Michael McNeil Forbes

Resonantly interacting fermions in a box.

We use two fundamental theoretical frameworks to study the finite-size (shell) properties of the unitary gas in a periodic box: (1) an ab initio quantum Monte Carlo (QMC) calculation for boxes containing 4 to 130 particles provides a precise and complete characterization of the finite-size behavior, and (2) a new density functional theory (DFT) fully encapsulates these effects. The DFT predicts vanishing shell structure for systems comprising more than 50 particles, and allows us to extrapolate the QMC results to the thermodynamic limit, providing the tightest bound to date on the ground-state energy of the unitary gas: ξ(S)≤0.383(1). We also apply the new functional to few-particle harmonically trapped systems, comparing with previous calculations.

Unitary Fermi supersolid: the Larkin-Ovchinnikov phase.

We present strong theoretical evidence that a Larkin-Ovchinnikov (LOFF/FFLO) pairing phase is favored over the homogeneous superfluid and normal phases in three-dimensional unitary Fermi systems. Using a density functional theory (DFT) based on the latest quantum Monte Carlo calculations and experimental results, we show that this phase is competitive over a large region of the phase diagram. The oscillations in the number densities and pairing field have a substantial amplitude, and a period some 3 to 10 times the average interparticle separation. Within the DFT, the transition to a normal polarized Fermi liquid at large polarizations is smooth, while the transition to a fully paired superfluid is abrupt.

Broyden's Method in Nuclear Structure Calculations

Broydens method, widely used in quantum chemistry electronic-structure calculations for the numerical solution of nonlinear equations in many variables, is applied in the context of the nuclear many-body problem. Examples include the unitary gas problem, the nuclear density functional theory with Skyrme functionals, and the nuclear coupled-cluster theory. The stability of the method, its ease of use, and its rapid convergence rates make Broydens method a tool of choice for large-scale nuclear structure calculations.

Induced P-wave superfluidity in asymmetric fermi gases.

We show that two new intraspecies P-wave superfluid phases appear in two-component asymmetric Fermi systems with short-range S-wave interactions. In the BEC limit, phonons of the molecular BEC induce P-wave superfluidity in the excess fermions. In the BCS limit, density fluctuations induce P-wave superfluidity in both the majority and the minority species. These phases may be realized in experiments with spin-polarized Fermi gases.

Negative-mass hydrodynamics in a spin-orbit coupled Bose-Einstein condensate

A negative effective mass can be realized in quantum systems by engineering the dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently at the center of intense research efforts. Here we measure an expanding spin-orbit coupled Bose-Einstein condensate whose dispersion features a region of negative effective mass. We observe a range of dynamical phenomena, including the breaking of parity and of Galilean covariance, dynamical instabilities, and self-trapping. The experimental findings are reproduced by a single-band Gross-Pitaevskii simulation, demonstrating that the emerging features-shock waves, soliton trains, self-trapping, etc.-originate from a modified dispersion. Our work also sheds new light on related phenomena in optical lattices, where the underlying periodic structure often complicates their interpretation.

The Unitary Fermi Gas: From Monte Carlo to Density Functionals

In this chapter, we describe three related studies of the universal physics of two-component unitary Fermi gases with resonant short-ranged interactions. First we discuss an ab initio auxiliary field quantum Monte Carlo technique for calculating thermodynamic properties of the unitary gas from first principles. We then describe in detail a Density Functional Theory (DFT) fit to these thermodynamic properties: the Superfluid Local Density Approximation (SLDA) and its Asymmetric (ASLDA) generalization. We present several applications, including vortex structure, trapped systems, and a supersolid Larkin–Ovchinnikov (FFLO/LOFF) state. Finally, we discuss the time-dependent extension to the density functional (TDDFT) which can describe quantum dynamics in these systems, including non-adiabatic evolution, superfluid to normal transitions and other modes not accessible in traditional frameworks such as a Landau–Ginzburg, Gross–Pitaevskii, or quantum hydrodynamics.

Use of the Discrete Variable Representation Basis in Nuclear Physics

The discrete variable representation (dvr ) basis is nearly optimal for numerically representing wave functions in nuclear physics: Suitable problems enjoy exponential convergence, yet the Hamiltonian remains sparse. We show that one can often use smaller basis sets than with the traditional harmonic oscillator basis, and still benefit from the simple analytic properties of the dvr bases which requires no overlap integrals, simply permit using various Jacobi coordinates, and admit straightforward analyses of the ultraviolet and infrared convergence properties.

Zero-temperature thermodynamics of asymmetric Fermi gases at unitarity

The equation of state of a dilute two-component asymmetric Fermi gas at unitarity is subject to strong constraints, which affect the spatial density profiles in atomic traps. These constraints require the existence of at least one nontrivial partially polarized (asymmetric) phase. We determine the relation between the structure of the spatial density profiles and the T=0 equation of state, based on the most accurate theoretical predictions available. We also show how the equation of state can be determined from experimental observations.

Diffuse x-rays: Directly observing dark matter?

Several independent observations of the galactic core suggest hitherto unexplained sources of energy. We suggest that dark matter in the form of dense antimatter nuggets could provide a natural site for electron and proton annihilation, providing 511 keV photons, gamma rays, and diffuse keV x-ray radiation. We show that identifying dark matter as antimatter nuggets is consistent with the observed emissions, and we make definite predictions about their spectrum and morphology. If correct, our proposal not only identifies dark matter and explains baryogenesis, but also allows x-ray observations to directly probe the matter distribution in our galaxy.

Electrosphere of macroscopic 'quark nuclei': A source for diffuse MeV emissions from dark matter

Using a Thomas-Fermi model, we calculate the structure of the electrosphere of the quark antimatter nuggets postulated to comprise much of the dark matter. This provides a single self-consistent density profile from ultrarelativistic densities to the nonrelativistic Boltzmann regime that we use to present microscopically justified calculations of several properties of the nuggets, including their net charge, and the ratio of MeV to 511 keV emissions from electron annihilation. We find that the calculated parameters agree with previous phenomenological estimates based on the observational supposition that the nuggets are a source of several unexplained diffuse emissions from the Galaxy. As no phenomenological parameters are required to describe these observations, the calculation provides another nontrivial verification of the dark-matter proposal. The structure of the electrosphere is quite general and will also be valid at the surface of strange-quark stars, should they exist.