In this thesis we investigate the phase structure of dense quark matter, the structure and stability of neutron and quark stars, and the phases of ultracold fermions in the presence of an artificial spin-orbit coupling. While spanning an extraordinary twenty orders of magnitude in energy scales, these systems exhibit some remarkable similarities including non-perturbative many-body interactions, perfect fluid behavior, the formation of Cooper pairs, and the possibility of BCS-BEC crossovers between weakly and strongly interacting regimes. Moreover, due to phenomenal advancements in laser cooling techniques and the ability to exert an unprecedented level of control over the interactions of ultracold atomic gases, the possibility of using these systems to simulate the complex behavior of systems not easily realized in the laboratory (e.g., non-Abelian gauge fields, quantum chromodynamics) is becoming increasingly real. Despite the widespread success of quantum chromodynamics (QCD), the theory of the strong nuclear force, much remains unknown about the properties of strongly-interacting quark matter. In large part, this continued ignorance is a result of the mathematical intractability of QCD and the limitations of current numerical techniques to very low densities. In the first part of this thesis, in order to gain some insight into the phase structure of dense quark matter we therefore apply an effective field theory which is built upon the symmetries of QCD, the Polyakov–Nambu–Jona-Lasinio (PNJL) model. We construct the QCD phase diagram for two and three quark flavors, giving special attention to the effect of the intermediate strange quark mass on the preferred quark pairing structure at intermediate to high density. In addition, we investigate the impact of the strange quark mass and axial anomaly on a recently proposed low temperature critical point, which may allow for a smooth crossover between hadronic and color superconducting matter. Finally, we investigate the impact of a local color neutrality constraint on phases of asymmetric quark pairing. While the Relativistic Heavy Ion Collider (RHIC) continues to probe the QCD phase diagram at ever-higher temperatures and researchers await the completion of the highly anticipated Facility for Antiprotons and Ion Research (FAIR), the only known “laboratories” in which low temperature dense quark matter is encountered are the cores of neutron stars. Fortunately, the structure of these astrophysical objects is highly dependent upon the properties of the dense matter in their cores, and observations of the mass-radius relationship of these stars impose constraints on the quark matter equation of state. In the second part of this thesis we investigate the possibility of realizing massive neutron stars, such as the recently observed PSRs J1614-2230, J0348+0432, and J1311-3430 with masses of two solar masses or larger, by including a flavor-symmetric vector coupling within an NJL model description of quark matter. By extracting the quark matter equation of state we show that in the absence of diquark pairing, a reasonable magnitude vector repulsion can to stabilize neutron stars against gravitational collapse up to 2.34 solar masses. We also investigate the possibility of realizing stable quark stars with densities much higher than those obtained in conventional neutron stars, but find that stars with central densities much greater than ten times nuclear density are always unstable to gravitational collapse. In the third part of this thesis we study the properties of ultracold atomic gases in the presence of artificial gauge fields. While neutral atoms do not naturally couple to the gauge fields in nature (e.g., magnetic fields, the strong nuclear force), recent advancements in laser techniques have led to the realization of synthetic gauge fields in which ultracold atoms behave as if they were charged. Combined with the Feshbach resonance, through which the two-body interactions which dominate these dilute gases can be arbitrarily tuned, these gases can be used to simulate a wide variety of systems, including those that occur naturally and those that do not. We study the phase structure of a two-species mixture of fermions in the presence of Rashba-Dresselhaus (RD) spin-orbit coupling, which is induced by a specific type of non-Abelian gauge field. In particular, we compute the dependence of the superfluid critical temperature on the RD coupling strength and the tunable two-body interaction. We also investigate the effects of the spin-orbit coupling on the crossover between weakly bound (BCS) atomic pairs and strongly bound (BEC) molecules and the effects of fluctuations on the stability of the superfluid phase.
