Aharonov-Casher Effect and the Coherent Flux Tunneling in the Hybrid Charge Quantum Interference Device

By exploiting the Aharonov-Casher effect we demonstrate a suppression of magnetic flux tunneling in a Hybrid Charge Quantum Interference Device. The main part of this device is two Josephson junctions with a small superconducting island between them. To minimize phase fluctuations across Josephson junctions, this structure is embedded in a compact super-inductive NbN loop. The Interference between the flux tunneling paths is determined by the island-induced charge, which is controlled by an external voltage. The charge sensitive operation of the device is subjected to poisoning by the quasiparticles generated in the NbN film.

💡 Research Summary

In this work the authors present a hybrid charge‑quantum‑interference device (h‑CQUID) that exploits the Aharonov‑Casher (AC) effect to control and, in the ideal case, completely suppress magnetic‑flux (fluxon) tunnelling. The device consists of two conventional Al/AlOx Josephson junctions (JJs) separated by a small Al island, all embedded in a compact, high‑kinetic‑inductance NbN loop. The loop provides a large inductance (≈ 90 nH) while keeping the footprint small, thereby reducing flux noise and phase fluctuations that would otherwise diminish the coherent quantum‑phase‑slip (CQPS) energy.

Theoretical analysis starts from a two‑level Hamiltonian in the flux basis, Ĥ = −(ε/2)σ_z − (E_S/2)σ_x, where ε = 2I_pΔΦ is the flux‑bias energy, I_p = Φ₀/2L_k the persistent current, and ΔΦ the deviation from the degeneracy point. The coupling term E_S is the magnitude of the complex sum of the two flux‑tunnelling amplitudes ν₁ and ν₂ across the JJs, E_S(Q)=h|ν₁+e^{i2πQ/e}ν₂|. The charge Q on the island is set by a gate voltage V_g (Q = C_gV_g). When Q equals an odd multiple of e (Q = (2n+1)e), the two amplitudes acquire a π phase difference and interfere destructively, driving E_S → 0 and thus suppressing flux tunnelling.

Experimentally the authors measured five nominally identical samples, each containing four h‑CQUIDs coupled to a λ/2 NbN resonator. Two‑tone spectroscopy was performed at 12 mK using the third resonator mode at 10.676 GHz (Q ≈ 520). Sweeping the second tone revealed a flux‑qubit transition that reaches a minimum frequency of 2.555 GHz at the flux degeneracy point, from which a persistent current I_p ≈ 11.5 nA and loop inductance ≈ 90 nH were extracted.

Gate‑voltage scans at the degeneracy point produced two periodic spectral lines with a 2e charge period, shifted by half a period relative to each other, exactly as expected from the AC interference formula. For a relatively symmetric device the individual tunnelling rates were ν₁ ≈ 1.48 GHz and ν₂ ≈ 1.08 GHz, giving a minimum E_S/h ≈ 0.4 GHz when the amplitudes are opposite in phase. A deliberately asymmetric device (ν₁ ≈ 3.15 GHz, ν₂ ≈ 1.45 GHz) showed a much larger contrast, confirming that the suppression depth is set by the degree of JJ symmetry.

Rabi‑oscillation measurements yielded a relaxation time T₁ ≈ 20 ns, far shorter than state‑of‑the‑art superconducting qubits. The authors attribute this to quasiparticle poisoning of the Al island, induced by microwave noise in the highly inductive NbN loop. The presence of two simultaneous spectral branches is taken as a signature of an unpaired electron occupying the island.

Theoretical estimates of the single‑junction tunnelling rate using the standard expression ν ≈ (8E_JE_C/π)^{1/4} exp