Turbulence in quantum fluids has, surprisingly, a lot in common with its classical counterpart. Recently, cold atomic gases has emerged as a well controlled experimental platform to study turbulent dynamics. In this work, we introduce a novel system to study quantum turbulence in optics, with the major advantage of having access to a wide range of characterization tools available for light fields. In particular we report the temporal dynamics of density and phase and we show the emergence of isotropy in momentum space and the presence of different scaling laws in the incompressible kinetic energy spectrum. The microscopic origin of the algebraic exponents in the energy spectrum is discussed by studying the internal structure of quantized vortices within the healing length and their clustering at larger length scales. These results are obtained using two counter-streaming fluids of light, which allows for a precise preparation of the initial state and the in-situ measurement of the compressible and incompressible fluid velocity.
Turbulence in quantum fluids has, surprisingly, a lot in common with its classical counterpart. Recently, cold atomic gases has emerged as a well controlled experimental platform to study turbulent dynamics. In this work, we introduce a novel system to study quantum turbulence in optics, with the major advantage of having access to a wide range of characterization tools available for light fields. In particular we report the temporal dynamics of density and phase and we show the emergence of isotropy in momentum space and the presence of different scaling laws in the incompressible kinetic energy spectrum. The microscopic origin of the algebraic exponents in the energy spectrum is discussed by studying the internal structure of quantized vortices within the healing length and their clustering at larger length scales. These results are obtained using two counter-streaming fluids of light, which allows for a precise preparation of the initial state and the in-situ measurement of the compressible and incompressible fluid velocity.
Turbulence in quantum fluids has, surprisingly, a lot in common with its classical counterpart. Recently, cold atomic gases has emerged as a well-controlled experimental platform to study turbulent dynamics. In this work, we introduce a system to study quantum turbulence in optics, with the major advantage of having access to a wide range of characterization tools available for light fields. In particular, we report the temporal dynamics of density and phase and we show the emergence of isotropy in momentum space and the presence of different scaling laws in the incompressible kinetic energy spectrum. The microscopic origin of the algebraic exponents in the energy spectrum is discussed by studying the internal structure of quantized vortices within the healing length and their clustering at larger length scales. These results are obtained using two counterstreaming fluids of light, which allows for a precise preparation of the initial state and the in situ measurement of the compressible and incompressible fluid velocity.
Turbulence in the quantum (superfluid) regime, similarly to its classical counterpart, continues to attract a great deal of scientific inquiry due to the yet high number of unresolved problems. While turbulent states can be routinely created in degenerate atomic gases, there is no generic scheme to produce turbulence in fluids of light. Under paraxial propagation, light in bulk nonlinear media behaves as a two-dimensional superfluid, described by a nonlinear Schr\"odinger equation formally equivalent to the Gross-Pitaevskii model of a weakly interacting Bose gas, where photon-photon interactions are mediated by a third-order (Kerr) nonlinearity. Here we develop the theory describing the onset of a kinetic instability when two paraxial optical fluids with different streaming velocities interact via the optical nonlinearity. From numerical simulations of the nonlinear Schr\"odinger equation, we further characterize the onset of the instability and describe its saturation in the form of vortex nucleation and excitation of turbulence. The experimental observation of such effects is also discussed. The class of instabilities described here thus provide a natural route towards the investigation of quantum (superfluid) turbulence, structure formation, and out-of-equilibrium dynamics in superfluids of light.
We review turbulence in ultracold quantum gases, using the scalar contact-interaction Bose-Einstein condensate as the reference system for quantized circulation, compressibility, vortices, sound, and cascades. We focus on the quantitative diagnostics that connect helium and classical phenomenology to microscopic wave-function dynamics: incompressible and compressible kinetic-energy spectra, wave-occupation spectra, spectral fluxes, vortex-resolved correlations, and velocity statistics. These diagnostics distinguish equilibrium vortex organization, decaying turbulent relaxation, forced cascade dynamics, and weak-wave turbulence, and show why power laws alone are insufficient evidence for a cascade. We survey experiments on two-dimensional Onsager clustering, three-dimensional vortex-line turbulence, box-trap wave cascades, engineered dissipation, and turbulent equations of state. We close by briefly placing the contact-interaction scalar superfluid system in a broader landscape of nonlocal, multicomponent, fermionic, and driven-dissipative quantum fluids, where turbulence concepts can be tested for universality.
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.
There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of stable topological defects called quantized vortices, and thus quantum turbulence provides a simpler prototype of turbulence than classical turbulence. In this paper, we investigate the dynamics and statistics of quantized vortices in quantum turbulence by numerically solving a modified Gross-Pitaevskii equation. First, to make decaying turbulence, we introduce a dissipation term that works only at scales below the healing length. Second, to obtain steady turbulence through the balance between injection and decay, we add energy injection at large scales. The energy spectrum is quantitatively consistent with the Kolmogorov law in both decaying and steady turbulence. Consequently, this is the first study that confirms the inertial range of quantum turbulence.
Abstract Chapter 5 delves into quantum turbulence in superfluid helium and atomic Bose-Einstein condensates (BECs). The foundation of quantum turbulence research lies in classical fluid dynamics and turbulence, which is why we begin by covering essential concepts like the Reynolds number and Kolmogorov’s -5/3 power law in the energy spectrum. These principles are crucial for understanding quantum turbulence. We then explore the shared aspects of quantum turbulence in superfluid helium and atomic BECs, such as the differences in vortex configurations compared to classical turbulence, energy spectra, cascades, and the distinction between quasiclassical (Kolmogorov) and ultraquantum (Vinen) turbulence, focusing on their decay behaviors. In superfluid helium, we emphasize experimental studies in thermal counterflow and numerical simulations using the Vortex Filament Model (VFM). The advent of visualization experiments in the mid-2000s was transformative, allowing the observation of normal fluid velocity profiles and accelerations via tracer particles, which led to more accurate simulations coupling the VFM with normal fluid dynamics. Another significant topic is the energy spectrum of quantum turbulence, and whether it mirrors classical turbulence remains a key question. In addition to thermal counterflow, localized quantum turbulence generated by oscillating objects has been a major area of study. We present research showing how quantized vortices grow and evolve into turbulence. Superfluid 3He-B also provides a platform for quantum turbulence, with advancements in microfabrication bringing MEMS and NEMS into focus for studying quantum hydrodynamics at micro- and nanoscale, influenced by boundary conditions. In atomic BECs, confined by potentials, turbulence is induced through techniques like shaking or moving potentials. A unique aspect of BECs is two-dimensional quantum turbulence, featuring inverse energy cascades, Onsager vortices, and negative temperature states. Finally, atomic BECs, being compressible, serve as a platform for both vortex and wave turbulence. Multicomponent BECs, such as spinor BECs, introduce spin turbulence, further diversifying the field.