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.
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.
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 develop an analytical approach for the description of an atomic Bose gas at unitarity. By focusing in first instance on the evaluation of the single-particle density matrix, we derive several universal properties of the unitary Bose gas, such as the chemical potential, the contact, the speed of sound, the condensate density and the effective interatomic interaction. The theory is also generalized to describe Bose gases with a finite scattering length and then reduces to the Bogoliubov theory in the weak-coupling limit.
We develop an analytical approach for the description of the crossover of an atomic Bose gas from small to infinitely large scattering length where the two-body interactions satisfy the unitarity bound. We obtain several properties of the Bose gas as a function of interaction strength, namely the chemical potential, the contact, the speed of sound, the condensate density, the effective interatomic interaction and the three-body recombination rate. Also, the energy dependence of the effective interaction at unitarity and the evolution of the Feshbach bound state are discussed. It is shown how the approach can be systematically improved with renormalization-group methods and how 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.
The quantum many-body problem is at the heart of some of the most formidable open problems in modern physics, such as high-Tc superconductivity or the behaviour of neutron stars. Ultracold atomic systems can now be used to simulate model Hamiltonians of condensed matter or nuclear physics, in very well-controlled environnement. In this thesis, we have developed a general method to probe the thermodynamics of homogeneous quantum systems using trapped atomic gases. These measurements are directly compared to the predictions of theories of the quantum many-body problem. We have applied this technique to the spin-1/2 Fermi gas and the Bose with short-range interactions. Using fermionic 6Li, we explored a part of the wide parameter space by changing the interaction strength, the spin-population imbalance or the temperature of the gas. This system exhibits remarkably rich physics, such as normal/superfluid phase transitions (that can be of thermal or quantum character) or a Fermi liquid-type behaviour of the normal phase. We have also used this method to probe a Bose gas of 7Li atoms close to a Feshbach resonance. We have measured the Equation of State of the Bose gas as a function of interactions at very low temperature. For the first time, we measured quantitatively the Lee-Huang-Yang beyond mean-field correction to the ground-state energy of the system, first predicted in 1957. We compared the experimental results to Quantum Monte-Carlo calculations. We have extended this study using out-of-equilibrium measurements of the Bose gas in the strongly interacting regime, which gives a first hint on the properties of the hypothetical unitary Bose gas.
We argue that the energy of a strongly interacting gas in the unitary limit is parametrized by a universal constant β. For fermions, this parameter is known, but not for bosons. Finding β for bosons is the goal of this thesis. We present the basics of scattering theory, including the s-wave scattering length, which is the characteristic length scale for the interactions at low energies and which goes to infinity at unitarity. Shape and Feshbach resonances are explained. The conventional theory for Bose gases, Bogoliubov theory, is presented, which takes into account quantum fluctuations. It is used to derive identities for the groundstate energy, the condensate fraction and the contact. These are given as expansions in the scattering length, which therefore only hold true for weak interactions. To improve on this, we present an effective action from an atom-molecule theory, which also allows bound states. By a mean-field approach we derive universal identities for the associated energy scales, and in the unitary limit an analytical expression is found for the chemical potential, from which the value β = −0.54 is found. However, this mean-field result is qualitatively not reliable, since quantum depletion is neglected. A new approach is introduced, starting with a Jastrow Ansatz, from which the energy is expressed in the Jastrow function f and radial distribution function g. A cluster expansion is made for g, where a diagrammatic analogy is found. The Hyper-Netted Chain approximation is introduced to calculate g systematically by summing infinitely many diagrams. In HNC/0, we minimize the energy by a variational method, which is based on a well-constructed Ansatz for g. Numerical results using the HNC/0 approximation are given not only for the ground-state energy, but also for the condensate density and the contact. For large scattering lengths the calculations became increasingly less accurate, but the results from Bogoliubov theory are correctly included for small a. An extrapolation for the ground-state energy is made to find β ' −0.20, which is expected to be an upper bound. Moreover, quantum depletion is found to be higher when calculated in HNC/0 for large scattering lengths. Also, it is found that the contact at this value for unitarity remains finite and acquires the value of C ' 10.3n4/3, which is remarkably close to the value for fermions, C ' 11n4/3. Cover image courtesy of [18].