Spatial interference changes the symmetry class of a Josephson element

Abstract

Spatial interference can break the inversion symmetry of an effective Josephson potential even in a laterally homogeneous junction with inversion-symmetric local energy. We derive a general criterion based on harmonic-dependent complex spatial form factors: a single local harmonic remains a shifted cosine, whereas multiple harmonics can acquire phases incompatible with any common inversion center, permitting cubic interactions and three-wave mixing. Phase reflection reverses all odd-order expansion coefficients about corresponding minima while preserving the even-order ones. For a capacitively shunted junction at fixed charging energy and arbitrary offset charge, it also preserves the complete quantum spectrum, enabling reversal of the odd nonlinear sector without spectral retuning. A centered cross junction with multiple local harmonics is one concrete example. Within the imposed-field model, a three-component magnetic field can generate an inversion-asymmetric effective potential, and reversing an odd number of field components exactly reflects it without changing the quantum spectrum of the capacitively shunted junction.