Direct Observation of Measurement-Induced Excitations in Bose-Einstein Condensates

The understanding of many-body quantum systems is limited by measurement. However important physical properties, such as the excitation spectrum, are encoded in terms of response functions that quantify how the system reacts to a perturbation: requiring separate techniques to first perturb the system and then measure its response. Here we show that this paradigm can be replaced simply with a pair of weak quantum measurements. Specifically, we employ a pair of time-separated measurements, where the first detects both real and quantum fluctuations, and the second informs how these evolved in time. We demonstrate this technique in an atomic Bose-Einstein condensate with density weakly measured by phase-contrast imaging from which we obtain a two-body Greens function. Our approach is fully general and will give access to response functions associated with any pair of weakly measurable observables.

[1] E. Altuntas and I. B. Spielman, Communications Physics 6, 66 (2023).

[2] E. Altuntas and I. B. Spielman, Phys. Rev. Res. 5, 023185 (2023).