Home Search Collections Journals About Contact us My IOPscience Towards quantum turbulence in cold atomic fermionic superfluids This content has been downloaded from IOPscience. Please scroll down to see the full text. 2017 J. Phys. B: At. Mol. Opt. Phys. 50 014001 (http://iopscience.iop.org/0953-4075/50/1/014001) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 134.148.10.13 This content was downloaded on 13/12/2016 at 06:56 Please note that terms and conditions apply. You may also be interested in: Dynamics of vortices and interfaces in superfluid 3He A P Finne, V B Eltsov, R Hänninen et al. Turbulence in quantum fluids Makoto Tsubota Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality Allan Adams, Lincoln D Carr, Thomas Schäfer et al. 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Phys. 50 (2017) 014001 (11pp) doi:10.1088/1361-6455/50/1/014001 Towards quantum turbulence in cold atomic fermionic superfluids Aurel Bulgac1,4, Michael McNeil Forbes1,2 and Gabriel Wlazłowski1,3 1 Department of Physics, University of Washington, Seattle, WA 98105–1560, USA 2 Department of Physics and Astronomy, Washington State University, Pullman, WA 99164–2814, USA 3 Faculty of Physics, Warsaw University of Technology, Ulica Koszykowa 75, 00–662 Warsaw, Poland E-mail: [email protected], [email protected] and [email protected] Received 31 August 2016, revised 25 October 2016 Accepted for publication 1 November 2016 Published 6 December 2016 Abstract Fermionic superfluids provide a new realization of quantum turbulence, accessible to both experiment and theory, yet relevant to phenomena from both cold atoms to nuclear astrophysics. In particular, the strongly interacting Fermi gas realized in cold-atom experiments is closely related to dilute neutron matter in neutron star crusts. Unlike the liquid superfluids 4He (bosons) and 3He (fermions), where quantum turbulence has been studied in laboratory for decades, superfluid Fermi gases stand apart for a number of reasons. They admit a rather reliable theoretical description based on density functional theory called the time-dependent superfluid local density approximation that describes both static and dynamic phenomena. Cold atom experiments demonstrate exquisite control over particle number, spin polarization, density, temperature, and interaction strength. Topological defects such as domain walls and quantized vortices, which lie at the heart of quantum turbulence, can be created and manipulated with time- dependent external potentials, and agree with the time-dependent theoretical techniques. While similar experimental and theoretical control exists for weakly interacting Bose gases, the unitary Fermi gas is strongly interacting. The resulting vortex line density is extremely high, and quantum turbulence may thus be realized in small systems where classical turbulence is suppressed. Fermi gases also permit the study of exotic superfluid phenomena such as the Larkin–Ovchinnikov–Fulde–Ferrell pairing mechanism for polarized superfluids which may give rise to 3D supersolids, and a pseudo-gap at finite temperatures that might affect the regime of classical turbulence. The dynamics associated with these phenomena has only started to be explored. Finally, superfluid mixtures have recently been realized, providing experimental access to phenomena like Andreev–Bashkin entrainment predicted decades ago. Superfluid Fermi gases thus provide a rich forum for addressing phenomena related to quantum turbulence with applications ranging from terrestrial superfluidity to astrophysical dynamics in neutron stars. Keywords: quantum turbulence, superfluid mixtures, cold atoms, fermions, vortex dynamics (Some figures may appear in colour only in the online journal) Hydrodynamic turbulence has fascinated thinkers and artists the shear viscosity. In three-dimensional fluids, turbulent since medieval times, and many authors use in their pre- motion is observed only if the Reynolds number is larger than sentations the works of Leonardo da Vinci and Katsushika Re10 4 [1, 2]. Since superfluids have no shear viscosity Hokusai to illustrate the complexity and beauty of turbulent and behave as a perfect classical fluid at zero temperature, flow (see figure 1). Classical flow is characterized by its turbulence was naively not expected to emerge at subcritical Reynolds number Re = rhvL , where ρ is the fluid mass velocities. However, in 1955 Feynman conjectured that the density, L the length of the system, v the flow velocity, and η quantized vortices [3] predicted by him and Onsager [4] could lead to a new type of turbulence: quantum turbulence. A 4 Author to whom all correspondence should be addressed. tangle of vortex lines, which visually appears as a bunch of / / + 0953-4075 17 014001 11$33.00 1 © 2016 IOP Publishing Ltd Printed in the UK J. Phys. B: