Quantum light spectroscopy of complex quantum systems

光谱学揭示了复杂系统的性质，如其结构和动力学-物理，分子，电子，通常无法直接访问，由于它们的原子或分子大小和超快（飞秒）的时间尺度。它的工作原理是将光照射在样品上，然后测量光与物质相互作用后的光。大多数光谱学技术使用激光在称为“相干”状态的经典状态下产生的光脉冲。最近，光的非经典或量子态在成像和干涉测量等领域提供了更高的精度来估计未知参数。后者的主要例子是激光干涉引力波探测器。除了激光的相干态外，这些探测器还使用“压缩”态来提高其性能。非线性超快光谱学是研究复杂量子系统动力学的最先进的工具，它提供了丰富的见解。然而，任何见解通常都是通过与理论结果的比较来实现的，理论结果必须结合计算光谱所需的复杂理论模型，以及所研究的材料和过程的细节。此外，感兴趣的信息往往被光谱展宽所掩盖，因此光谱的解释有时被描述为“blobology”。虽然已经有人提出用量子光进行光谱学来克服这些限制，但已知的方法在实验上仍然很遥远。其中一个挑战是量子光非线性光谱中典型的低光强。另一个挑战是量子光谱学的建议通常依赖于改进现有的经典光技术的原理，通过用量子光取代一个或多个经典脉冲来揭示某些感兴趣的特征，使它们在实践中变得越来越巴洛克。我的想法是从相反的一端开始。我将寻求最精确和最佳的光谱方法-根据输入光的量子态，光与样品之间的相互作用，以及光的检测-在量子力学定律允许的情况下，用于研究复杂的量子系统。为此，我将引入量子和经典估计理论的新概念，以及非线性光谱学、量子光学和开放量子系统的统计学。

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.