One-Dimensional Gases of Dysprosium

这个项目将研究量子力学和热力学之间的界面。这是一个尖端的研究方向，因为量子系统如何达到平衡，或“热化”，仍然是一个谜。对于孤立的经典系统来说，情况更加清晰。例如，在经典动力学中，如果一个相互作用的粒子系统探索所有可能的构型，那么它就可以热化。这样的系统也被称为“混沌”和缺乏“可积性”，这意味着粒子轨迹不能用一系列积分来预测。对于可积系统，未来的动力学是可以预测的。然而，有趣的是，如果可积条件被弱打破，仍然存在可以预测稳定动力学的场景。这是著名的Kolmogorov-Arnold-Moser(KAM)定理的结果，该定理表明微小的扰动不足以使系统变得混乱。这一效应在很大程度上是我们太阳系轨道稳定性的原因。既然量子物理学也描述动力学，人们自然会问，量子系统的Kam定理是否有类似的东西。这个项目将通过首先创建一个量子可积系统来探索这个问题，该系统使用限制在一维陷阱中的超冷原子气体。然后，通过调整原子之间的磁性远程相互作用，将导致系统行为的变化。动量冲击后气体热化所需的时间将提供系统中可积性崩溃的量度。这项工作将对量子信息处理以及其他依赖量子动力学可预测性的技术产生影响。从事这一项目的学生还将受益于为在高科技行业或学术生涯中的工作做准备的研究培训。为了实现这些目标，该团队将在二维光学晶格中限制最具磁性的镝(Dy)原子。到第一个横向运动激发态的能隙将大于气体温度和化学势，从而确保每个雪茄管中的气体处于准一维区域。对于足够大的散射长度，气体将近似实现可积Lieb-Liniger模型的Tonks-Girardeau极限。磁场将设置偶极子相对于管轴的角度。磁偶极-偶极相互作用的大小可以通过这个角度来调节，从而允许我们控制可积性破缺微扰强度。布拉格衍射脉冲会将气体一分为二。由于弱的纵向简谐约束，气体的这些部分每隔10毫秒就会发生碰撞。这个偶极版本的量子牛顿摇篮实验将允许这个团队探索量子领域中经典KAM场景的类似情况。此外，在费米子Dy的一维气体的Feshbach共振附近，将引入自旋-轨道耦合(这个小组以前用Dy演示过)来尝试诱导p波超流。通过这种方式，一维原子系统将被用来探索当原子的自旋取决于原子的移动方向时出现的新型超流体。这一点很重要，因为像这样的奇异超流体支持不寻常的激发，这可能对量子信息处理有用。

This project will study the interface between quantum mechanics and thermodynamics. This is a cutting edge research direction because the way quantum systems come into equilibrium, or "thermalize", remains a mystery. The picture is clearer for isolated classical systems. For example, in classical dynamics if a system of interacting particles explores all possible configurations, then it can thermalize. Such a system is also said to be "chaotic" and to lack "integrability", which means the particle trajectories cannot be predicted with a sequence of integrals. For integrable systems, future dynamics can be predicted. Interestingly, however, if the conditions for integrability are weakly broken, there are still scenarios for which stable dynamics can be predicted. This is a consequence of the celebrated Kolmogorov-Arnold-Moser (KAM) theorem, which shows that small perturbations are insufficient to render the system chaotic. This effect is largely responsible for the orbital stability for our own solar system. Since quantum physics describes dynamics too, it is natural to ask if there is an analogue to the KAM theorem for quantum systems. This project will explore this question by first creating a quantum integrable system using a gas of ultracold atoms confined in one-dimensional traps. Changes to the system's behavior will then be caused by adjusting magnetic long-range interactions between the atoms. The time it takes for the gas to thermalize after a momentum kick will provide a measure of the breakdown of integrability in the system. This work will have an impact on quantum information processing, and other technologies that rely on the predictability of quantum dynamics. Students working on this project will also benefit from research training that will prepare them for jobs in high tech industry or academic careers.To achieve these goals, this team will confine atoms of dysprosium (Dy), the most magnetic element, in two-dimensional optical lattices. The energy gap to the first transverse motional excited state will be larger than the gas temperature and chemical potential, ensuring that the gas in each cigar-shaped tube is in the quasi-1D regime. For large-enough scattering lengths, the gas will approximately realize the Tonks-Girardeau limit of the integrable Lieb-Liniger model. A magnetic field will set the angle of the dipoles with respect to the tube axis. The magnitude of the magnetic dipole-dipole interaction can be tuned by this angle, allowing us to control the integrability-breaking perturbation strength. A Bragg diffraction pulse will split the gas in two. These parts of the gas will collide every 10 ms due to weak longitudinal harmonic confinement. This dipolar version of the quantum Newton's cradle experiment will allow this team to explore analogs of the classical KAM scenario in the quantum realm. Moreover, spin-orbit coupling (previously demonstrated by this group with Dy) will be introduced in attempts to induce p-wave superfluidity near Feshbach resonances in one-dimensional gases of fermionic Dy. In this way, one-dimensional atomic systems will be used to explore novel types of superfluids that arise when the spin of the atom depends on the direction the atom is moving. This is important because exotic superfluids such as these support unusual excitations that may be useful for quantum information processing.