We investigate the spin-interaction energy spectrum of spin turbulence in a driven spinor Bose-Einstein condensate. Continuous spin driving of a spin-1 condensate produces a nonequilibrium steady state with spatially fluctuating magnetization. We observe a power-law scaling consistent with the
−7/3 exponent predicted for spin-wave turbulence, which persists across our full range of drive strengths despite substantial changes in the spectral anisotropy. After switching off the drive, we track the free-decay evolution and find evidence consistent with a direct cascade of spin-interaction energy toward higher wavenumbers. These results establish an energy-spectral hallmark of spin turbulence and enable quantitative studies of cascade dynamics in spinor superfluids.
The persistent flow of superfluids is essential for understanding the fundamental characteristics of superfluidity and shows promise for applications in high-precision metrology and atomtronics. We proposed a protocol for generating persistent flows with significant winding numbers by employing a geometric quench and leveraging two-dimensional (2D) quantum turbulence. By subjecting the trap potential to sudden geometric quenches to drive the system far from equilibrium, we can reveal intriguing nonequilibrium phenomena. Our study demonstrates that transitioning from a single ring-shaped configuration to a double concentric ring-shaped configuration through a geometric quench does not induce a persistent current in Bose−Einstein condensates (BECs). The energy transfer from small to large length scales during the 2D turbulent cascade of vortices can generate persistent flow with a small winding number in toroidal BECs. Nonetheless, the interplay of geometric quench and turbulent cascade can lead to circulation flows that exhibit high stability, uniformity, and are devoid of topological excitations. We showcase the intricate nature of turbulence in our investigation, which is influenced by factors like boundaries and spatial dimensionality. This advancement holds promise for innovative atomtronic designs and provides insights into quantum tunneling and interacting quantum systems under extreme non-equilibrium conditions.
Identified as a unique regime of fluid flow some 500 years ago, turbulence has fascinated and confounded for centuries. Indeed, a fundamental understanding of the turbulence phenomenon remains one of the most important unsolved problems in classical physics. Interestingly, superfluid atomic Bose-Einstein condensates (BECs) can also be agitated into highly excited states of chaotic vortex motion, suggestive of turbulence. However, in contrast to classical fluids, the vortices in these quantum systems exhibit topological stability, the restriction of quantized circulation, and a well defined length scale characterized by the so-called healing length of the superfluid. Such simplifying aspects motivate the study of turbulence in these systems, which may shed new light on the longstanding classical problem. \n\nWhilst a considerable number of studies have been conducted on turbulence in three-dimensional BEC systems, and such studies have uncovered similarities between the classical and quantum counterparts, including the presence of the Kolmogorov
k−5/3 law in the kinetic energy spectrum and the associated direct energy cascade, comparatively few studies have been conducted on two-dimensional quantum turbulence. An important question for such systems is whether the inverse energy cascade, a defining feature of classical two-dimensional turbulent fluid flows, may occur in these systems. In addition to a Kolmogorov kinetic energy spectrum, this process is signified by the clustering of same-circulation vortices, which results in the emergence of macroscopic vortex structures from the turbulent flow. \n\nAlthough intermittent few-vortex clustering has been observed in the break-down of superfluid flow around an obstacle, current attempts to observe a sustained inverse cascade have been unsuccessful, largely due to complications which arise due to the compressibility of the dilute Bose gas - a feature not considered in the classical theory.\n\nWe present a study of two-dimensional quantum turbulence in atomic BECs within the framework of damped Gross-Pitaevskii theory. With the motivation of determining the existence of the inverse cascade phenomenon in such systems, we focusing on experimentally realistic forcing procedures, and study the details of kinetic energy spectra, the statistics of vortex clustering, and the transport of kinetic energy through scale space in the resulting turbulent flows.\nWe investigate a range of vortex injection regimes produced through the circular stirring of a harmonically confined system with a repulsive Gaussian obstacle potential, identifying distinct regimes of turbulence. In the incompressible regime relevant to the inverse cascade, we identify numerous problems with the system and forcing procedure. Motivated by these findings, we investigate turbulence in a minimal model of the spindown of a toroidal persistent current. In this system, we identify a regime of forcing and damping in which the inverse cascade is corroborated by three independent measures: I) merging of vortex clusters; II) a Kolmogorov scaling in the incompressible kinetic energy spectrum; and III) Spectral condensation, associated with the emergence of large scale rotating structures from the turbulent flow. We provide clear evidence that the inverse cascade phenomenon, previously observed in a range of classical fluid systems, can also occur in quantum turbulence.