Local Weak Measurements as a Probe of the Spectrum of Quantum Magnets

Weak measurements are a powerful but under-explored tool in physics. In essence, weak measurements indirectly probe a system by way of an ancillary degree of freedom in order to avoid total collapse of the measured state at the cost of gaining less information about it. Their unique ability to preserve a degree of coherence while extracting information from a system in a tunable tradeoff opens up possibilities for a vast array of interesting ways to interact with and study quantum systems. In this work, we explore how sequences of local weak measurements can allow us to induce and then simultaneously detect excitations in quantum magnets. In particular, we examine how repeated weak measurements of a spin on the end of a Heisenberg chain give rise to oscillations connected to features of the spectrum that depend on the entire chain. We will discuss the origin and symmetry considerations of these oscillations, and comment on how this and similar measurement schemes could be practically useful.