Compact description of quantum phase slips and the fate of the Aharonov–Casher effect

Quantum circuit theory is a powerful and ever-evolving tool to predict the dynamics of superconducting circuits. In its language, quantum phase slips (QPSs) are famously considered to be the exact dual to the Josephson effect. We argue that this duality suffers from issues with the topology and the size of the Hilbert space, and is incompatible with charge quantization. We provide a treatment with a reduced, compactified Hilbert space, which changes the predictions of various quantum circuits. In this talk we focus in particular on circuits with multiple QPS junctions, where the observed offset-charge dispersion is believed to emerge due to a quantum circuit version of the Aharonov-Casher effect: a coherent interference between phase slips occurring on neighbouring junctions. By means of our compact theory, we reassess the physics of such circuits, and find to the contrary that these oscillations emerge from the compactness of the phase variable. Moreover, we show that our theory does not provide a regime where the offset charge dependence can be reduced to a simple interference pattern of quantum phase slip amplitudes. Our theory thus provides both a significant qualitative and quantitative revision of QPS physics.