Superfluidity is perhaps one of the most remarkable observed macroscopic quantum effect. Superfluidity appears when a macroscopic number of particles occupies a single quantum state. Using modern experimental techniques one dark solitons) and vortices. There is a large literature on theoretical work studying the properties of such solitons using semiclassical methods. This thesis describes an alternative method for the study of superfluid solitons. The method used here is a holographic duality between a class of quantum field theories and gravitational theories. The classical limit of the gravitational system maps into a strong coupling limit of the quantum field theory. We use a holographic model of superfluidity to study solitons in these systems. One particularly appealing feature of this technique is that it allows us to take into account finite temperature effects in a large range of temperatures.
Superfluidity is perhaps one of the most remarkable observed macroscopic quantum effect. Superfluidity appears when a macroscopic number of particles occupies a single quantum state. Using modern experimental techniques one dark solitons) and vortices. There is a large literature on theoretical work studying the properties of such solitons using semiclassical methods. This thesis describes an alternative method for the study of superfluid solitons. The method used here is a holographic duality between a class of quantum field theories and gravitational theories. The classical limit of the gravitational system maps into a strong coupling limit of the quantum field theory. We use a holographic model of superfluidity to study solitons in these systems. One particularly appealing feature of this technique is that it allows us to take into account finite temperature effects in a large range of temperatures.
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.
A pioneering treatise presenting how the new mathematical techniques of holographic duality unify seemingly unrelated fields of physics. This innovative development morphs quantum field theory, general relativity and the renormalisation group into a single computational framework and this book is the first to bring together a wide range of research in this rapidly developing field. Set within the context of condensed matter physics and using boxes highlighting the specific techniques required, it examines the holographic description of thermal properties of matter, Fermi liquids and superconductors, and hitherto unknown forms of macroscopically entangled quantum matter in terms of general relativity, stars and black holes. Showing that holographic duality can succeed where classic mathematical approaches fail, this text provides a thorough overview of this major breakthrough at the heart of modern physics. The inclusion of extensive introductory material using non-technical language and online Mathematica notebooks ensures the appeal to students and researchers alike.
In 1995 two different research groups observed for the first time the Bose-Einstein condensation (BEC) in ultracold gases. When the confining magnetic trap was turned off the gas was left free to expand, and the velocity of the particles showed a clear peak: most of the particles were occupying the same single particle state, the one of lowest energy. The Bose-Einstein condensation had been predicted in 1925 by Einstein, written by inspiration of a work on the statistic of the photons by Bose (1924). In this work Bose described the behavior of an ensemble of photons, treating them as massless particles, with no number conservation associated. Einstein extended this approach to particles with a mass and with fixed number, creating what is now called the Bose-Einstein distribution. The particles that follow such a description are called ``bosons'', as opposed to the ``fermions'' of the Fermi-Dirac statistics. Einstein predicted that in a gas of bosons - under a critical temperature - a finite fraction of the total number of particles would have been in the ground state, and act as a single entity. This amusing theoretical discovery found its utility a few years later. In the late thirties, new techniques allowed to cool Helium-4 at few Kelvins above the absolute zero. The properties of the resulting liquid were a puzzlement to the scientific community: among others, it could flow without experiencing friction. The liquid was called a ``superfluid''. A first explanation was given by London in 1938, which linked the superfluid behavior to the presence of a BEC among the bosonic Helium particles. The fermions cannot condense by themselves. On the other hand, they can form bound pairs and act as bosons, as it happens in a metal at low temperature. Using this approach, in 1957 Bardeen, Cooper and Schrieffer created a successful model of superconductivity by describing a superconductor as a superfluid in a charged system. During the course of these years we explored the superfluid properties of Bosons and Fermions in different settings. The original contributions of the thesis are described starting from the third chapter, where we speak about the generation and stability of solitons in a periodic optical lattices, both fixed or in motion. In the fourth chapter we study the generation of giant vortices in cold fermions, by using a generalized hydrodynamical approach. In chapter 5 we study the effect of a quasiperiodic lattice and the glassy phase it produces on a gas of bosons. Finally, we study the interaction of normal matter and superfluids with gravitational waves. While this interaction is seen to be extremely small, we believe that the resulting formalism is interesting by itself.
A tour guide of holographic matter A quake is rumbling through the core of physics. Suddenly apparently unrelated areas appear to have a common ground, showing an eerie capacity to fertilise each other. In physics such occasions are invariably propelled by novel mathematical machinery and the present case is no exception. This new mathematical contraption is “holographic duality” (or “anti-de Sitter/conformal field theory correspondence”), which was originally discovered in string theory in the 1990s. Until recently its use was limited to the historic scope of string theory – particle physics and quantum gravity. At a breathtaking pace it has since rolled out over many of the subject areas of modern fundamental physics, even yielding new insights into old subjects such as the nineteenth-century theory of hydrodynamics. Several books of this kind could be written, and are being written, highlighting how anti-de Sitter/conformal field theory (AdS/CFT) impacts on various fields in physics. This book will focus on a prominent area where the developments have been particularly stunning. This is the application to equilibrium condensed matter physics. This started in 2007, and in a matter of a few years condensed matter theory was rewritten in a different mathematical language. This language is the one that one would perhaps least expect: general relativity. On its own a rewriting of condensed matter might not sound like a great advance, no matter how unconventional the language. However, the correspondence makes it possible to explore regimes of quantum many-body physics that are completely inaccessible with conventional techniques. In particular we refer to non-Fermi-liquid states of matter formed in finite-density systems of strongly interacting fermion systems. The holographic mathematics here becomes particularly expressive, suggesting that a general principle of a new kind is at work. It appears that this principle relates to the physics of compressible quantum matter: the notion that the nature of this state of matter is governed by a macroscopic quantum entanglement involving allof its constituents. This discovery is not just remarkable on its own. “Holographic strange matter” also has tantalisingly suggestive resemblances to the mysterious phenomena observed experimentally in strongly interacting electron systems that have been realised in special materials such as the high-T c superconductors. First seen around thirty years ago, these have defied any reasonable explanation despite countless attempts resting on the available mathematical techniques.
By holographic duality, we identify a novel dynamical phase transition which results from the temperature dependence of nonequilibrium dynamics of dark solitons in a superfluid. For a nonequilibrium superfluid system with an initial density of dark solitons, there exists a critical temperature T_{d}, above which the system relaxes to equilibrium by producing sound waves, while below which it goes through an intermediate phase with a finite density of vortex-antivortex pairs. In particular, as T_{d} is approached from below, the density of vortex pairs scales as (T_{d}-T)^{γ} with the critical exponent γ=1/2.
By holographic duality, we identify a novel dynamical phase transition which results from the temperature dependence of non-equilibrium dynamics of dark solitons in a superfluid.For a non-equilibrium superfluid system with an initial density of dark solitons, there exists a critical temperature Td,above which the system relaxes to equilibrium by producing sound waves, while below which it goes through an intermediate phase with a finite density of vortex-antivortex pairs. In particular, as Td is approached from below, the density of vortex pairs scales as (Td−T)γ with the critical exponent γ=1/2.