AI 中文总结
研究线性势中量子波包三次方相位动力学，基于本征态无量纲化确定本征力，得出三次方系数解析形式，通过两碰撞波包干涉外差解调提取相对三次方系数，其值与预测高精度相符，分析涵盖多领域。
AI 中文摘要
线性势中的量子波包，即在如重力等恒力作用下，会积累一个与时间三次方相关的相位，该相位在薛定谔型平台中具有普遍性且可由艾里本征态自然实现。经典作用在力上是二次方的，此相位恰好包含三个贡献：固有、力致和交叉项贡献。力致贡献与形状无关，而艾里本征态使形状相关贡献无弥散。基于本征态的无量纲化确定了本征力，它是在无外力时波包加速的固有力。三次方系数作为两种力的函数，具有解析封闭且物理可解释的形式，沿两条零线分解。通过两个碰撞波包的模拟干涉外差解调提取的一般相对三次方系数，其中心值在拟合不确定度内与预测符合到亚百分比精度。分析涵盖超冷原子凝聚体、傍轴光学和表面重力水波。
英文摘要
A quantum wave packet in a linear potential, i.e., under a constant force such as gravity, accumulates a cubic-in-time phase that is universal across Schrodinger-type platforms and naturally realized by Airy eigenstates. Because the classical action is quadratic in the force, this phase comprises exactly three contributions: intrinsic, force-induced, and a cross term. The force-induced contribution alone is shape-independent, whereas the Airy eigenstate renders the shape-dependent contributions non-dispersing. An eigenstate-based nondimensionalization identifies the eigenforce, namely the intrinsic force underlying the packet's acceleration in the absence of an applied force, as a natural parameter. As a function of both forces, the cubic coefficient takes an analytically closed and physically interpretable form that factors along two zero lines: the static Airy eigenstate and a nontrivial zero at which the phase cancels without stationarity. This exposes the eigenforce as an effective antagonist to the applied force, not only in the caustic's self-acceleration but also within the phase, while leaving the centroid unaffected in accordance with Ehrenfest's theorem. Spatially uniform within each packet, the phase cannot be measured directly and is accessible only through the relative phase of two colliding packets, each evolving in its own potential. The general relative cubic coefficient, forbidden by symmetry for identical packets and activated by preparation asymmetry, therefore provides a designable signal. Extracted through heterodyne demodulation of the simulated interference between two Airy packets, its central value agrees with the prediction to sub-percent accuracy within the fitting uncertainty. The analysis spans ultracold-atom condensates, paraxial optics, and surface-gravity water waves.
Comments9 pages, 4 figures
