Vortices in trapped superfluid fermi gases

We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size, temperature regimes for the existence of a vortex, and the effects of rotation and interactions with normal fermions. The parameter dependence of the vortex core size (healing length) is found to be essentially different from that of the healing length in metallic superconductors or in trapped atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.     

Spectroscopy of superfluid pairing in atomic fermi gases

We study the dynamic structure factor for density and spin within the crossover from BCS superfluidity of atomic fermions to the Bose-Einstein condensation of molecules. Both structure factors are experimentally accessible via Bragg spectroscopy and allow for the identification of the pairing mechanism: the spin structure factor allows for the determination of the two particle gap, while the collective sound mode in the density structure reveals the superfluid state.     

Static properties of trapped bose gases at finite temperature: Thomas-Fermi limit

We rely on a variational approach to derive a set of equations governing a trapped self-interacting Bose gas at finite temperature. In this work, we analyze the static situation both at zero and finite temperature in the Thomas-Fermi limit for the repulsive case. We derive simple analytic expressions for the condensate properties at finite temperature. The noncondensate and anomalous density profiles are also analyzed in terms of the condensate fraction. The results are quite encouraging owing to the simplicity of the formalism.     

Determination of the superfluid gap in atomic Fermi gases by quasiparticle spectroscopy

We present majority and minority radio frequency spectra of strongly interacting imbalanced Fermi gases of 6Li. We observed a smooth evolution in the nature of pairing correlations from pairing in the superfluid region to polaron binding in the highly polarized normal region. The imbalance induces quasiparticles in the superfluid region even at very low temperature. This leads to a local bimodal spectral response, which allowed us to determine the superfluid gap Delta and the Hartree energy U.     

The quantum pressure correction to the excitation spectrum of the trapped superfluid Fermi gases in a BEC-BCS crossover

Using quantum hydrodynamic approaches, we study the quantum pressure correction to the collective excitation spectrum of the interacting trapped superfluid Fermi gases in the BEC-BCS crossover. Based on a phenomenological equation of state, we derive hydrodynamic equations of the system in the whole BEC-BCS crossover regime. Beyond the Thomas--Fermi approximation, expressions of the frequency corrections of collective modes for both spherical and axial symmetric traps excited in the BEC-BCS crossover are given explicitly. The corrections of the eigenfrequencies due to the quantum pressure and their dependence on the inverse interaction strength, anisotropic parameter and particle numbers of the condensate are discussed in detail.     

Many-body atomic potentials in Thomas-Fermi theory

Many-body atomic potentials, ?, are functions of the nuclear coordinates, and are defined by differences of ground state energies, E, e.g., ?(1, 2) ≡ E(1, 2) ? E(1) ? E(2). We prove that in Thomas-Fermi theory the n-body potential always has the sign (?1)ⁿ for all coordinates. We also prove that the remainder in the expansion of the total energy E in terms of the ?'s, when truncated at the n-body terms, has the sign (?1)ⁿ⁺¹.     

Ion core approximation in calculations of excited atomic states

A one-configuration approximation is used to analyze the possibility of employing the frozen ion core model to calculate excited states with low-lying configurations of the same symmetry when the wave functions of the excited states are orthogonal to the function of the ground state. The nonorthogonality of the wave functions of different excited configurations is then weak. A calculation is made for certain Isns¹S and 1s²2sns¹S terms of two-and four-electron ions, respectively, and the relaxation effects in the core are investigated for these excited states. This approximation is employed to obtain a variational equation for virtual orbitals allowing for the core relaxation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 71–77, June, 1980.     

Visualization of vortex bound states in polarized fermi gases at unitarity

We theoretically analyze a single vortex in a spin polarized 3D trapped atomic Fermi gas near a broad Feshbach resonance. Above a critical polarization the Andreev-like bound states inside the core become occupied by the majority spin component. As a result, the local density difference at the core center suddenly rises at low temperatures. This provides a way to visualize the lowest bound state using phase-contrast imaging. As the polarization increases, the core expands gradually and the energy of the lowest bound state decreases.     

Sound emission due to superfluid vortex reconnections

By performing numerical simulations based on the Gross-Pitaevskii equation, we make direct quantitative measurements of the sound energy released due to superfluid vortex reconnections. We show that the energy radiated expressed in terms of the loss of vortex line length is a simple function of the reconnection angle. In addition, we study the temporal and spatial distribution of the radiation and show that energy is emitted in the form of a sound pulse with a wavelength of a few healing lengths.     

Highly excited atomic states in a static electric field

We have performed exact numerical calculations for a hydrogen atom perturbed by a uniform electric field for some Stark sublevels with n = 12, 13, 14, 15. The results are compared with recent experimental data for excited states of sodium.     

Long range atomic potentials in Thomas-Fermi theory

We prove that the interaction among neutral atoms in Thomas-Fermi theory behaves, for large separationl, likel ^–7. The constant is independent of the atomic nuclear charges, but does depend on the relative positions of the nuclei. We also show that is not a simple sum of pair terms, i.e. in TF theory three and higher body terms persist into the asymptotic (inl) region.Work partially supported by U.S. National Science Foundation grant MCS 75 21684 A02     

Introduction to the vortex sheet of superfluid He-A

It is well known that superfluids respond to rotation by forming vortex lines. It has been recently discovered that a different type of state consisting of a vortex sheet, instead of lines, can be created in the A phase of superfluid ³He. This paper presents an introduction to the vortex sheet. We first discuss ⁴He, where a vortex sheet is unstable. The way to realize a stable sheet in ³He-A is called a vortex soliton. It consists of a topologically stable domain wall to which nonsingular vorticity is bound. The vortex soliton has been observed by nuclear magnetic resonance, and its most prominent experimental properties are explained. The macroscopic shape of the sheet and the superfluid flow in a rotating container are discussed.     

Complex quantum gases: spinor Bose–Einstein condensates of trapped atomic vapors

We discuss the energy eigenstates, ground and spin mixing dynamics of a spin-1 spinor Bose–Einstein condensate for a dilute atomic vapor confined in an optical trap. Our results go beyond the mean field picture and are developed within a fully quantized framework.     

Pairing fluctuations in trapped fermi gases

We examine the contribution of pairing fluctuations to the superfluid order parameter for harmonically trapped atomic Fermi gases in the BCS regime. In the limit of small systems we consider, both analytically and numerically, their space and temperature dependence. We predict a parity effect, i.e., that pairing fluctuations show a maximum or a minimum at the center of the trap, depending on the value of the last occupied shell being even or odd. We propose to detect pairing fluctuations by measuring the density-density correlation function after a ballistic expansion of the gas.     

Bose-einstein condensation in trapped dipolar gases

We discuss Bose-Einstein condensation in a trapped gas of bosonic particles interacting dominantly via dipole-dipole forces. We find that in this case the mean-field interparticle interaction and, hence, the stability diagram are governed by the trapping geometry. Possible physical realizations include ultracold heteronuclear molecules, or atoms with laser induced electric dipole moments.