RUI: Bosons in Optical Lattices: Physics of the Inhomogeneous Phases

该奖项将支持对冷却到超低温的原子性质的理论研究。 这项研究将在韦尔斯利学院的本科环境中进行。 该研究课题是当前最令人兴奋的课题之一，是高度跨学科的，位于凝聚态物理学和原子物理学之间的界面。 本科生将有机会参与。拟议的工作探讨了超冷玻色子原子在周期性光学晶格势中的新特性，这是研究玻色子超流和莫特绝缘相的理想系统。使用的分析和数值技术相结合，系统的显着特点，超流和莫特绝缘区共存并排将推导。研究内容包括：（1）共存系统超流区的光谱信号，（2）三维超流壳层的集体模，（3）系统从陷阱释放后的演化，（4）具有Mott绝缘层的同心超流壳层的Josephson物理，（5）用新的约束几何探讨超流与Mott绝缘体之间量子相变的临界性质。拟议的工作利用了前所未有的实验室控制的强度的原子间的相互作用，强度的光学晶格势，和形状的限制陷阱独特的超冷原子系统。由于这种依赖，与积极开发该系统新探头的实验组密切合作是研究的一个组成部分。建议的工作特点参与的本科生在韦尔斯利学院在独立研究这些课题在整个project.Intellectual优点：控制微观参数以及宏观几何存在于被困的稀气体允许创建近乎完美的超流体和莫特绝缘系统，从而提高我们的量子行为的基本理解。对超流壳层的研究将有助于我们对超流在新的几何结构中的预期行为有一个定性的了解，并有助于我们对非均匀系统实验的定量预测。利用原子系统探测多体凝聚态模型的可能性显示出巨大的前景，是一个非常活跃的研究领域。这种模型（如玻色-哈伯德模型）中的量子相变在多大程度上可以在原子系统中实现是一个开放的重要问题。更广泛的影响：玻色子的超流和莫特绝缘相理论，以及它们之间的量子相变，对超导系统有着直接的影响。增加对玻色-哈伯德模型的理解可以导致对强相互作用超导系统的深入了解，并可能因此有助于新电子设备的开发。基于光学晶格中超冷玻色子的量子计算方案的进一步进展取决于更好地理解超流体和有限捕获系统中Mott绝缘行为的相互作用。拟议的工作将在韦尔斯利学院进行，这是一个非博士学位-授予女子学院。该项目将在整个期间让本科生参与独立的研究项目，包括高级论文和暑期研究。拟议的本科项目包括分析和数值工作的超流区域与时变磁场的相互作用，超流区域的流体动力学模式，以及超流系统从陷阱释放后的膨胀。该项目的本科生研究部分将为一所小型文科学院中代表性不足的物理学学生（所有女性）提供机会，以获得理论建模技能和稀释气体中玻色-爱因斯坦凝聚这一新兴领域的工作知识。

This award will support theoretical research on the properties of atoms cooled to ultralow temperatures. The research will be done in an undergraduate environment at Wellesley College. The research topic is one of great current excitement and is highly interdisciplinary, residing at the interface between condensed matter physics and atomic physics. There will be opportunities for undergraduate students to participate.The proposed work explores novel properties of ultracold bosonic atoms in a periodic optical lattice potential, an ideal system for the study of superfluid and Mott-insulating phases of bosons. Using a combination of analytical and numerical techniques, salient features of systems where superfluid and Mott-insulating regions coexist side by side will be deduced. Investigations include (1) the spectroscopic signal from the superfluid regions of a coexisting system, (2) the collective modes of a three dimensional shell of superfluid, (3) the evolution of the system after its release from the trap, (4) the Josephson physics of concentric superfluid shells with an intervening Mott-insulating layer, and (5) critical properties of the quantum phase transition between superfluid and Mott insulator probed by new geometries of confinement. The proposed work exploits the unprecedented laboratory control over the strength of the interatomic interactions, strength of the optical lattice potential, and shape of the confining trap unique to the ultracold atomic system. Because of this reliance, close collaboration with an experimental group actively developing new probes of this system is an integral element of the research. The proposed work features involvement of undergraduates at Wellesley College in independent research on these topics throughout the project.Intellectual Merit: The control over microscopic parameters as well as macroscopic geometry present in trapped dilute gases allows the creation of nearly perfect superfluid and Mott-insulating systems, thereby improving our fundamental understanding of quantum behavior. The proposed work on superfluid shells will yield qualitative understanding of the expected behavior of superfluids in new geometries and quantitative predictions relevant to experiments on inhomogeneous systems.The possibility of using atomic systems to probe models of many-body condensed matter shows great promise and is a very active area of research. The extent to which the quantum phase transitions present in such models (e.g. the Bose-Hubbard model) can be realized in atomic systems is an open and important question. The proposed research will develop and model promising directions for future experiments in this area.Broader Impact: Theories of superfluid and Mott-insulating phases of bosons, as well as the quantum phase transition between them, have direct bearing on superconducting systems. Increased understanding of the Bose-Hubbard model can lead to insights into strongly-interacting superconducting systems and may consequently aid the development of new electronic devices. Further progress of quantum computing schemes based on ultracold bosons in optical lattices depends on a better understanding of the interplay of superfluid and Mott-insulating behavior in finite, trapped systems. The proposed work will be carried out at Wellesley College, a non-Ph.D.-granting women's college. The project will engage undergraduates in independent research projects, including senior theses and summer research, throughout its duration. The proposed undergraduate projects include analytical and numerical work on the interaction of a superfluid region with a time-varying magnetic field, hydrodynamic modes of the superfluid regions, and the expansion of superfluid systems after release from their traps. The undergraduate research component of the project will give underrepresented physics students (all women) at a small liberal arts college the opportunity to gain theoretical modeling skills and working knowledge of the emerging field of Bose-Einstein condensation in dilute gases.