Turbulence is characterized by a large number of degrees of freedom, distributed over several length scales, that result into a disordered state of a fluid. The field of quantum turbulence deals with the manifestation of turbulence in quantum fluids, such as liquid helium and ultracold gases. We review, from both experimental and theoretical points of view, advances in quantum turbulence focusing on atomic Bose-Einstein condensates. We also explore the similarities and differences between quantum and classical turbulence. Lastly, we present challenges and possible directions for the field. We summarize questions that are being asked in recent works, which need to be answered in order to understand fundamental properties of quantum turbulence, and we provide some possible ways of investigating them. arXiv:1903.12215v1 [cond-mat.quant-gas]

We present a pedagogical introduction to Bose-Einstein condensation in traps with spherical symmetry, namely the spherical box and the thick shell, sometimes called bubble trap. In order to obtain the critical temperature for Bose-Einstein condensation, we describe how to calculate the cumulative state number and density of states in these geometries, using numerical and analytical (semi-classical) approaches. The differences in the results of both methods are a manifestation of Weyl's theorem, i.e., they reveal how the geometry of the trap (boundary condition) affects the number of the eigenstates counted. Using the same calculation procedure, we analyzed the impact of going from three-dimensions to two-dimensions, as we move from a thick shell to a two-dimensional shell. The temperature range we obtained, for most commonly used atomic species and reasonable confinement volumes, is compatible with current cold atom experiments, which demonstrates that these trapping potentials may be employed in experiments.

In turbulence phenomena, including the quantum turbulence in superfluids, an energy flux flows from large to small length scales, composing a cascade of energy. It is a well-known fact that for multi-scale energy flow, dissipation can be scale-dependent. In particular, the existence of a range of scales where there is no energy accumulation, the inertial range, is an indication of universal behavior in turbulence. There are intrinsic difficulties associated with the measurement of the energy flux during the time evolution of turbulence. Here we present a procedure to measure the energy flux during the time evolution of turbulence in a sample of a trapped Bose-Einstein condensate. The energy flux is evaluated using the energy spectrum and the continuity equation. We identified intervals of momentum where the flux is constant using two different procedures. The identification of a region with constant flux in turbulent BECs is a manifestation of the universal character of turbulence in these quantum systems. These measurements pave the way for studies of energy conservation and dissipation in a scale-dependent manner in trapped atomic superfluids, and also analogies with the related processes that take place in ordinary fluids.

The field of quantum turbulence is related to the manifestation of turbulence in quantum fluids, such as liquid helium and ultracold gases. The concept of turbulence in quantum systems was conceived more than 70 years ago by Onsager and Feynman, but the study of turbulent ultracold gases is very recent. Although it is a young field, it already provides new approaches to the problem of turbulence. We review the advances and present status, of both theory and experiments, concerning atomic Bose-Einstein condensates (BECs). We present the difficulties of characterizing turbulence in trapped BECs, if compared to classical turbulence or turbulence in liquid helium. We summarize the challenges ahead, mostly related to the understanding of fundamental properties of quantum turbulence, including what is being done to investigate them.

We report diffusion Monte Carlo results for the ground state of unpolarized spin-1/2 fermions in a cylindrical container and properties of the system with a vortex-line excitation. The density profile of the system with a vortex line presents a non-zero density at the core. We calculate the ground-state energy per particle, the superfluid pairing gap, and the excitation energy per particle. These simulations can be extended to calculate the properties of vortex excitations in other strongly interacting systems, such as superfluid neutron matter using realistic nuclear Hamiltonians.

We report T = 0 diffusion Monte Carlo results for the ground-state and vortex excitation of unpolarized spin-1/2 fermions in a two-dimensional disk. We investigate how vortex core structure properties behave over the BEC-BCS crossover. We calculate the vortex excitation energy, density profiles, and vortex core properties related to the current. We find a density suppression at the vortex core on the BCS side of the crossover, and a depleted core on the BEC limit. Size-effect dependencies in the disk geometry were carefully studied.

Cold gas experiments can be tuned to achieve strongly-interacting regimes such as that of lowdensity neutron matter found in neutron-stars' crusts. We report T =0 diffusion Monte Carlo results (i) for the ground state of both spin-1/2 fermions with short-range interactions and low-density neutron matter in a cylindrical container, and (ii) properties of these systems with a vortex line excitation. We calculate the equation of state for cold atoms and low-density neutron matter in the bulk systems, and we contrast it to our results in the cylindrical container. We compute the vortex line excitation energy for different interaction strengths, and we find agreement between cold gases and neutron matter for very low densities. We also calculate density profiles, which allow us to determine the density depletion at the vortex core, which depends strongly on the short-ranged interaction in cold atomic gases, but it is of ≈ 25% for neutron matter in the density regimes studied in this work. Our results can be used to constrain neutron matter properties by using measurements from cold Fermi gases experiments.

In most simulations of nonrelativistic nuclear systems, the wave functions found solving the manybody Schrödinger equations describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. In this work we present an alternative quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. We report the renormalization of the nucleon mass as a function of the momentum cutoff, an Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two-nucleon sector we show that the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and we fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. We show that the method can be readily applied to light-nuclei.