This thesis describes how the rich internal degrees of freedom of molecules can be exploited to construct the first “clock” based on ultracold molecules, rather than atoms. By holding the molecules in an optical lattice trap, the vibrational clock is engineered to have a high oscillation quality factor, facilitating the full characterization of frequency shifts affecting the clock at the hertz level. The prototypical vibrational molecular clock is shown to have a systematic fractional uncertainty at the 14th decimal place, matching the performance of the earliest optical atomic lattice clocks. As part of this effort, deeply bound strontium dimers are coherently created, and ultracold collisions of these Van der Waals molecules are studied for the first time, revealing inelastic losses at the universal rate. The thesis reports one of the most accurate measurements of a molecule’s vibrational transition frequency to date. The molecular clock lays the groundwork for explorations into terahertz metrology, quantum chemistry, and fundamental interactions at atomic length scales.

This thesis investigates ultracold molecules as a resource for novel quantum many-body physics, in particular by utilizing their rich internal structure and strong, long-range dipole-dipole interactions. In addition, numerical methods based on matrix product states are analyzed in detail, and general algorithms for investigating the static and dynamic properties of essentially arbitrary one-dimensional quantum many-body systems are put forth. Finally, this thesis covers open-source implementations of matrix product state algorithms, as well as educational material designed to aid in the use of understanding such methods.

The First Book on Ultracold MoleculesCold molecules offer intriguing properties on which new operational principles can be based (e.g., quantum computing) or that may allow researchers to study a qualitatively new behavior of matter (e.g., Bose-Einstein condensates structured by the electric dipole interaction). This interdisciplinary book discusse

This collection of articles provides authoritative and up-to-date reviews on the Hubbard Model. It will be useful to graduate students and researchers in the field.

The field of atomic, molecular, and optical (AMO) science underpins many technologies and continues to progress at an exciting pace for both scientific discoveries and technological innovations. AMO physics studies the fundamental building blocks of functioning matter to help advance the understanding of the universe. It is a foundational discipline within the physical sciences, relating to atoms and their constituents, to molecules, and to light at the quantum level. AMO physics combines fundamental research with practical application, coupling fundamental scientific discovery to rapidly evolving technological advances, innovation and commercialization. Due to the wide-reaching intellectual, societal, and economical impact of AMO, it is important to review recent advances and future opportunities in AMO physics. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States assesses opportunities in AMO science and technology over the coming decade. Key topics in this report include tools made of light; emerging phenomena from few- to many-body systems; the foundations of quantum information science and technologies; quantum dynamics in the time and frequency domains; precision and the nature of the universe, and the broader impact of AMO science.

This thesis unites the fields of optical atomic clocks and ultracold molecular science, laying the foundation for optical molecular measurements of unprecedented precision. Building upon optical manipulation techniques developed by the atomic clock community, this work delves into attaining surgical control of molecular quantum states. The thesis develops two experimental observables that one can measure with optical-lattice-trapped ultracold molecules: extremely narrow optical spectra, and angular distributions of photofragments that are ejected when the diatomic molecules are dissociated by laser light pulses. The former allows molecular spectroscopy approaching the level of atomic clocks, leading into molecular metrology and tests of fundamental physics. The latter opens the field of ultracold chemistry through observation of quantum effects such as matter-wave interference of photofragments and tunneling through reaction barriers. The thesis also describes a discovery of a new method of thermometry that can be used near absolute zero temperatures for particles lacking cycling transitions, solving a long-standing experimental problem in atomic and molecular physics.