Self-accelerating Airy matter waves offer a clean setting to access the intrinsic cubic-in-time phase. Here we reconstruct the relative phase of simulated Airy-shaped Bose-Einstein condensates from interference fringes in free space, a regime approached in microgravity. The cubic phase dynamics are quantified via approximately debiased, windowed polynomial fits with systematics-aware uncertainty estimates that account for window-induced correlations. We compare two physically feasible phase-extraction methods, heterodyne-based and density-based, and show that an Airy-Gaussian geometry yields substantially improved robustness to fit-window selection relative to an Airy-Airy collision. In the weakly interacting regime, the extracted cubic coefficient responds linearly to leading order to the effective interaction strength, its shift from the noninteracting value providing a calibrated probe of weak mean-field nonlinearities in self-accelerating condensates.
Self-accelerating Airy matter waves offer a clean setting to access the intrinsic cubic-in-time phase. Here we reconstruct the relative phase of simulated Airy-shaped Bose-Einstein condensates from interference fringes in free space, a regime approached in microgravity. The cubic phase dynamics are quantified via approximately debiased, windowed polynomial fits with systematics-aware uncertainty estimates that account for window-induced correlations. We compare two physically feasible phase-extraction methods, heterodyne-based and density-based, and show that an Airy-Gaussian geometry yields substantially improved robustness to fit-window selection relative to an Airy-Airy collision. In the weakly interacting regime, the extracted cubic coefficient responds linearly to leading order to the effective interaction strength, its shift from the noninteracting value providing a calibrated probe of weak mean-field nonlinearities in self-accelerating condensates.
We predict that classes of coherent matter waves can self-accelerate without the presence of an external potential. Such Bose-Einstein condensates can follow arbitrary power-law trajectories and can also take the form of diffraction-free Airy waves. We also show that suitably engineered radially symmetric matter waves can abruptly autofocus in space and time. We suggest different schemes for the preparation of the condensate using laser beams to imprint an amplitude or a phase pattern onto the matter wave. Direct and Fourier space generation of such waves is discussed using continuous and binary masks as well as magnetic mirrors and lenses. We study the effect of interactions and find that independently of the type and strength of the nonlinearity, the dynamics are associated with the generation of accelerating matter waves. In the case of strong attractive interactions, the acceleration is increased while the radiation reorganizes itself in the form of soliton(s).
Self-accelerating waves in conservative systems, which usually feature slowly decaying tails, such as Airy waves, have drawn great interest in studies of quantum and classical wave dynamics. They typically appear in linear media, while nonlinearities tend to deform and eventually destroy them. We demonstrate, by means of analytical and numerical methods, the existence of robust one- and two-dimensional (1D and 2D) self-accelerating tailless solitons and solitary vortices in a model of two-component Bose-Einstein condensates, dressed by a microwave (MW) field, whose magnetic component mediates long-range interaction between the matter-wave constituents, with the feedback of the matter waves on the MW field taken into account. In particular, self-accelerating 2D solitons may move along a curved trajectory in the coordinate plane. The system may also include the spin-orbit coupling between the components, leading to similar results for the self-acceleration. The effect persists if the contact cubic nonlinearity is included. A similar mechanism may generate 1D and 2D self-accelerating solitons in optical media with thermal nonlinearity.
A quantum wave packet evolving in a linear potential, i.e. a constant force such as gravity, accumulates a cubic-in-time phase. This cubic phase is universal across Schrödinger-type platforms, and the Airy functions, as the eigenstates of the linear potential, provide its natural realization. Because the classical action is quadratic in the force, the cubic-in- time phase comprises exactly three contributions – intrinsic, force-induced, and a cross term – of which the force-induced component alone is shape-independent, while the Airy eigenstate renders the remaining, shape-dependent terms in clean, non-dispersing form. An eigenstate-based non-dimensionalization fixes the eigenforce, the intrinsic force behind the packet’s acceleration even without an applied force, as a natural parameter. As a function of this eigenforce and the applied force, the cubic coefficient takes an analytically closed, physically interpretable form that factors along two zero lines, the static Airy eigenstate and a non-trivial zero where the phase cancels while the packet keeps accelerating. This exposes the eigenforce as an effective antagonist to the applied force not only in the caustic’s self-acceleration but here also within the phase, yet it leaves the centroid untouched, in accordance with Ehrenfest’s theorem. Being spatially uniform within each packet, the phase escapes direct measurement and becomes accessible only as the relative phase between two colliding packets, each subject to its own linear potential. The resulting general relative cubic coefficient, symmetry-forbidden for identical packets and activated by the preparation asymmetry, is hence a designable signal. Extracted by heterodyne demodulation from the simulated interference of two Airy packets, its central value matches the theoretical prediction to sub-percent accuracy, within the fit uncertainty. Spanning ultracold-atom condensates, paraxial optics, and surface-gravity water waves, this framework provides a platform-independent probe of the cubic phase and, through its force dependence, of the constant force itself.
A quantum wave packet in a linear potential, i.e. a constant force such as gravity, accumulates a cubic-in-time phase, universal across Schrödinger-type platforms. The natural formulation of the cubic phase dynamics follows from their canonical realization, the Airy eigenstates. The eigenforce, the potential gradient for which the Airy profile is stationary and hence the intrinsic force behind its known self-acceleration absent any applied force, derives from the eigenvalue problem and characterizes the state uniquely up to a rigid translation. Alongside the applied force, it underlies the analytically closed form of these dynamics, comprising three known contributions, intrinsic, force-induced, and a cross term. The force-induced one alone is shape-independent, whereas the Airy eigenstate renders the other two non-dispersing. The cubic coefficient factorizes into two Newtonian force balances, vanishing at the stationary eigenstate and at a non-trivial zero where the phase cancels while the packet keeps accelerating. This exposes the eigenforce as an effective antagonist to the applied force, not only in the caustic's self-acceleration but here also within the phase, while leaving the centroid untouched by Ehrenfest's theorem. Spatially uniform within each packet, it escapes direct measurement, accessible only as the relative phase of two colliding packets, each in its own potential. The relative cubic coefficient is symmetry-forbidden for identical packets and activated by preparation asymmetry. Simulated interference of two truncated Airy packets demonstrates the extraction. Spanning ultracold atoms, paraxial optics, and surface-gravity water waves, it provides a platform-independent probe of the cubic phase and, through its force dependence, of the constant force itself.
Interference upon free expansion gives access to the relative phase between two interfering matter waves. Such measurements can be used to reconstruct the spatially-resolved relative phase, which is a key observable in many quantum simulations of quantum field theory and non-equilibrium experiments. However, in 1D systems, longitudinal dynamics is typically ignored in the analysis of experimental data. In our work, we give a detailed account of various effects and corrections that occur in finite temperatures due to longitudinal expansion. We provide an analytical formula showing a correction to the readout of the relative phase due to longitudinal expansion and mixing with the common phase. Furthermore, we numerically assess the error propagation to the estimation of the gases’ physical quantities such as correlation functions and temperature. We also incorporate systematic errors arising from experimental imaging devices. Our work characterizes the reliability and robustness of interferometric measurements, directing us to the improvement of existing phase extraction methods necessary to observe new physical phenomena in cold-atomic quantum simulators.