probability of traversing avoided energy level crossings.
• The tunneling rate was modeled using a modified BCS-type environment function P(E) ∝ E^{2z′−1}, with z′ = z/4 and z = R/RQ, accounting for damping effects.
• Theoretical analysis used the Landau-Zener model to estimate transition probabilities and relaxation rates, predicting p_LZ ≈ exp(−f₀/f) with f₀ ≈ 400 MHz.
• Experimental I-V curves were measured to observe current plateaus at I ≈ 2ef, indicating one Cooper pair transferred per rf cycle.

Experimental results

Research questions

• RQ1 Can dissipative coupling enable unidirectional, coherent transport of single Cooper pairs in a voltage-biased superconducting single-electron transistor?
• RQ2 How does the resistor value R affect the tunneling rate and the fidelity of single-pair transfer?
• RQ3 What are the dominant decoherence mechanisms limiting the accuracy of the current plateaus, such as Landau-Zener transitions or quasiparticle tunneling?
• RQ4 Can the device operate at higher frequencies with improved fidelity by tuning R and E_c?
• RQ5 To what extent can the plateaus be sharpened and their height stabilized for metrological applications?

Key findings

• Current plateaus at I ≈ 2ef were experimentally observed in the I-V curves, confirming one Cooper pair transferred per rf cycle.
• The highest and most stable plateaus were observed at low drive frequencies (f = 2–3 MHz), indicating adiabatic operation.
• The tunneling rate Γ(E) ∝ E^{2z′−1} with z′ ≈ 1 at R ≈ 20–30 kΩ, enabling faster and more reliable transfer at lower voltages.
• Landau-Zener transition errors were estimated at p_LZ < 10⁻⁸ for f ≤ 20 MHz, indicating high fidelity under optimal conditions.
• Quasiparticle tunneling degraded plateau quality due to E_c > Δ_Al, which suppressed even-odd parity blockade; this could be mitigated in Nb-Cr samples with E_c ≈ Δ_Nb.
• Theoretical modeling suggests that with E_c ≈ Δ_Nb and V < 80 μV, errors could be reduced to ∼10⁻⁸, meeting metrology-grade standards.