Cascading boson turbulence

  • Research
Published on June 12, 2023 Updated on July 28, 2023

on the June 12, 2023


Theoretical work carried out by researchers at the Lagrange Laboratory and the Nice Institute of Physics, on Bose-Einstein condensates maintained in stationary turbulence predicts accurately how energy and density are organized on average at different scales of the system.

In the mid-1920s, Bose and Einstein predicted that certain atomic particles, since known as bosons, could under certain conditions exhibit quantum behavior on the macroscopic scale. They showed that 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. It took another 70 years to conduct the first experiment demonstrating this singular state of matter, known as a Bose-Einstein condensate (BEC). Since then, BECs have been the subject of intense experimental and theoretical research. Over the last decade, for example, scientists achieved such excellent experimental control of these condensates that they were able to bring them out of their equilibrium state to study their dynamics in a controlled and reproducible way, even going so far as to study the statistical properties of turbulent BECs.

In a turbulent BEC, because of the intrinsic nonlinear properties of the system, energy is transferred from large to small scales by a cascading process similar to standard hydrodynamic turbulence. In addition to energy, the number of particles involved at each scale also follows a turbulent cascade, but in the opposite direction, from small to large scales. A collaboration involving teams from the Nice Institute of Physics (INPHYNI, CNRS / Université Côte d'Azur) and the Laboratoire J.L. Lagrange (LAGRANGE, CNRS / Observatoire de la Côte d'Azur / Université Côte d'Azur) carried out a theoretical and numerical study of these turbulent cascades. They examined existing theories critically and deduced new analytical predictions for the scaling laws that describe how energy and particles are statistically distributed according to the different scales of the system. Their predictions are so accurate that they can be compared with experiments, but in their case no unknown parameter adjustments are needed. 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 some of the contradictions in previous experimental results and open the possibility for new experiments to create a reverse cascade of energy in BECs, unobserved to date. Their work was published in the Physical Review Letters.

schema boson 1
schema boson 1

Diagram 1
 3D density field in a numerical simulation of BEC turbulence in a cubic trap. © Y. Zhu, B. Semisalov, G. Krstulovic, and S. Nazarenko

schema Boson 2
schema Boson 2

Diagram 2
Figure: 3D density field in a numerical simulation of BEC turbulence in a cubic trap.
© Y. Zhu, B. Semisalov, G. Krstulovic, and S. Nazarenko

Sergey Nazarenko | Directeur de recherche CNRS, Institut de physique de Nice |
Giorgio Krstulovic | Chargé de recherche CNRS, Laboratoire J-L Lagrange |


Direct and inverse cascades in turbulent Bose-Einstein condensate, Y. Zhu, B. Semisalov, G. Krstulovic, and S. Nazarenko, Physical Review Letters, published March 27, 2023
DOI :10.1103/PhysRevLett.130.133001
Open archives: arXiv