Isolated quantum many-body systems with integrable dynamics generically do not thermalize when taken far from equilibrium. As one perturbs such systems away from the integrable point, thermalization sets in, but the nature of the crossover from integrable to thermalizing behavior is an unresolved and actively discussed question. We explore this question by studying the dynamics of the momentum distribution function in a dipolar quantum Newton's cradle consisting of highly magnetic dysprosium atoms. This is accomplished by creating the first one-dimensional Bose gas with strong magnetic dipole-dipole interactions. These interactions provide tunability of both the strength of the integrability-breaking perturbation and the nature of the near-integrable dynamics. We provide the first experimental evidence that thermalization close to a strongly interacting integrable point occurs in two steps: prethermalization followed by near-exponential thermalization. Exact numerical calculations on a two-rung lattice model yield a similar two-timescale process, suggesting that this is generic in strongly interacting near-integrable models. Moreover, the measured thermalization rate is consistent with a parameter-free theoretical estimate, based on identifying the types of collisions that dominate thermalization. By providing tunability between regimes of integrable and nonintegrable dynamics, our work sheds light on the mechanisms by which isolated quantum many-body systems thermalize and on the temporal structure of the onset of thermalization.

We demonstrate the tuning of the magnetic dipole-dipole interaction (DDI) within a dysprosium Bose-Einstein condensate by rapidly rotating the orientation of the atomic dipoles. The tunability of the dipolar mean-field energy manifests as a modified gas aspect ratio after time-of-flight expansion. We demonstrate that both the magnitude and the sign of the DDI can be tuned using this technique. In particular, we show that a magic rotation angle exists at which the mean-field DDI can be eliminated, and at this angle, we observe that the expansion dynamics of the condensate is close to that predicted for a nondipolar gas. The ability to tune the strength of the DDI opens new avenues toward the creation of exotic soliton and vortex states as well as unusual quantum lattice phases and Weyl superfluids.

Volume imaging based on a fast focus-tunable lens (FTL) allows three-dimensional (3D) observation within milliseconds by extending the depth-of-field (DOF) with sub-micrometer transverse resolution on optical sectioning microscopes. However, the previously published DOF extensions were neither axially uniform nor fit with theoretical prediction. In this work, complete theoretical treatments of focus extension with confocal and various multiphoton microscopes are established to correctly explain the previous results. Moreover, by correctly placing the FTL and properly adjusting incident beam diameter, a uniform DOF is achieved in which the actual extension nicely agrees with the theory. Our work not only provides a theoretical platform for volumetric imaging with FTL but also demonstrates the optimized imaging condition.

One-dimensional ultracold bosonic gases with contact interactions are described by the integrable Lieb-Liniger model. In the case of 1D dysprosium gases, two open questions are whether its strong dipole-dipole interactions produce measurable effects in equilibrium and whether a description based on the Lieb-Liniger model is still applicable. In this work, we measure the rapidity and momentum distributions of low-temperature equilibrium states of highly magnetic 1D dysprosium Bose gases. We tune the strength of the dipolar interactions by changing the magnetic field orientation and compare the measurements to the Lieb-Liniger model predictions obtained using the thermodynamic Bethe ansatz (for rapidity) and path-integral quantum Monte Carlo (for momentum). The theory quantitatively describes the experiments most closely in the Tonks-Girardeau limit. The agreement worsens at intermediate interactions, but theory nevertheless tracks the overall experimental trends. Our results show that the dipolar interactions have a significant effect, which weakens as one approaches the Tonks-Girardeau limit, and suggest that the Lieb-Liniger model is a good starting point for describing near-ground-state dipolar 1D gases.

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