[Paper Review] Could two degenerate energy states be observed for a superconducting ring at $\Phi_{0}$/2?

A. A. Burlakov, В. Л. Гуртовой+3 more|arXiv (Cornell University)|Mar 1, 2006

Quantum and electron transport phenomena1 references3 citations

TL;DR

This study investigates quantum macroscopic superposition in asymmetric aluminum superconducting rings by measuring critical current and rectified voltage oscillations. At half-flux quantum (Φ₀/2), conflicting results between resistance and critical current oscillations suggest a violation of macroscopic realism, providing experimental evidence for two degenerate ground states at Φ₀/2, challenging classical realism in mesoscopic superconductors.

ABSTRACT

The Little-Parks oscillations of the resistance and the quantum oscillations of the rectified voltage observed for asymmetric superconducting Al rings give experimental evidence of two degenerate energy states at the magnetic flux $\Phi_{0}$/2. The quantum oscillations of the critical current as a function of magnetic field have also been measured. On the one hand, these oscillations confirm that the quantum oscillations of the rectified voltage are a consequence of periodical dependence of the asymmetry of the current-voltage curves and, on the other hand, comparison of the oscillations with Little-Parks measurements results in contradiction.

Motivation & Objective

• . To test the existence of two degenerate ground states in superconducting rings at Φ₀/2.
• . To investigate whether quantum oscillations in resistance and critical current are consistent with a single quantum state or indicate superposition.
• . To resolve contradictions between Little-Parks resistance oscillations and critical current measurements in asymmetric rings.
• . To probe the validity of macroscopic realism in mesoscopic superconducting systems.
• . To determine whether persistent currents at Φ₀/2 imply non-classical behavior consistent with quantum superposition.

Proposed method

• . Fabricated asymmetric aluminum rings with radii r = 2 µm, widths wn = 0.2 µm and ww = 0.25–0.4 µm using e-beam lithography and lift-off.
• . Measured resistance and critical current Ic+ and Ic− as functions of magnetic flux Φ/Φ₀ at T ≈ 0.95–1.0 Tc.
• . Compared rectified voltage oscillations with critical current and resistance oscillations to assess consistency with velocity quantization (1).
• . Analyzed asymmetry-induced shifts in Ic+ and Ic− relative to symmetric rings to detect persistent current dependence on flux phase.
• . Used the London equation and quantized circulation condition ∫v dl = 2πℏ/m (n − Φ/Φ₀) to model velocity and current behavior.
• . Evaluated the persistent current Ip ∝ (n − Φ/Φ₀) and its effect on critical current anisotropy Ic,an ∝ Ip (sw/sn − sn/sw) in asymmetric arms.

Experimental results

Research questions

• RQ1 . Can two degenerate energy states be observed at Φ₀/2 in a superconducting ring, as predicted by quantum mechanics?
• RQ2 . Do the observed quantum oscillations in resistance and critical current agree with a single quantum state or imply superposition?
• RQ3 . Why do critical current oscillations in asymmetric rings show a 0.25 flux quantum shift relative to symmetric rings, contradicting resistance measurements?
• RQ4 . Is the observed discrepancy evidence for a violation of macroscopic realism in mesoscopic superconductors?
• RQ5 . Can persistent current at Φ₀/2 be experimentally distinguished from classical fluxoid quantization?

Key findings

• . At Φ₀/2, resistance oscillations show maxima consistent with velocity quantization, indicating v² ∝ (n − Φ/Φ₀)² reaches maximum.
• . Critical current Ic+ and Ic− in asymmetric rings (ww/wn ≥ 1.25) exhibit a 0.25 flux quantum shift relative to symmetric rings, with Ic+(Φ/Φ₀) = Ic(Φ/Φ₀ − 0.25).
• . The shift in critical current cannot be explained by inductive flux contributions (ΦI < 0.04Φ₀), ruling out geometric or inductive artifacts.
• . The contradiction between resistance maxima at Φ₀/2 and critical current minima at Φ₀/2 implies inconsistency with classical realism.
• . The data suggest that the system may be in a superposition of states at Φ₀/2, violating the principle of macroscopic realism.
• . The observed discrepancy between resistance and critical current oscillations provides experimental evidence for quantum macroscopic superposition in mesoscopic superconducting rings.