At. Mol. Opt. Phys. 50 (2017) 014001 A Bulgac et al Figure 1. Works by Leonardo da Vinci (left) and Katsushika Hokusai (right) illustrating the complexity and the captivating beauty of the turbulent flow. tangled spaghetti, will evolve in time in a rather chaotic [25–27] in which quantized vortices and their crossing and fashion, cross and recombine in similar fashion to strands of reconnections are introduced ad hoc using the Biot–Savart DNA and lead to quantum turbulence. At finite temperatures, law as a recipe to construct the resulting velocity from the but below the critical temperature, a normal component is also vortex lines. present and the normal and superfluid components interact. In Unlike BECs, the unitary Fermi gas (UFG) or a Fermi gas the literature, the term quantum turbulence also refers to the near unitarity—a gas of cold fermionic atoms with interac- dynamics of finite-temperature superfluids where the vortices tions tuned at or near a Feshbach resonance—is strongly in the superfluid component interacts with a classically tur- interacting, and exhibits a large pairing gap of the order of the bulent normal component. Fermi energy, a short coherence length of the order of the Until recently studies of quantum turbulence have been average interparticle separation, and a high critical velocity of 4 3 performed mostly in liquid He and He [5–10], and lately the order of the Fermi velocity [28–33]. The UFG shares many also in Bose–Einstein condensates (BECs) of cold atoms [11]. similarities with the dilute neutron matter, which is present in 4 3 Both liquid He and He are strongly interacting systems of the skin of neutron-rich nuclei, and in the crust of neutron bosons and fermions respectively, but unfortunately a stars where neutron-rich nuclei form a Coulomb lattice microscopic theory describing their dynamics does not exists immersed in a neutron superfluid. This motivated the initial yet. On the other hand the BECs of cold atoms can be independent microscopic studies of the UFG by nuclear the- described quite accurately either by the Gross–Pitaevskii orists [28, 34, 35]5. A system of fermions with zero-range equation (GPE) [12, 13] at very low temperatures, when the interaction and infinite scattering length should have a ground fraction of the normal component is negligible, or by the state energy and properties determined by their only existing fi ( ) [ ] theory of Zaremba, Nikuni, and Grif n ZNG 14 , in which dimensional scale, namely their density, similarly to a free the dynamics and the coupling between the normal and Fermi gas. Theoretical quantum Monte Carlo (QMC) studies fl super uid components are accounted for. There exists also of the Fermi gas near unitarity have achieved percent-level [ ] stochastic extensions of the GPEs 15, 16 , in which two types accuracy [36–39] and agree with experiment [40] at an acc- of modes are introduced, slow quantum modes describes by uracy better than 1% for the energy per particle, and a few the GP equation, and the fast modes modeled stochastically, percent for the magnitude of the pairing gap [41, 42]. separated by a cutoff energy. Unfortunately, these stochastic A microscopic theoretical framework capable of extensions appear to generate results which are dependent on describing quantum turbulence in fermionic superfluids and [ ] the choice of the cutoff energy 17 . The BECs of cold gases implementable in realistic calculations has became possible are systems of weakly interacting atoms, which is the main only recently. Two factors played an crucial role: (i)the reason why the derivation of either the GPE or the ZNG fra- development and validation against experiment of an appro- mework were possible. priate microscopic framework for the structure and dynamics There exist a number of alternative phenomenological of fermionic superfluids, and (ii)the implementation of this approaches to study superfluid dynamics. As noted by Sato framework using sophisticated numerical algorithms that fully and Packard [18], in the case of Bose superfluids ‘two phe- utilize the advanced capabilities of modern leadership class nomenological theories explain almost all experiments’: the computers, such as Titan6. two-fluid hydrodynamics due to Tisza and Landau [19–24], QMC algorithms cannot be used to describe turbulent and the ‘complementary view provided by Fritz London, Lars dynamics and the only available theoretical candidate with a Onsager, and Richard Feynman, [that] treats the superfluid as ’ fl 5 a macroscopic quantum state. A shortcoming of the two- uid The Many-Body Challenge Problem (MBX) formulated by G F Bertsch in hydrodynamics, which is ‘essentially thermodynamics’ [18], 1999, See also [34, 35]. is the absence of the Planck’s constant and the corresponding 6 https://olcf.ornl.gov/computing-resources/titan-cray-xk7/.