In this thesis we investigate the phase structure of dense quark matter, the structure and stability of neutron and quark stars, and the phases of ultracold fermions in the presence of an artificial spin-orbit coupling. While spanning an extraordinary twenty orders of magnitude in energy scales, these systems exhibit some remarkable similarities including non-perturbative many-body interactions, perfect fluid behavior, the formation of Cooper pairs, and the possibility of BCS-BEC crossovers between weakly and strongly interacting regimes. Moreover, due to phenomenal advancements in laser cooling techniques and the ability to exert an unprecedented level of control over the interactions of ultracold atomic gases, the possibility of using these systems to simulate the complex behavior of systems not easily realized in the laboratory (e.g., non-Abelian gauge fields, quantum chromodynamics) is becoming increasingly real. Despite the widespread success of quantum chromodynamics (QCD), the theory of the strong nuclear force, much remains unknown about the properties of strongly-interacting quark matter. In large part, this continued ignorance is a result of the mathematical intractability of QCD and the limitations of current numerical techniques to very low densities. In the first part of this thesis, in order to gain some insight into the phase structure of dense quark matter we therefore apply an effective field theory which is built upon the symmetries of QCD, the Polyakov–Nambu–Jona-Lasinio (PNJL) model. We construct the QCD phase diagram for two and three quark flavors, giving special attention to the effect of the intermediate strange quark mass on the preferred quark pairing structure at intermediate to high density. In addition, we investigate the impact of the strange quark mass and axial anomaly on a recently proposed low temperature critical point, which may allow for a smooth crossover between hadronic and color superconducting matter. Finally, we investigate the impact of a local color neutrality constraint on phases of asymmetric quark pairing. While the Relativistic Heavy Ion Collider (RHIC) continues to probe the QCD phase diagram at ever-higher temperatures and researchers await the completion of the highly anticipated Facility for Antiprotons and Ion Research (FAIR), the only known “laboratories” in which low temperature dense quark matter is encountered are the cores of neutron stars. Fortunately, the structure of these astrophysical objects is highly dependent upon the properties of the dense matter in their cores, and observations of the mass-radius relationship of these stars impose constraints on the quark matter equation of state. In the second part of this thesis we investigate the possibility of realizing massive neutron stars, such as the recently observed PSRs J1614-2230, J0348+0432, and J1311-3430 with masses of two solar masses or larger, by including a flavor-symmetric vector coupling within an NJL model description of quark matter. By extracting the quark matter equation of state we show that in the absence of diquark pairing, a reasonable magnitude vector repulsion can to stabilize neutron stars against gravitational collapse up to 2.34 solar masses. We also investigate the possibility of realizing stable quark stars with densities much higher than those obtained in conventional neutron stars, but find that stars with central densities much greater than ten times nuclear density are always unstable to gravitational collapse. In the third part of this thesis we study the properties of ultracold atomic gases in the presence of artificial gauge fields. While neutral atoms do not naturally couple to the gauge fields in nature (e.g., magnetic fields, the strong nuclear force), recent advancements in laser techniques have led to the realization of synthetic gauge fields in which ultracold atoms behave as if they were charged. Combined with the Feshbach resonance, through which the two-body interactions which dominate these dilute gases can be arbitrarily tuned, these gases can be used to simulate a wide variety of systems, including those that occur naturally and those that do not. We study the phase structure of a two-species mixture of fermions in the presence of Rashba-Dresselhaus (RD) spin-orbit coupling, which is induced by a specific type of non-Abelian gauge field. In particular, we compute the dependence of the superfluid critical temperature on the RD coupling strength and the tunable two-body interaction. We also investigate the effects of the spin-orbit coupling on the crossover between weakly bound (BCS) atomic pairs and strongly bound (BEC) molecules and the effects of fluctuations on the stability of the superfluid phase.
We investigate the many-body properties of two distinct degenerate systems with strong interactions, namely that of a quark-gluon plasma and of an atomic Bose gas. In the first part of this thesis, the temperature dependence of the thermodynamic potential of quantum chromodynamics is studied. In particular, the specific heat and the quark effective mass are calculated for imbalanced quark matter in the limit of a large number of quark flavors (large-Nf), which corresponds to the random phase approximation. Also, a generalization of the Landau effective-mass relation for the imbalanced case within relativistic Landau-Fermi liquid theory is derived. The effects of imbalance is expected to have important consequences on the properties of quark matter in the core of neutron stars. In the second part, we develop an analytical approach for the description of the crossover of an atomic Bose gas from small to infinitely large scattering length (unitarity). We obtain several properties of the Bose gas as a function of interaction strength, such as the chemical potential, the contact, the speed of sound, the condensate density, the effective interatomic interaction and the three-body recombination rate. It is shown how the approach can be systematically improved with renormalization-group methods and that it reduces to the Bogoliubov theory in the weak-coupling limit.
