Quantum state tomography through multi-frequency Josephson effect

Macroscopic quantum effects emerge when the coherent behavior of countless microscopic quantum states manifests collectively at a visible scale, as exemplified by the supercurrent carried by innumerable finite-momentum Cooper pairs. By rigorously analyzing the time evolution of superconducting nanodevices including finite-momentum superconductors and quantum-dot Josephson junctions, we analytically derive the ubiquitous macroscopic supercurrent that originates from quantum interference between distinct many-body eigenstates, which we term as the dynamic interference supercurrent. The dynamic interference supercurrent in a system of two Andreev spin qubits exhibits multi-frequency Josephson effect in the absence of external voltage and is governed by the response of the many-body eigenfunctions ($\vert r\rangle$) to variations in the superconducting phase $ϕ$, determined by the $ϕ$-space Berry connection $C_{rr'}=\langle r|\partial_ϕ|r'\rangle$. The macroscopic dynamic interference supercurrent, an inherent property of the superposition state itself, enables an advanced quantum entanglement measurement of the Andreev spin qubits. These findings open new avenues for investigating superconducting nanodevice properties from a wave-function level, with substantial implications for advancing quantum science and technology in solid-state superconducting devices, such as quantum computer, communication, memory, and sensor.