Pumps are transport mechanisms in which direct currents result from a cyclic evolution of the potential^1,2. As Thouless showed, the pumping process can have topological origins, when considering the motion of quantum particles in spatially and temporally periodic potentials³. However, the periodic evolution that drives these pumps has always been assumed to be imparted from outside, as has been the case in the experimental systems studied so far^{4,5,6,7,8,9,10,11,12}. Here we report on an emergent mechanism for pumping in a quantum gas coupled to an optical resonator, where we observe a particle current without applying a periodic drive. The pumping potential experienced by the atoms is formed by the self-consistent cavity field interfering with the static laser field driving the atoms. Owing to dissipation, the cavity field evolves between its two quadratures¹³, each corresponding to a different centrosymmetric crystal configuration¹⁴. This self-oscillation results in a time-periodic potential analogous to that describing the transport of electrons in topological tight-binding models, such as the paradigmatic Rice–Mele pump¹⁵. In the experiment, we directly follow the evolution by measuring the phase winding of the cavity field with respect to the driving field and observing the atomic motion in situ. The observed mechanism combines the dynamics of topological and open systems, and features characteristics of continuous dissipative time crystals.

泵是一种传输机制，其中直流电是由电位^1,2的循环演化产生的。正如 Thouless 所展示的，当考虑量子粒子在空间和时间周期势³中的运动时，泵浦过程可能具有拓扑起源。然而，驱动这些泵的周期性演化一直被认为是从外部传授的，就像迄今为止研究的实验系统中的情况一样^{4,5,6,7,8,9,10,11,12}. 在这里，我们报告了一种用于泵送耦合到光学谐振器的量子气体的紧急机制，在该机制中，我们在不应用周期性驱动的情况下观察粒子电流。原子所经历的泵浦势是由自洽的腔场干扰驱动原子的静态激光场形成的。由于耗散，腔场在其两个正交¹³之间演变，每个正交对应于不同的中心对称晶体配置¹⁴。这种自激振荡导致时间周期电位，类似于在拓扑紧束缚模型中描述电子传输的时间周期电位，例如典型的 Rice-Mele 泵¹⁵. 在实验中，我们通过测量腔场相对于驱动场的相位绕组并在原位观察原子运动来直接跟踪演变。观察到的机制结合了拓扑和开放系统的动力学，并具有连续耗散时间晶体的特征。