Bosons in a cascading turbulence state!

In the mid-1920s, Bose and Einstein predicted that certain atomic particles, thereafter known as bosons, could, under certain conditions, exhibit quantum behavior on the macroscopic scale. Indeed, when a dilute gas of bosons is cooled to temperatures close to absolute zero (-273⁰C), a macroscopic fraction of the gas occupies the fundamental quantum state of the system. We had to wait 70 years for the first experimental realization of this singular state of matter, called Bose-Einstein condensate (BEC). Since then, BECs have been the subject of intense experimental and theoretical studies. In particular, over the past decade, an excellent experimental control that scientists have achieved over these condensates has enabled them to bring BEC out of its equilibrium state and its dynamics to be studied in a controlled and reproducible way, even going so far as to study the statistical properties of turbulent BEC.

In a turbulent BEC, due to the intrinsic non-linear properties of the system, energy is transferred from large to small scales by a cascading process analogous to classical hydrodynamic turbulence. In addition to energy, the number of particles at a given scale also follows a turbulent cascade, but in the opposite direction, from small to large scales. A collaboration involving teams from the Institut de Physique de Nice (INPHYNI, CNRS / Université Côte d'Azur) and the Laboratoire J.L. Lagrange (LAGRANGE, CNRS / Observatoire de la Côte d'Azur / Université Côte d'Azur) has carried out a theoretical and numerical study of these turbulent cascades. In particular, they have critically revised existing theories and deduced new analytical predictions for the scaling laws describing how energy and particles are statistically distributed across the different scales of the system. The accuracy of these predictions means that they can be compared with experiments without having to adjust any unknown parameters. As a result, the researchers were able to validate their predictions quantitatively using, among other things , high-resolution numerical simulations of the Gross-Pitaevskii equation describing BECs.


These new results explain and resolve certain contradictions that existed in previous experimental results, and suggest new experiments to create a reverse cascade of energy in BECs, unobserved to date. The study was published in Physical Review Letters.

Figure : 3D density field in a numerical simulation of BEC turbulence in a cubic potential trap.
© Y. Zhu, B. Semisalov, G. Krstulovic, and S. Nazarenko