The BCS-BEC Crossover

This chapter presents the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly-correlated pairs of fermions to the Bose-Einstein condensation (BEC) of diatomic molecules in the atomic Fermi gas. Our aim is to provide a pedagogical review of the BCS-BEC crossover, with an emphasis on the basic concepts, particularly those that are not generally known or are difficult to find in the literature. We shall not attempt to give an exhaustive survey of current research in the limited space here; where possible, we will direct the reader to more extensive reviews.Comment: 19 pages, 6 figures. This article will be published as Chapter 9 in "Quantum gas experiments - exploring many-body states", edited by P. Torma and K. Sengstock, Imperial College Press, London, to be published 201

Three-body correlations in a two-dimensional SU(3) Fermi gas

We consider a three-component Fermi gas that has SU(3) symmetry and is confined to two dimensions (2D). For realistic cold atomic gas experiments, we show that the phase diagram of the quasi-2D system can be characterized using two 2D scattering parameters: the scattering length and the effective range. Unlike the case in 3D, we argue that three-body bound states (trimers) in the quasi-2D system can be stable against three-body losses. Using a low-density expansion coupled with a variational approach, we investigate the fate of such trimers in the many-body system as the attractive interactions are decreased (or, conversely, as the density of particles is increased). We find that remnants of trimers can persist in the form of strong three-body correlations in the weak-coupling (high-density) limit.Comment: 13 pages, 4 figure

Dipolar fermions in a multilayer geometry

We investigate the behavior of identical dipolar fermions with aligned dipole moments in two-dimensional multilayers at zero temperature. We consider density instabilities that are driven by the attractive part of the dipolar interaction and, for the case of bilayers, we elucidate the properties of the stripe phase recently predicted to exist in this interaction regime. When the number of layers is increased, we find that this "attractive" stripe phase exists for an increasingly larger range of dipole angles, and if the interlayer distance is sufficiently small, the stripe phase eventually spans the full range of angles, including the situation where the dipole moments are aligned perpendicular to the planes. In the limit of an infinite number of layers, we derive an analytic expression for the interlayer effects in the density-density response function and, using this result, we find that the stripe phase is replaced by a collapse of the dipolar system.Comment: 9 pages, 8 figure

Density-wave phases of dipolar fermions in a bilayer

We investigate the phase diagram of dipolar fermions with aligned dipole moments in a two-dimensional (2D) bilayer. Using a version of the Singwi-Tosi-Land-Sjolander scheme recently adapted to dipolar fermions in a single layer [M. M. Parish and F. M. Marchetti, Phys. Rev. Lett. 108, 145304 (2012)], we determine the density-wave instabilities of the bilayer system within linear response theory. We find that the bilayer geometry can stabilize the collapse of the 2D dipolar Fermi gas with intralayer attraction to form a new density wave phase that has an orientation perpendicular to the density wave expected for strong intralayer repulsion. We thus obtain a quantum phase transition between stripe phases that is driven by the interplay between strong correlations and the architecture of the low dimensional system.Comment: 5 pages, 3 figure

Microscopic description of exciton-polaritons in microcavities

We investigate the microscopic description of exciton-polaritons that involves electrons, holes and photons within a two-dimensional microcavity. We show that in order to recover the simplified exciton-photon model that is typically used to describe polaritons, one must correctly define the exciton-photon detuning and exciton-photon (Rabi) coupling in terms of the bare microscopic parameters. For the case of unscreened Coulomb interactions, we find that the exciton-photon detuning is strongly shifted from its bare value in a manner akin to renormalization in quantum electrodynamics. Within the renormalized theory, we exactly solve the problem of a single exciton-polariton for the first time and obtain the full spectral response of the microcavity. In particular, we find that the electron-hole wave function of the polariton can be significantly modified by the very strong Rabi couplings achieved in current experiments. Our microscopic approach furthermore allows us to properly determine the effective interaction between identical polaritons, which goes beyond previous theoretical work. Our findings are thus important for understanding and characterizing exciton-polariton systems across the whole range of polariton densities.Comment: 14 pages, 5 figure

Efimov trimers under strong confinement

The dimensionality of a system can fundamentally impact the behaviour of interacting quantum particles. Classic examples range from the fractional quantum Hall effect to high temperature superconductivity. As a general rule, one expects confinement to favour the binding of particles. However, attractively interacting bosons apparently defy this expectation: while three identical bosons in three dimensions can support an infinite tower of Efimov trimers, only two universal trimers exist in the two dimensional case. We reveal how these two limits are connected by investigating the problem of three identical bosons confined by a harmonic potential along one direction. We show that the confinement breaks the discrete Efimov scaling symmetry and destroys the weakest bound trimers. However, the deepest bound Efimov trimer persists under strong confinement and hybridizes with the quasi-two-dimensional trimers, yielding a superposition of trimer configurations that effectively involves tunnelling through a short-range repulsive barrier. Our results suggest a way to use strong confinement to engineer more stable Efimov-like trimers, which have so far proved elusive.Comment: 8 pages, 4 figures. Typos corrected, published versio