Khalid Hossain^{2}, Konrad Kobuszewski^{1}, Michael McNeil Forbes^{2,3}, Piotr Magierski^{1,3}, Kazuyuki Sekizawa^{4,5}, and Gabriel Wlazłowski^{1,3}

^{1}Faculty of Physics, Warsaw University of Technology

^{2}Department of Physics and Astronomy, Washington State University

^{3}Department of Physics, University of Washington

^{4}Center for Transdisciplinary Research, Institute for Research Promotion, Niigata University

^{5}Division of Nuclear Physics, Center for Computational Sciences, University of Tsukuba

*When you use data from this webpage, please make credit to: *

K. Hossain, K. Kobuszewski, M. M. Forbes, P. Magierski, K. Sekizawa, G. Wlazłowski, Phys. Rev. A **105**, 013304 (2022)

**Quantum turbulence** is complex and non-equilibrium flow of superfluid. Typically the flow is accompanied by tangled vortices which can collide and reconnect, transferring energy between length scales, bringing the system back towards equilibrium, and giving rise to an effective dissipation at large scales, despite the superfluid nature of the system. If in addition to turbulent flow the system is subject of rotation (the total angular momentum of the system is non-zero) then we have **rotating quantum turbulence**.

The turbulent process has been observed for superfluid ^{4}He and ^{3}He experiments. In our paper, we the study this phenomenon in an ultracold atomic gas of strongly interacting fermions – the unitary Fermi gas (UFG).

If you want to learn more about the quantum turbulence see here.

**Generation and decay of the quantum tubulent state in unitary Fermi gas (Movie 1)**

Simulation demonstrating development and decay of rotating turbulence in the spin- symmetric UFG. The turbulence was generated by imprinting of 4 solitons on top of existing vortex lattice. Time evolution of the total vortex lines lenght (inset with read curve) reveals existance of two regimes of decay: one dominated by vortex reconnection near the boundary, and the other dominated by vortex reconnection in the bulk. The calculation was executed by means of fermionic theory TDASLDA.

**Generation of quantum turbulence via amplification of Kelvin waves (Movie 5)**

Simulation demonstrating generation of turbulence by meas of imprinting gray solitons. As they move towards each other Kelvin waves are amplified, see central panel. These waves are growing until they reach the intervortex spacing, whereupon they interact with other vortices, creating finally a vortex tangle. Other panels show: total length of vortex lines (left up), occurrence of reconnection events (left bottom) number of vortex ends touching boundary (right up) and number of vortices (right bottom).

**Rotating quantum turbulence in the unitary Fermi gas by means of GPE (Movie 7)**

Simulation of rotating turbulence by means of simplified approach: modified Gross-Pitaevskii equation (GPE). The calculation demonstrate that the GPE can be tuned to give the same qualitative features as the full fermionic calculations, including the initial generation of turbulence, followed by two independent decay regimes with power-law decays.

In these movies contour plot of |∆| is shown. Left upper panel shows corresponding total length of vortex lines, while left bottom panel shows integrated along z direction value of |∆|^{2}, i.e. ρ_{2d}(x, y) = ∫ |∆(x, y, z)|^{2}dz.

**TDASLDA calculations for polarized system P=10% (Movie 2)**

TDASLDA simulation demonstrating development and decay of rotating turbulence in the spin-imbalanced UFG with total polarization P=10%. All other conditions are the same as for Movie 1

T**DASLDA calculations for polarized system P=20% (Movie 3)**

The same as Movie 2, but for total spin polarization P = 20%

** TDASLDA calculation: turbulence is generated by two solitons (Movie 4)**

TDASLDA simulation where turbulence was gen- erated by imprinting 2 solitons with phase differ- ence of π. Qualitatively the movie is similar to Movie 1.

**TDASLDA calculation: amplification of Kelvin waves (Movie 5)**

The same as Movie 4, except value of the imprinted of phase difference which here is π/2. This imprint generates moving solitons which in- duce amplification of kelvin waves.

** TDASLDA calculation: collision of clouds (Movie 6)**

Movie showing result of collision of clouds with vortices where the phase imprint procedure is not applied. In such case the vortex tangle is not generated.

** GPE calculation: turbulence is generated by two solitons (Movie 8)**

GPE simulation of the same setup as presented on Movie 4. Visualization is presented in co-rotating frame system.

**GPE calculation: turbulence is generated by gray solitons (Movie 9)**

GPE simulations of the same setup as pre- sented on Movie 5.

Alternative visualization of vortex tangles. Central panel shows vortex lines given as output of vortex detection algorithm and isocontours of |∆|, left upper shows corresponding total length of vortex lines, left bottom panel shows occurrence of reconnection events (current ones are marked with red color) and right upper and bottom panels are number of vortex ends touching boundary #b and number of vortices N_{V} , respectively.

**TDASLDA calculations for spin-symmetric system (Movie 1)**

**TDASLDA calculations for polarized system P=10% (Movie 2)**

T**DASLDA calculations for polarized system P=20% (Movie 3)**

** TDASLDA calculation: turbulence is generated by two solitons (Movie 4)**

** TDASLDA calculation: collision of clouds (Movie 6)**

** GPE calculation: turbulence is generated by two solitons (Movie 8)**

**GPE calculation: turbulence is generated by gray solitons (Movie 9)**

- P. Magierski,
*Fermionic turbulence within the framework of time dependent density functional theory*,

INT Program INT-19-1a Quantum Turbulence: Cold Atoms, Heavy Ions, and Neutron Stars, March 18 - April 19, 2019, Seattle, USA - G. Wlazłowski,
*Nonequilibrium phenomena in superfluid systems: Quantum turbulence*,

Workshop: Nonequilibrium phenomena in superfluid systems, Warsaw University of Technology, Warsaw, Poland, 2-4 March 2020 - G. Wlazłowski,
*From dynamics of a single vortex to quantum turbulence in fermionic superfluids*,

Seminar, University of Warsaw, Warsaw, Poland, 12 April 2019, - G. Wlazłowski,
*Towards exascale simulations of quantum turbulence in Fermi superfluids: status and challenges*,

Supercomputing Frontiers Europe 2018, Warsaw, Poland, 12-15 March 2018

Faculty of Physics @ WUT