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。 这是一个前沿的研究方向，因为量子系统进入平衡或“热化”的方式仍然是一个谜。 对于孤立的经典系统，这幅图更为清晰。 例如，在经典动力学中，如果一个相互作用的粒子系统探索了所有可能的构型，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，未来的动力学可以预测。 然而，有趣的是，如果可积性的条件被弱打破，仍然有稳定动力学可以预测的情况。 这是著名的Kolmogorov-Arnold-Moser（KAM）定理的结果，该定理表明小扰动不足以使系统混沌。 这种效应在很大程度上是我们太阳系轨道稳定性的原因。 由于量子物理学也描述动力学，因此很自然地会问是否存在量子系统的KAM定理的类似物。 这个项目将探索这个问题，首先使用一维陷阱中的超冷原子气体创建一个量子可积系统。 系统行为的改变将通过调整原子之间的磁性长程相互作用来引起。 动量反冲后气体热化所需的时间将提供系统中可积性崩溃的度量。 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。 参与该项目的学生还将受益于研究培训，为他们在高科技行业或学术生涯中的工作做好准备。为了实现这些目标，该团队将把最具磁性的元素镝（Dy）原子限制在二维光学晶格中。 到第一横向运动激发态的能隙将大于气体温度和化学势，确保每个雪茄形管中的气体处于准1D状态。 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，使我们能够控制可积性破坏微扰强度。 布拉格衍射脉冲会将气体一分为二。 由于弱的纵向谐波约束，这些气体部分将每10 ms碰撞一次。 这个量子牛顿摇篮实验的偶极版本将使这个团队能够探索量子领域中经典KAM场景的类似物。 此外，自旋-轨道耦合（先前由这个小组用Dy证明）将被引入，试图在费米子Dy的一维气体中诱导接近Feshbach共振的p波超流性。 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移动的方向时产生的新型超流体。 这很重要，因为像这样的奇异超流体支持可能对量子信息处理有用的不寻常的激发。

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.