The last few years have witnessed a dramatic convergence of three distinct lines of research concerned with different kinds of extreme quantum matter. Two of these involve new quantum fluids that can be studied in the laboratory, ultracold quantum gases and quantum chromodynamics (QCD) plasmas. Even though these systems involve vastly different energy scales, the physical properties of the two quantum fluids are remarkably similar. The third line of research is based on the discovery of a new theoretical tool for investigating the properties of extreme quantum matter, holographic dualties. The main goal of this focus issue is to foster communication and understanding between these three fields. We proceed to describe each in more detail. Ultracold quantum gases offer a new paradigm for the study of nonperturbative quantum many-body physics. With widely tunable interaction strength, spin composition, and temperature, using different hyperfine states one can model spin-1/2 fermions, spin-3/2 fermions, and many other spin structures of bosons, fermions, and mixtures thereof. Such systems have produced a revolution in the study of strongly interacting Fermi systems, for example in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover region, where a close collaboration between experimentalists and theorists—typical in this field—enabled ground-breaking studies in an area spanning several decades. Half-way through this crossover, when the scattering length characterizing low-energy collisions diverges, one obtains a unitary quantum gas , which is universal and scale invariant. The unitary gas has close parallels in the hydrodynamics of QCD plasmas, where the ratio of viscosity to entropy density is extremely low and comparable to the minimum viscosity conjecture, an important prediction of AdS/CFT (see below). Exciting developments in the thermodynamic and transport properties of strongly interacting Fermi gases are of broad interdisciplinary appeal and include new studies of high temperature superfluidity, viscosity, spin-transport, spin-imbalanced mixtures, and three-component gases, this last having a close parallel to color superconductivity. Another system important for the field of strongly-interacting quantum fluids was revealed by analysis of data from the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory. Despite naive expectations based on asymptotic freedom that the deconfinement of quarks and gluons at high temperatures would lead to a weakly-interacting quark gluon plasma (QGP), the system appeared to be quite strongly coupled. Subsequent estimates of the viscosity-to-entropy ratio suggest that the system is tantalizingly close to the postulated bound from AdS/CFT calculations. The field is quite dynamic at the moment; new measurements are expected from upgraded detectors at RHIC, and an entirely new energy regime is being opened up by heavy ion collisions at the Large Hadron Collider (LHC) at CERN. On the theoretical side, much work remains to be done to extract the precise values of the transport coefficients, and to characterize the nature of quasi-particle excitations in the plasma. Finally, holographic dualities such as anti-de Sitter/conformal field theory (AdS/CFT) have opened a new theoretical window on strongly correlated fluids. Holography relates strongly-interacting quantum many-body systems to weakly-coupled semi-classical gravitational systems, replacing quasiparticles with geometry and translating various difficult questions about quantum fluids into simple and calculable geometric exercises. Already, some of the earliest lessons of holography, such as the conjectural bound on the viscosity-to-entropy ratio, have had a considerable impact on the theoretical and experimental study of strongly correlated fluids, from RHIC to ultracold atoms. More recently, the study of holographic superconductors, non-Fermi liquids and unitary quantum gases has touched off a flurry of interest in holography as a toolkit for studying strongly-correlated many-body systems more generally. Holography also allows us to use results from quantum fluids to study classical and quantum gravity; for example, the phase structure of a quantum many-body system translates into a rich classification of black holes in the dual space–time. Given both the rapid progress in applied holography and the exciting developments in ultracold quantum gases and QCD plasmas discussed above, the time is ripe for new collaborations across traditional lines of specialization. This focus issue explores the convergence between three heretofore separate areas of physics. Over forty research groups have contributed original work, and there will be a review article which complements these advances, overviewing them and presenting them in the context of all three fields and their interconnections. The review concludes with a list of open questions. This sets the tone for the present focus issue; namely, interdisciplinary dialog, openness, innovation, and possibility, an emphasis for which New Journal of Physics , an open-access journal of the highest quality, is especially fitted.
This thesis explores certain extraordinary phenomena that occur when a gas of neutral atoms is cooled to the coldest temperatures in the universe --- much colder, in fact, than the electromagnetic radiation that permeates the vacuum of interstellar space. At those extreme temperatures, quantum effects dominate and the collective behaviour of the atoms can have unexpected consequences. For example, Bose-Einstein condensation may occur where the atoms lose their individual identities to coalesce into a macroscopic quantum particle. Although such ultracold atomic gases are interesting in their own right, much of the excitement generated in this field is due to the possibility that studying these gases could shed light on intractable problems in other areas of physics. This is predominantly due to the uniquely high degree of control over various physical parameters that ultracold atomic gases afford to experimentalists. Recent technological advances exploit this advantage to study quantum phenomena in a detail that would not be possible in other systems. For instance, atoms can be made to attract or repel each other, the strength of this interaction can be set to almost any value, and external potentials of various geometries and periodicities can be introduced. In this way, atoms can be used to model phenomena as diverse as the quark-gluon plasmas arising in high-energy particle physics, the colour superfluids conjectured to exist in the core of neutron stars, and the high-temperature superconductivity exhibited by electrons on the ion lattice of certain compounds. Indeed, ultracold atomic gases also have a demonstrated applicability to quantum information and computation. Due to a subtle interplay between electronic and nuclear spins known as the hyperfine interaction, atoms can have either an integer or half-integer total spin quantum number, making them either bosonic or fermionic at low temperatures, respectively. With the exception of chapter 7, the work presented here concerns fermionic atoms in periodic potential formed by interfering laser beams. Indeed, the standing light wave created by the interfering beams gives rise to a lattice potential because of the Stark effect which couples the electronic energy levels of the atoms to the spatially undulating electric field. Furthermore, fermionic atoms can be prepared in two different hyperfine states corresponding to the the \\spin-up" and \\spin-down" quantum states, and as such mimic electrons moving in the lattice structure of solids. This system is well described by the famous Hubbard model which we introduce in chapter 2 and, under certain conditions, undergoes a phase transition into the N eel state which believed to be a precursor to superconductivity in certain high-temperature superconductors. In chapter 3, we calculate precisely how the N eel state may be achieved in an ultracold fermionic atom gas. When the number of spin-up and spin-down atoms is unequal the system becomes spin-canted and exhibits both ferro- and antiferromagnetic characteristics, as we show in chapter 4. We also nd there are topological excitations present in the quantum spin texture known as merons which have never unambiguously been observed before. In order to form a Bose-Einstein condensate, fermionic atoms must rst form pairs, and can do so in two contrasting ways. The relationship between these two qualitatively di erent forms of pairing is described in chapter 5, and we examine how these two types of pairs transform into one another in an optical lattice in chapter 6. Finally, chapter 7 is a detailed eld-theoretic study of pairing as it occurs in an ultracold Bose gas. There, we nd there is an intriguing bosonic analogy of the two forms of fermion pairing and explore the properties of these pairs.
