Towards quantum turbulence in cold atomic fermionic superfluids

Chapter 1 Energy Spectra of Quantum Turbulence

Superfluid turbulence has been one of the most important problems of superfluid hydrodynamics, in which quantized vortices play a significant role. The recent research on superfluid turbulence enters a new stage rather different from the old ones chiefly devoted to thermal counterflow. After describing the current motivation on these topics, we discuss our research which studies the energy spectrum both by the vortex filament model and the Gross-Pitaevskii model. Both energy spectra are consistent with the Kolmogorov law, which shows a close similarity between superfluid (quantum) and classical turbulence.

The effect of isospin-dependent nuclear forces on the inner crust of neutron stars is modeled within the framework of Quantum Molecular Dynamics (QMD). To successfully control the density dependence of the symmetry energy of neutron-star matter below nuclear saturation density, a mixed vector-isovector potential is introduced. This approach is inspired by the baryon density and isospin density-dependent repulsive Skyrme force of asymmetric nuclear matter. In isospin-asymmetric nuclear matter, the system shows nucleation, as nucleons are arranged into shapes resembling nuclear pasta. The dependence of clusterization in the system on the isospin properties is also explored by calculating two-point correlation functions. We show that, as compared to previous results that did not involve such mixed interaction terms, the energy symmetry slope L is successfully controlled by varying the corresponding coupling strength. Nevertheless, the effect of changing the slope of the nuclear symmetry energy L on the crust-core transition density does not seem significant. To the knowledge of the authors, this is the first implementation of such a coupling in a QMD model for isospin asymmetric matter, which is relevant to the inner crust of neutron and proto-neutron stars.

Superfluid dilute neutron matter and ultracold gas, close to the unitary regime, exhibit several similarities. Therefore, to a certain extent, fermionic ultracold gases may serve as emulators of dilute neutron matter, which forms the inner crust of neutron stars and is not directly accessed experimentally. Quantum vortices are one of the most significant properties of neutron superfluid, essential for comprehending neutron stars’ dynamics. The structure and dynamics of quantum vortices as a function of pairing correlations’ strength are being investigated experimentally and theoretically in ultracold gases. Certain aspects of these studies are relevant to neutron stars. We provide an overview of the characteristics of quantum vortices in s-wave-type fermionic and electrically neutral superfluids. The main focus is on the dynamics of fermionic vortices and their intrinsic structure.

The recent discovery of high frequency oscillations during giant flares from the Soft Gamma Repeaters SGR 1806-20 and SGR 1900+14 may be the first direct detection of vibrations in a neutron star crust. If this interpretation is correct it offers a novel means of testing the neutron star equation of state, crustal breaking strain, and magnetic field configuration. We review the observational data on the magnetar oscillations, including new timing analysis of the SGR 1806-20 giant flare using data from the Ramaty High Energy Solar Spectroscopic Imager and the Rossi X-ray Timing Explorer. We discuss the implications for the study of neutron star structure and crust thickness, and outline areas for future investigation.

The cell structure of $\ensuremath{\beta}$-stable clusters in the inner crust of cold and warm neutron stars is studied within the Thomas--Fermi approach by using relativistic mean-field nuclear models. The relative size of the inner crust and the pasta phase of neutron stars is calculated, and the effect of the symmetry energy slope parameter $L$ on the profile of the neutron star crust is discussed. It is shown that, while the size of the total crust is mainly determined by the incompressibility modulus, the relative size of the inner crust depends on $L$. It is found that the inner crust represents a larger fraction of the total crust for smaller values of $L$. Finally, it is shown that, at finite temperature the pasta phase in $\ensuremath{\beta}$-equilibrium matter essentially melts above $5\phantom{\rule{4.pt}{0ex}}\text{to}\phantom{\rule{4.pt}{0ex}}6$ MeV, and that the onset density of the rod-like and slab-like structures does not depend on the temperature.

We describe the first measurements of line-density fluctuations and spatial correlations of quantum turbulence in superfluid 3He-B. All of the measurements are performed in the low-temperature regime, where the normal-fluid density is negligible. The quantum turbulence is generated by a vibrating grid. The vortex-line density is found to have large length-scale correlations, indicating large-scale collective motion of vortices. Furthermore, we find that the power spectrum of fluctuations versus frequency obeys a -5/3 power law which verifies recent speculations that this behavior is a generic feature of fully developed quantum turbulence, reminiscent of the Kolmogorov spectrum for velocity fluctuations in classical turbulence.

Very different strongly interacting quantum systems such as Fermi gases, quark-gluon plasmas formed in high energy ion collisions and black holes studied theoretically in string theory are known to exhibit quantitatively similar damping of hydrodynamic modes. It is not known if such similarities extend beyond the hydrodynamic limit. Do non-hydrodynamic collective modes in Fermi gases with strong interactions also match those from string theory calculations? In order to answer this question, we use calculations based on string theory to make predictions for novel types of modes outside the hydrodynamic regime in trapped Fermi gases. These predictions are amenable to direct testing with current state-of-the-art cold atom experiments.

