When light and matter are weakly coupled, they can be described as two distinctive systems exchanging quanta of energy. By contrast, for very large coupling strength, the systems hybridize and form compounds that cannot be described in terms of light or matter only. In this Thesis, we study some exotic properties which arise in this regime. In particular, we are interested in the possibility to engineer quantum phase transitions in these systems. One direction we explore is the study of two-photon coupling, a mechanism in which matter creates or absorb photons by pairs. This mechanism creates a rich phase diagram containing both phase transitions and instabilities. A second topic is the use of these transitions for sensing applications. Indeed, near the critical point, the system becomes extremely sensitive to external perturbations. We study a setup in which a single qubit is coupled to a bosonic field. We show that even this finite-size system displays a phase transition, which can be used to measure the frequency of the qubit and the field with improved accuracy. This protocol could be used to develop small-scale sensors. Finally, we study how the ability of a system to perform certain metrological tasks could be used to characterize and quantify nonclassicality, by using the formalism of resource theories. The first three chapters present the main concepts and key results in the fields of ultrastrong light-matter coupling, superradiant phase transitions, and quantum metrology. I have strived to write these chapters pedagogically; they can be used by non-specialists or students as an introduction to these domains. The three other chapters present my own research contributions. Although most of those have already been published elsewhere, this manuscript contains additional results, remarks, and perspectives, and should be considered as an improved version of the original papers.
Institut de Science et d’Ingénierie Supramoléculaires (ISIS, UMR7006), Université de Strasbourg（斯特拉斯堡大学超分子科学与工程学院）；Institut für Physik, Johannes Gutenberg Universität Mainz（美因茨约翰内斯·古腾堡大学物理研究所）；Department of Physics, Texas AM University（德克萨斯农工大学物理系）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Institute of Physics, Czech Academy of Sciences（捷克科学院物理研究所）；Department of Physics, The State University of New York at Buffalo（纽约州立大学布法罗分校物理系）
Sensing Short-Range Forces with a Nanosphere Matter-Wave Interferometer
我们描述了一种利用介电纳米球中的物质波干涉来感测短程力的方法。与原子干涉仪相比，纳米球的质量更大，导致波包膨胀减少，从而能够在自由落体干涉仪中研究更接近表面的力。通过激光将纳米球冷却到光势的基态并通过关闭光阱将其释放，可以在$10^{-8}$ m/s $^2$水平上进行加速度感测。该方法可以产生改进的灵敏度，汤川型偏离牛顿重力在$5$ $μ$ m长度尺度的$10^4$超过目前的限制。
Enhanced Dark Matter Quantum Sensing via Phase-Space Geometric Interferometry
International Center for Quantum-field Measurement Systems for Studies of the Universe and Particles (QUP, WPI), High Energy Accelerator Research Organization (KEK)（宇宙与粒子研究量子场测量系统国际中心（QUP，WPI），高能加速器研究机构（KEK））；Kavli IPMU (WPI), UTIAS, University of Tokyo（Kavli 宇宙起源研究所（WPI），东京大学宇宙线研究所（UTIAS））
Entanglement advantage in sensing power-law spatiotemporal noise correlations
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机科学联合中心，美国国家标准与技术研究院/马里兰大学）；Joint Quantum Institute, NIST/University of Maryland（量子联合研究所，美国国家标准与技术研究院/马里兰大学）；Pritzker School of Molecular Engineering, University of Chicago（普里茨克分子工程学院，芝加哥大学）
Background Suppression in Quantum Sensing of Dark Matter via Collective Entangled-State Projection
Kyoto University（京都大学）；The University of Tokyo（东京大学）；International Center for Elementary Particle Physics (ICEPP), The University of Tokyo（东京大学基础粒子物理国际中心）；IQM Quantum Computers（IQM量子计算机公司）；QUP (WPI), KEK（高能加速器研究机构夸克与宇称统一世界前沿研究所）
The Boundary Time Crystal as a light source for collectively enhanced sensing
Universität Tübingen（蒂宾根大学）；The University of Nottingham（诺丁汉大学）；Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) UIB-CSIC（跨学科物理与复杂系统研究所（IFISC）巴伊利亚大学-西班牙国家科研委员会）
Photon-resolved Floquet theory approach to spectroscopic quantum sensing
International Quantum Academy（国际量子学院）；Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology（南方科技大学深圳量子科学与工程研究院）；Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology（南方科技大学广东省量子科学与工程重点实验室）；Center for Theoretical Physics and School of Physics and Optoelectronic Engineering, Hainan University（海南大学理论物理中心暨物理与光电工程学院）；Himalayan Institute for Advanced Study（喜马拉雅高等研究院）；City University of Hong Kong（香港城市大学）
Atom-light hybrid interferometer for atomic sensing with quantum memory
Southern University of Science and Technology（南方科技大学）；International Shenzhen Quantum Academy（深圳量子研究院）；City University of Hong Kong（香港城市大学）；University of Crete（克里特大学）；Institute of Electronic Structure and Laser (IESL), FORTH（FORTH电子结构与激光研究所）
Thermal robustness of sensing quantum phases of matter via qubit probes
FZU - Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Department of Physics, King’s College London（伦敦国王学院物理系）；School of Physics, Trinity College Dublin（都柏林三一学院物理学院）
