We study ultra-cold bosons out of equilibrium in a one-dimensional (1D) setting and probe the breaking of integrability and the resulting relaxation at the onset of the crossover from one to three dimensions. In a quantum Newton's cradle type experiment, we excite the atoms to oscillate and collide in an array of 1D tubes and observe the evolution for up to 4.8 seconds (400 oscillations) with minimal heating and loss. By investigating the dynamics of the longitudinal momentum distribution function and the transverse excitation, we observe and quantify a two-stage relaxation process. In the initial stage single-body dephasing reduces the 1D densities, thus rapidly drives the 1D gas out of the quantum degenerate regime. The momentum distribution function asymptotically approaches the distribution of quasimomenta (rapidities), which are conserved in an integrable system. In the subsequent long time evolution, the 1D gas slowly relaxes towards thermal equilibrium through the collisions with transversely excited atoms. Moreover, we tune the dynamics in the dimensional crossover by initializing the evolution with different imprinted longitudinal momenta (energies). The dynamical evolution towards the relaxed state is quantitatively described by a semiclassical molecular dynamics simulation.

中文翻译：

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一维玻色子的弛豫和维数交叉的开始

我们研究了一维（1D）环境中超冷玻色子的失衡现象，并探讨了从一维到三维交叉时可积性的破坏以及由此引起的弛豫。在量子牛顿的摇篮式实验中，我们激发原子在一系列一维管中振荡和碰撞，并观察到演化时间长达4.8秒（400次振荡），而发热和损失最小。通过研究纵向动量分布函数和横向激励的动力学，我们观察和量化了两个阶段的松弛过程。在初始阶段，单相移相会降低1D密度，从而将1D气体迅速驱离量子简并状态。动量分布函数渐近地接近准动量（快速度）的分布，在一个可积系统中是保守的。在随后的长时间演化中，一维气体通过与横向激发原子的碰撞而缓慢地向热平衡松弛。此外，我们通过用不同的压印纵向动量（能量）来初始化演化，从而调整尺寸交叉中的动力学。通过半经典分子动力学模拟定量描述了向松弛态的动力学演化。