It is of central importance to probe the \emph{local} spectral function $A(\mathbf{k},\omega)$ of a strongly interacting Fermi gas in a trap. Momentum resolved rf spectroscopy has been demonstrated to be able to probe the trap averaged $A(\mathbf{k},\omega)$. However, the usefulness of this technique was limited by the trap inhomogeneity. Independent of a specific theory, here we propose that by studying the momentum resolved rf spectra of the minority fermions of a phase separated, population imbalanced Fermi gas at low temperature, one can effectively extract $A(\mathbf{k},\omega)$ of a homogeneous superfluid Fermi gas (at the trap center). In support, we present calculated spectral functions and spectral intensity maps for various cases from BCS through BEC regimes using different theories.

We report the first observation of the quantum Joule-Thomson (JT) effect in ideal and unitary Fermi gases. We study the temperature dynamics of these systems while they undergo an energy-per-particle conserving rarefaction. For scale-invariant systems, whose equations of state satisfy the relation U∝PV, this rarefaction conserves the specific enthalpy, which makes it thermodynamically equivalent to a JT throttling process. We observe JT heating in an ideal Fermi gas, a direct consequence of Pauli blocking. In a unitary Fermi gas, we observe that the JT heating is marginal in the temperature range 0.2≲T/T_{F}≲0.8 as the repulsive quantum-statistical effect is lessened by the attractive interparticle interactions.

Shear viscosity in the strong interaction regime of a p-wave superfluid Fermi gas

The contact I, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the interaction parameter 1/(k(F)a), where k(F) is the Fermi wave vector and a is the s-wave scattering length, and the temperature T/T(F), where T(F) is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature.

Comments to ‘Vortex clustering, polarisation and circulation intermittency in classical and quantum turbulence’

Aql X-1 is a prolific transient neutron star low-mass X-ray binary that exhibits an accretion outburst approximately once every year. Whether the thermal X-rays detected in intervening quiescent episodes are the result of cooling of the neutron star or due to continued lowlevel accretion remains unclear. In this work, we use Swift data obtained after the long and bright 2011 and 2013 outbursts, as well as the short and faint 2015 outburst, to investigate the hypothesis that cooling of the accretion-heated neutron star crust dominates the quiescent thermal emission in Aql X-1. We demonstrate that the X-ray light curves and measured neutron star surface temperatures are consistent with the expectations of the crust cooling paradigm. By using a thermal evolution code, we find that 1.2-3.2 MeV nucleon -1 of shallow heat release describes the observational data well, depending on the assumed mass-accretion rate and temperature of the stellar core. We find no evidence for varying strengths of this shallow heating after different outbursts, but this could be due to limitations of the data. We argue that monitoring Aql X-1 for up to 1 yr after future outbursts can be a powerful tool to break model degeneracies and solve open questions about the magnitude, depth, and origin of shallow heating in neutron star crusts.

We propose a novel theory of dark matter (DM) superfluidity that matches the\nsuccesses of the LambdaCDM model on cosmological scales while simultaneously\nreproducing the MOdified Newtonian Dynamics (MOND) phenomenology on galactic\nscales. The DM and MOND components have a common origin, representing different\nphases of a single underlying substance. DM consists of axion-like particles\nwith mass of order eV and strong self-interactions. The condensate has a\npolytropic equation of state P~rho^3 giving rise to a superfluid core within\ngalaxies. Instead of behaving as individual collisionless particles, the DM\nsuperfluid is more aptly described as collective excitations. Superfluid\nphonons, in particular, are assumed to be governed by a MOND-like effective\naction and mediate a MONDian acceleration between baryonic matter particles.\nOur framework naturally distinguishes between galaxies (where MOND is\nsuccessful) and galaxy clusters (where MOND is not): due to the higher velocity\ndispersion in clusters, and correspondingly higher temperature, the DM in\nclusters is either in a mixture of superfluid and normal phase, or fully in the\nnormal phase. The rich and well-studied physics of superfluidity leads to a\nnumber of observational signatures: array of low-density vortices in galaxies,\nmerger dynamics that depend on the infall velocity vs phonon sound speed;\ndistinct mass peaks in bullet-like cluster mergers, corresponding to superfluid\nand normal components; interference patters in super-critical mergers.\nRemarkably, the superfluid phonon effective theory is strikingly similar to\nthat of the unitary Fermi gas, which has attracted much excitement in the cold\natom community in recent years. The critical temperature for DM superfluidity\nis of order mK, comparable to known cold atom Bose-Einstein condensates.\n