Topics in quantum measurement of many-body systems

In quantum physics, measurement exhibits fundamentally different behaviour to the classical case, having direct effect on the observed system. As a result, the very act of observation in quantum systems plays a non-trivial role, and can be used as a method of controlling the dynamics of the system. With the rise of quantum technologies, understanding and exploiting these phenomena offers a great boon. Here, we investigate a selection of the possibilities offered by quantum measurement for characterising and manipulating many-body systems, with particular focus on ultracold atomic gases. We first study how microscopic quantum structures can be used to indirectly probe larger systems. After deriving a general result, we consider the specific case of impurity atoms immersed in a quantum gas, and demonstrate that this enables density-related properties of the gas to be inferred from measurements of solely the impurity internal state. Following this, we explore how the backaction from measurement can be used for control of quantum systems. Utilising the quantum Zeno effect that results from persistent measurement of a quantum state, we show how fully-quantum many-body light-matter interactions enable the engineering of atomic states and dynamics through measurement of the light, leading to an abundance of interesting phenomena, including genuinely multipartite entangled states, long-range correlated tunnelling, and the quantum simulation of long-range and correlated interactions. The resulting structure imparted by the light on the matter can also be used to detect and measure atomic entanglement. Finally, we generalise quantum Zeno dynamics to the regime where the measurement timestep is finite, and demonstrate that the resulting system evolution can exhibit correlated processes.