Not yet reviewed by Pith; the record is open.

Shake-up is a fundamental phenomenon in photoionisation of many-electron systems whereby the ionisation of one electron is accompanied by the simultaneous excitation of another. As a single-photon two-electron excitation, it is the most basic manifestation of electron correlation in nature. In a standard experiment using, for example, a synchrotron light source, shake-up states are populated incoherently and their relative excitation intensities describe the process completely. In this work, we use high-accuracy ab initio theoretical methods to show that the physics of shake-up differs qualitatively when ionisation is achieved with an attosecond pulse such as those produced by free-electron laser or high-harmonic generation sources. These coherent light sources possess sufficient bandwidth to enable the new phenomenon of coherent shake-up, a process whose result cannot be described solely by the shake-up state populations. We show theoretically that the ensuing coherent many-electron wavepackets exhibit attosecond quantum beats in the form of a radial expansion and contraction of the electron density which we term "breathing ions". We predict that such attosecond oscillatory dynamics will persist for as long as nanoseconds before being damped by radiative decay. Our modelling shows that the predicted coherent shake-up dynamics are readily measurable by presently available attosecond-pump attosecond-probe techniques.