Theja N. De Silva

Breathing mode frequencies of a rotating Fermi gas in the BCS-BEC crossover region

We study the breathing mode frequencies of a rotating Fermi gas trapped in a harmonic plus radial quartic potential. We find that as the radial anharmonicity increases, the lowest order radial mode frequency increases while the next lowest order radial mode frequency decreases. Then at a critical anharmonicity, these two modes merge and beyond this merge the cloud is unstable against the oscillations. The critical anharmonicity depends on both rotational frequency and the chemical potential. As a result of the large chemical potential in the BCS regime, even with a weak anharmonicity the lowest order mode frequency increases with decreasing the attractive interaction. For large enough anharmonicities in the weak coupling BCS limit, we find that the excitation of the breathing mode frequencies make the atomic cloud unstable.

Theory of the normal-superfluid interface in population-imbalanced Fermi gases

We present a series of theoretical studies of the boundary between a superfluid and normal region in a partially polarized gas of strongly interacting fermions. We present mean-field estimates of the surface energy in this boundary as a function of temperature and scattering length. We discuss the structure of the domain wall, and use a previously introduced phenomonological model to study its influence on experimental observables. Our microscopic mean-field calculations are not consistent with the magnitude of the surface tension found from our phenomonological modelling of data from the Rice experiments. We conclude that one must search for novel mechanisms to explain the experiments.

Collective oscillations of a Fermi gas near a Feshbach resonance

A sum rule approach is used to calculate the zero temperature oscillation frequencies of a two component trapped atomic Fermi gas in the Bardeen, Cooper, and Schrieffer-Bose Einstein condensation crossover region. These sum rules are evaluated using a local density approximation which explicitly includes Feshbach molecules. Breathing modes show nonmonotonic behavior as a function of the interaction strength, while quadrupole modes are insensitive to interactions for both spherically symmetric and axially symmetric traps. Quantitative agreement is found with experiments on atomic {sup 6}Li systems and with other theoretical approaches.

Phase diagram of two-component dipolar fermions in one-dimensional optical lattices

Abstract We theoretically map out the ground state phase diagram of interacting dipolar fermions in one-dimensional lattice. Using a bosonization theory in the weak coupling limit at half filing, we show that one can construct a rich phase diagram by changing the angle between the lattice orientation and the polarization direction of the dipoles. In the strong coupling limit, at a general filing factor, we employ a variational approach and find that the emergence of a Wigner crystal phases. The structure factor provides clear signatures of the particle ordering in the Wigner crystal phases.

Compressibility and entropy of cold fermions in one-dimensional optical lattices

We calculate several thermodynamic quantities for repulsively interacting one-dimensional fermions. We solve the Hubbard model at both zero and finite temperatures using the Bethe-ansatz method. For arbitrary values of the chemical potential, we calculate the particle number density, the double occupancy, various compressibilities, and the entropy as a function of temperature and interaction. We find that these thermodynamic quantities show a characteristic behavior so that measurements of these quantities can be used as a detection of temperature, the metal-insulator transition, and metallic and insulating phases in the trap environment. Further, we discuss an experimental scheme to extract these thermodynamic quantities from the column density profiles. The entropy and the compressibility of the entire trapped atomic cloud also reveal characteristic features indicating whether insulating and/or metallic phases coexist in the trap.

Fermionic superfluid properties in a one-dimensional optical lattice

We discuss various superfluid properties of a two-component Fermi system in the presence of a tight one-dimensional periodic potential in a three-dimensional system. We use a zero temperature mean field theory and derive analytical expressions for the Josephson current, the sound velocity and the center of mass oscillations in the BCS-Bose Einstein condensation crossover region.

Population imbalanced Fermi gases in quasi two dimensions

We study s-wave pairing of population imbalanced Fermi atoms in quasi two dimensions using a mean-field theory. At zero temperature, we map out the phase diagram in the entire Bardeen, Cooper and Schrieffer?Bose?Einstein condensation (BCS?BEC) crossover region by investigating the effect of weak atom tunnelling between layers. We find that the superfluid phase stabilizes as one decreases the atom tunnelling between layers. This allows one to control the superfluid?normal first-order phase transition by tuning a single experimental parameter. Further, we find that a tunnelling induced polarized superfluid phase appears in a narrow parameter region in the BEC regime. At finite temperatures, we use a Landau?Ginzberg functional approach to investigate the possibility of a spatially inhomogeneous Fulde?Ferrel?Larkin?Ovchinnikov (FFLO) phase in the weakly interacting BCS limit near the tricritical point of spatially homogenous superfluid, FFLO and normal phases. We find that the normal?FFLO phase transition is the first-order transition as opposed to the continuous transition predicted in zero-temperature theories.

An effective mean field theory for the coexistence of anti-ferromagnetism and superconductivity: Applications to iron-based superconductors and cold Bose–Fermi atomic mixtures

Abstract We study an effective fermion model on a square lattice to investigate the cooperation and competition of superconductivity and anti-ferromagnetism. In addition to particle tunneling and on-site interaction, a bosonic excitation mediated attractive interaction is also included in the model. We assume that the attractive interaction is mediated by spin fluctuations and excitations of Bose–Einstein condensation (BEC) in electronic systems and Bose–Fermi mixtures on optical lattices, respectively. Using an effective mean-field theory to treat both superconductivity and anti-ferromagnetism at equal footing, we study a single effective model relevant for both systems within the Landau energy functional approach and a linearized theory. Within our approaches, we find possible co-existence of superconductivity and anti-ferromagnetism for both electronic and cold-atomic models. Our linearized theory shows while spin fluctuations favor d-wave superconductivity and BEC excitations favor s-wave superconductivity.

An effective series expansion to the equation of state of unitary Fermi gases

Using universal properties and a basic statistical mechanical approach, we propose a general equation of state for unitary Fermi gases. The universal equation of state is written as a series solution to a self consistent integral equation where the general solution is a linear combination of Fermi functions. First, by truncating our series solution to four terms with already known exact theoretical inputs at limiting cases, namely the first \emph{three} virial coefficients and using the Bertsch parameter as a free parameter, we find a good agreement with experimental measurements in the entire temperature region in the normal state. This analytical equation of state agrees with experimental data up to the fugacity

Thermodynamic properties of universal Fermi gases

z = 18