Quantum light spectroscopy of complex quantum systems

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Spectroscopy reveals properties of complex systems such as its structure and dynamics - physical, molecular, electronic which are typically inaccessible directly due to their atomic or molecular size and ultrafast (femtosecond) timescales. It works by shining light on a sample and measuring the light after the light-matter interaction. Most spectroscopy techniques use light pulses produced by a laser in a classical state called the 'coherent' state. Recently, non-classical or quantum states of light have provided greater precision is estimating unknown parameters in areas such as imaging and interferometry. The premier example of the latter are laser-interferometric gravitational wave detectors. In addition to coherent states from lasers, these detectors use 'squeezed' states to improve their performance. Nonlinear ultrafast spectroscopy, the state-of-the-art tool used to study dynamics in complex quantum systems has provided rich insights. However, any insight is routinely realised via comparison to theoretical results, which must incorporate both the elaborate theoretical models needed to calculate the spectra in addition to particulars of the materials and processes being studied. Furthermore, the information of interest is often obscured by spectral broadening such that interpretation of the spectra is sometimes described as "blobology". While proposals have been made towards overcoming some of these limitations by performing spectroscopy with quantum light, the known methods remain distant experimentally. One challenge is the low light intensity typical in nonlinear spectroscopy with quantum light. Another challenge is that quantum light spectroscopy proposals often rely on the principle of improving existing classical light techniques by replacing one or more classical pulses by quantum light to reveal certain features of interest, rendering them increasingly baroque in practice.My idea is to start from the opposite end. I will seek the most precise and optimal spectroscopic method - in terms of the quantum state of the input light, the interaction between the light and sample, and the detection of the light - allowed by the laws of quantum mechanics for investigating complex quantum systems. To that end I will introduce new concepts from quantum and classical estimation theory, and statistics into nonlinear spectroscopy, quantum optics, and open quantum systems.