SU(N) Fermions in a One-Dimensional Harmonic Trap

We conduct a theoretical study of SU(N) fermions confined by a one-dimensional harmonic potential. Firstly, we introduce a new numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the SU(N) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz - derived for a Heisenberg SU(2) spin chain - is extendable to these N-component systems. Lastly, we consider balanced SU(N) Fermi gases that have an equal number of particles in each spin state for N=2, 3, 4. In the weak- and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of N-component fermions may be accurately inferred from the corresponding few-body systems of N distinguishable particles.Comment: 15 pages, 6 figure

High-polarization limit of the quasi-two-dimensional Fermi gas

We demonstrate that the theoretical description of current experiments of quasi-2D Fermi gases requires going beyond usual 2D theories. We provide such a theory for the highly spin-imbalanced quasi-2D Fermi gas. For typical experimental conditions, we find that the location of the recently predicted polaron-molecule transition is shifted to lower values of the vacuum binding energy due to the interplay between transverse confinement and many-body physics. The energy of the attractive polaron is calculated in the 2D-3D crossover and displays a series of cusps before converging towards the 3D limit. The repulsive polaron is shown to be accurately described by a 2D theory with a single interaction parameter.Comment: 7 pages, 6 figures, published versio

Frustrated orbital Feshbach resonances in a Fermi gas

The orbital Feshbach resonance (OFR) is a novel scheme for magnetically tuning the interactions in closed-shell fermionic atoms. Remarkably, unlike the Feshbach resonances in alkali atoms, the open and closed channels of the OFR are only very weakly detuned in energy. This leads to a unique effect whereby a medium in the closed channel can Pauli block, or frustrate, the two-body scattering processes. Here, we theoretically investigate the impact of frustration in the few- and many-body limits of the experimentally accessible three-dimensional $^{173}$Yb system. We find that by adding a closed-channel atom to the two-body problem, the binding energy of the ground state is significantly suppressed, and by introducing a closed-channel Fermi sea to the many-body problem, we can drive the system towards weaker fermion pairing. These results are potentially relevant to superconductivity in solid-state multiband materials, as well as to the current and continuing exploration of unconventional Fermi-gas superfluids near the OFR.Comment: 14 pages, 6 figure

Rydberg exciton-polaritons in a magnetic field

We theoretically investigate exciton-polaritons in a two-dimensional (2D) semiconductor heterostructure, where a static magnetic field is applied perpendicular to the plane. To explore the interplay between the magnetic field and strong light-matter coupling, we employ a fully microscopic theory that explicitly incorporates electrons, holes, and photons in a semiconductor microcavity. Furthermore, we exploit a mapping between the 2D harmonic oscillator and the 2D hydrogen atom that allows us to efficiently solve the problem numerically for the entire Rydberg series as well as for the ground-state exciton. In contrast to previous approaches, we can readily obtain the real-space exciton wave functions and we show how they shrink in size with the increasing magnetic field, which mirrors their increasing interaction energy and oscillator strength. We compare our theory with recent experiments on exciton-polaritons in GaAs heterostructures in an external magnetic field and we find excellent agreement with the measured polariton energies. Crucially, we are able to capture the observed light-induced changes to the exciton in the regime of very strong light-matter coupling where a perturbative coupled oscillator description breaks down. Our work can guide future experimental efforts to engineer and control Rydberg excitons and exciton-polaritons in a range of 2D material

Rydberg Exciton-Polaritons in a Magnetic Field

We theoretically investigate exciton-polaritons in a two-dimensional (2D) semiconductor heterostructure, where a static magnetic field is applied perpendicular to the plane. To explore the interplay between magnetic field and a strong light-matter coupling, we employ a fully microscopic theory that explicitly incorporates electrons, holes and photons in a semiconductor microcavity. Furthermore, we exploit a mapping between the 2D harmonic oscillator and the 2D hydrogen atom that allows us to efficiently solve the problem numerically for the entire Rydberg series as well as for the ground-state exciton. In contrast to previous approaches, we can readily obtain the real-space exciton wave functions and we show how they shrink in size with increasing magnetic field, which mirrors their increasing interaction energy and oscillator strength. We compare our theory with recent experiments on exciton-polaritons in GaAs heterostructures in an external magnetic field and we find excellent agreement with the measured polariton energies. Crucially, we are able to capture the observed light-induced changes to the exciton in the regime of very strong light-matter coupling where a perturbative coupled oscillator description breaks down. Our work can guide future experimental efforts to engineer and control Rydberg excitons and exciton-polaritons in a range of 2D materials.Comment: 17 pages, 11 figure

Spectra of pinned charge density waves with background current

We develop techniques which allow us to calculate the spectra of pinned charge density waves with background current

Bound Chains of Tilted Dipoles in Layered Systems

Ultracold polar molecules in multilayered systems have been experimentally realized very recently. While experiments study these systems almost exclusively through their chemical reactivity, the outlook for creating and manipulating exotic few- and many-body physics in dipolar systems is fascinating. Here we concentrate on few-body states in a multilayered setup. We exploit the geometry of the interlayer potential to calculate the two- and three-body chains with one molecule in each layer. The focus is on dipoles that are aligned at some angle with respect to the layer planes by means of an external eletric field. The binding energy and the spatial structure of the bound states are studied in several different ways using analytical approaches. The results are compared to stochastic variational calculations and very good agreement is found. We conclude that approximations based on harmonic oscillator potentials are accurate even for tilted dipoles when the geometry of the potential landscape is taken into account.Comment: 10 pages, 6 figures. Submitted to Few-body Systems special issue on Critical Stability, revised versio