Bright matter-wave solitons: formation, dynamics and quantum reflection

从落在池塘中的鹅卵石向外传播的涟漪是我们熟悉的景象。更仔细的观察发现，每个涟漪或波在传播时都会扩散，这样做会降低高度或幅度，直到到达池塘边缘时几乎消失。然而，值得注意的是，存在一种不会扩散或扩散的波，因此它可以在不改变幅度的情况下传播很远的距离。这种波被称为孤波，1834年在苏格兰的一条运河上首次被观察到是由狭窄的船只产生的船头波。今天，孤子出现在许多不同的物理系统中，从等离子体中的波到非线性介质中的光脉冲传输。后一个例子现在在长距离光纤通信系统中得到了重要的应用。所有这些例子的共同之处是存在一个控制系统中波传播的非线性波动方程。现在，碱性原子的稀薄气体通常用激光冷却到绝对零度的百万分之一以内，允许它们被限制在由于外加磁场与每个原子的微小磁矩相互作用而形成的陷阱中。通过蒸发进一步冷却导致了一种被称为玻色-爱因斯坦凝聚的新物质状态的产生，在这种凝聚中，粒子的量子力学性质决定了它们的经典行为。这个系统的状态也受一个非线性波动方程的支配，其中的非线性是由原子与原子的相互作用引起的。此外，如果系统中的原子相互作用是吸引的，那么凝聚体可以形成一个明亮的物质波孤子；一个原子的脉冲或波包，就像运河上的弓波一样，在传播时不会扩散。这项提议的目的是研究这种孤子在Rb-85原子凝聚体中的形成和动力学。Rb-85原子之间的碰撞表现出一种散射共振，即所谓的Feshbach共振，它允许精确控制原子相互作用，这对于系统地研究孤子形成是必不可少的。此外，光学偶极陷阱的使用允许实时修改限制势，并使得能够操纵孤子的位置和速度来进行精确的碰撞研究。正如孤子在日常生活中的应用一样，明亮物质波孤子的产生为原子干涉测量和原子光学提供了潜在的未来应用。这项提议将评估使用物质波孤子来研究原子与固体表面之间相互作用的可行性，作为构建可调谐物质波表面探测器的长期研究目标的一部分。吸引原子-表面相互作用是量子电动力学中的一个基本问题，有着悠久而重要的理论历史。然而，直到最近，这种相互作用才得到实验测量。最近，可以操纵超冷原子的高度控制导致了几种新的实验方法来探索这种相互作用。与测量原子-表面相互作用密切相关的是量子反射现象，即由于粒子的波动性质，粒子从势能反射而不达到经典的转折点。这一提议旨在演示孤子在固体表面的量子反射，作为测量原子-表面相互作用的第一步。局域孤子的使用，加上对其速度的精确控制，有可能将原子-表面相互作用的研究带到一个新的水平。这类研究的动机是这样一种可能性，即对原子-表面相互作用的精确测量在未来可能会对重力的短期修正设定新的限制，这是由于超出标准模型的异常力。

The ripples that travel outwards from a pebble dropped in a pond are a familiar sight. Closer inspection reveals that each ripple or wave spreads out as it travels and in so doing decreases in height or amplitude until it has all but vanished by the time it reaches the edge of the pond. Remarkably, however, there exists a form of wave that does not spread out or disperse and which can therefore travel great distances without any change in amplitude. Such waves are known as solitons and were first observed as bow-waves produced by narrow boats on a canal in Scotland in 1834. Today solitons are seen in many different physical systems ranging from waves in plasmas to optical pulse propagation in nonlinear media. The latter example now finds important applications in long distance optical fibre communication systems. Common to all these examples is the existence of a nonlinear wave equation governing wave propagation in the system.Dilute gases of alkali atoms are now routinely cooled to within a millionth of a degree of absolute zero using laser light, permitting them to be confined in traps formed due to the interaction of an applied magnetic field with the minute magnetic moment of each atom. Further cooling by evaporation leads to the creation of a new state of matter, known as a Bose-Einstein condensate, in which the quantum mechanical nature of the particles dominates over their classical behaviour. The state of this system is also governed by a nonlinear wave equation in which the nonlinearity results from the atom-atom interactions. Moreover, if the atomic interactions in the system are attractive then the condensate can form a bright matter-wave soliton; a pulse or wave-packet of atoms which, just as for the bow-wave on the canal, does not spread out as it propagates. The objective of this proposal is to investigate the formation and dynamics of such solitons in condensates of rubidium-85 atoms. Collisions between rubidium-85 atoms exhibit a scattering resonance, known as a Feshbach resonance, which permits the precise control of the atomic interactions essential for a systematic investigation of soliton formation. Moreover, the use of optical dipole traps permits the real-time modification of the confinement potential and enables the manipulation of the position and velocity of the solitons for precise collision studies.Just as solitons have found applications in everyday life, the creation of bright matter-wave solitons offers potential future applications in atom interferometry and atom optics. This proposal will assess the feasibility of using matter-wave solitons to investigate the interaction between an atom and a solid surface, as part of the longer-term research goal to construct a tunable matter-wave surface probe . The attractive atom-surface interaction is a fundamental problem in QED and has a long and important theoretical history. It is only relatively recently, however, that this interaction has been measured experimentally. More recently, the high degree of control with which ultracold atoms can be manipulated has lead to several new experimental approaches to probe this interaction. Intimately connected to the measurement of atom-surface interactions is the phenomenon of quantum reflection, whereby a particle is reflected from a potential without reaching a classical turning point as a result of the wave nature of the particle. This proposal aims to demonstrate the quantum reflection of solitons from a solid surface, as a first step towards measuring the atom-surface interaction. The use of well-localized solitons, coupled to the precise control of their velocity, has the potential to take the study of atom-surface interactions to a new level. Such studies are motivated by the possibility that precision measurements of atom-surface interactions may, in the future, set new limits on short range corrections to gravity due to exotic forces beyond the Standard model.