Ultracold dilute atomic gases can be considered as model systems to address some pending problem in Many-Body physics that occur in condensed matter systems, nuclear physics, and astrophysics. We have developed a general method to probe with high precision the thermodynamics of locally homogeneous ultracold Bose and Fermi gases. This method allows stringent tests of recent many-body theories. For attractive spin 1/2 fermions with tunable interaction (6Li), we will show that the gas thermodynamic properties can continuously change from those of weakly interacting Cooper pairs described by BardeenCooper-Schrieffer theory to those of strongly bound molecules undergoing Bose-Einstein condensation. First, we focus on the finite-temperature Equation of State (EoS) of the unpolarized unitary gas. Surprisingly, the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid phase transition. A detailed comparison with theories including Monte-Carlo calculations has revealed some surprises and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids are quantitatively measured for the first time. Despite orders of magnitude difference in density and temperature, our equation of state can be used to describe low density neutron matter such as the outer shell of neutron stars.
We delineate, as an analog of two-flavor dense quark matter, the phase structure of a many-body mixture of atomic bosons and fermions in two internal states with a tunable boson-fermion attraction. The bosons b correspond to diquarks, and the fermions f to unpaired quarks. For weak b-f attraction, the system is a mixture of a Bose-Einstein condensate and degenerate fermions, while for strong attraction composite b-f fermions N, analogs of the nucleon, are formed, which are superfluid due to the N-N attraction in the spin-singlet channel. We determine the symmetry breaking patterns at finite temperature as a function of the b-f coupling strength, and relate the phase diagram to that of dense QCD.
In this thesis, we present theoretical studies on three topics related to multi-component ultracold gases and gauge fields. The first topic that we discuss is artificial gauge fields in ultracold gases. Recently, methods to create artificial gauge fields coupled to neutral ultracold systems using a light-induced Berry's connection have been rapidly developing. These methods are not only capable of creating Abelian gauge fields, such as a conventional magnetic field, but also non-Abelian gauge fields, which opens a way to explore and simulate a wide variety of physical models. In this thesis, we discuss various properties of bosons with Rashba-Dresselhaus spin-orbit coupling, which is a special type of non-Abelian gauge field. We investigate the stability of Bose-Einstein condensates with Rashba-Dresselhaus spin-orbit coupling, and show that the condensates are stable against quantum and thermal fluctuations. We also consider the renormalization of the bare interaction by calculating the t-matrix and its consequence on the ground state phase diagrams. The second topic discussed here is three-component ultracold fermionic systems. It is known that ferromagnetism and superfluidity can coexist at low enough temperature in three-component ultracold fermions. In this thesis, we elucidate how fermionic pairing and population imbalance enhance each other. We also describe a crossover from Bardeen-Cooper-Schrieffer state of fermionic pairing state to the limit of Bose-Einstein condensate of three weakly interacting species of molecules, as the interaction increases. Furthermore, we find an interesting similarity in the free energies between three-component ultracold fermions and quantum chromodynamics. The last topic discussed here is Niels Bohr's double-slit interference gedankenexperiment with charged particles, which argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances. Under these conditions the interference pattern must be suppressed; otherwise quantum mechanics is not consistent. The mechanism for the suppression of the interference pattern is that, as the particle's trajectory is bent in diffraction by the slits, it must radiate and the radiation must carry away phase information. Thus, the radiation field must be a quantized dynamical degree of freedom. We also consider the related setup in which one attempts to determine the path of a massive particle through an interferometer by measuring the Newtonian gravitational potential the particle produces. In this case, we show that the interference pattern would have to be finer than the Planck length and thus indiscernible. Therefore, unlike for the electromagnetic field, Bohr's argument does not imply that the gravitational field must be quantized.