Over the past decade, ultracold gases have been studied extensively, both theoretically and experimentally. This is due to the discovery that the relevant measure for the interatomic interactions in such systems can be controlled experimentally by simply applying a magnetic field. Consequently, these gases can be conveniently studied in both the weakly and the strongly coupled regime. In particular, it is possible to tune the magnetic field such that the interaction strength between the atoms diverges. This is called the unitarity limit.
Interestingly, at unitarity the system becomes almost scale invariant, which means that the only scales left in the problem are set by the temperature and the density of the gas. The unitary gas then exhibits universal behavior. It therefore constitutes a perfect candidate for the application of the AdS/CFT duality, also known as holography, to a nonrelativistic condensed-matter system. According to this duality, a strongly coupled, scale-invariant system can be described using a dual gravitational model with one additional spatial dimension.
In this thesis we apply the AdS/CFT duality to construct holographic models for ultracold gases at unitarity. To this end, we start by studying properties of a well-known holographic model of a condensed-matter system, namely the holographic superconductor. We then show how we can use a very similar model to describe elementary fermions with a nonzero mass in holography. Subsequently, we study these holographic models in the nonrelativistic limit. We find that the resulting models exhibit thermodynamic properties that are qualitatively similar to those of a unitary Fermi gas. Lastly, we take some first steps towards holographically modelling Bose gases at unitarity. In particular, we show that we can describe massive elementary bosons using AdS/CFT.