We investigate the stability of the Sarma phase in two-component fermion systems in three spatial dimensions. For this purpose we compare strongly-correlated systems with either relativistic or non-relativistic dispersion relation: relativistic quarks and mesons at finite isospin density and spin-imbalanced ultracold Fermi gases . Using a Functional Renormalization Group approach, we resolve fluctuation effects onto the corresponding phase diagrams beyond the mean-field approximation. We find that fluctuations induce a second-order phase transition at zero temperature, and thus a Sarma phase, in the relativistic setup for large isospin chemical potential. This motivates the investigation of the cold atoms setup with comparable mean-field phase structure, where the Sarma phase could then be realized in experiment. However, for the non-relativistic system we find the stability region of the Sarma phase to be smaller than the one predicted from mean-field theory. It is limited to the BEC side of the phase diagram, and the unitary Fermi gas does not support a Sarma phase at zero temperature. Finally, we propose an ultracold quantum gas with four fermion species that has a good chance to realize a zero-temperature Sarma phase.
We investigate the stability of the Sarma phase in two-component fermion systems in three spatial dimensions. For this purpose we compare strongly-correlated systems with either relativistic or non-relativistic dispersion relation: relativistic quarks and mesons at finite isospin density and spin-imbalanced ultracold Fermi gases . Using a Functional Renormalization Group approach, we resolve fluctuation effects onto the corresponding phase diagrams beyond the mean-field approximation. We find that fluctuations induce a second-order phase transition at zero temperature, and thus a Sarma phase, in the relativistic setup for large isospin chemical potential. This motivates the investigation of the cold atoms setup with comparable mean-field phase structure, where the Sarma phase could then be realized in experiment. However, for the non-relativistic system we find the stability region of the Sarma phase to be smaller than the one predicted from mean-field theory. It is limited to the BEC side of the phase diagram, and the unitary Fermi gas does not support a Sarma phase at zero temperature. Finally, we propose an ultracold quantum gas with four fermion species that has a good chance to realize a zero-temperature Sarma phase.
We investigate the phase structure of spin-imbalanced unitary Fermi gases beyond mean-field theory by means of the functional renormalization group. In this approach, quantum and thermal fluctuations are resolved in a systematic manner. The discretization of the effective potential on a grid allows us to accurately account for both first- and second-order phase transitions that are present on the mean-field level. We compute the full phase diagram in the plane of temperature and spin imbalance and discuss the existence of other conjectured phases such as the Sarma phase and a precondensation region. In addition, we explain on a qualitative level how we expect that in situ density images are affected by our findings and which experimental signatures may potentially be used to probe the phase structure.
Strongly correlated fermionic many-body systems are ubiquitous in nature. Their theoretical description poses challenging problems which are further complicated when imbalances in, e.g., the particle numbers of the involved species or their masses are introduced. In this thesis, a number of different approaches is developed and applied in order to obtain predictions for physical observables of such systems that mutually support and confirm each other. In a first step, analytically well-founded mean-field analyses are carried through. One- and three-dimensional ultracold Fermi gases with spin and mass imbalance as well as Gross-Neveu and NJL-type relativistic models at finite baryon chemical potential are investigated with respect to their analytic properties in general and the occurrence of spontaneous breaking of translational invariance in particular. Based on these studies, further methods are devised or adapted allowing for investigations also beyond the mean-field approximation. Lattice Monte Carlo simulations with imaginary imbalance parameters are employed to surmount the infamous sign problem and compute the equation of state of the respective unitary Fermi gases. Moreover, in-medium two-body analyses are used to confirm and explain the characteristics of inhomogeneously ordered phases. Finally, functional RG methods are applied to the unitary Fermi gas with spin and mass imbalance. Besides quantitatively competitive predictions for critical temperatures for the superfluid state, strong hints on the stability of inhomogeneous phases with respect to order parameter fluctuations in the regime of large mass imbalance are obtained. Combining the findings from these different theoretical studies suggests the possibility to find such phases in experiments presently in preparation.
We investigate thermodynamics and phase structure of ultracold Fermi gases, which can be realized and measured in the laboratory with modern trapping techniques. We approach the subject from a both theoretical and experimental perspective. Central to the analysis is the systematic comparison of the BCS-BEC crossover of two-component fermions in both three and two dimensions. A dimensional reduction can be achieved in experiments by means of highly anisotropic traps. The Functional Renormalization Group (FRG) allows for a description of both cases in a unified theoretical framework. In three dimensions we discuss with the FRG the influence of high momentum particles onto the density, extend previous approaches to the Unitary Fermi Gas to reach quantitative precision, and study the breakdown of superfluidity due to an asymmetry in the population of the two fermion components. In this context we also investigate the stability of the Sarma phase. For the two-dimensional system scattering theory in reduced dimension plays an important role. We present both the theoretically as well as experimentally relevant aspects thereof. After a qualitative analysis of the phase diagram and the equation of state in two dimensions with the FRG we describe the experimental determination of the phase diagram of the two-dimensional BCS-BEC crossover in collaboration with the group of S. Jochim at PI Heidelberg.
Motivated by potential realizations in cold-atom or cold-molecule systems, we have performed quantum Monte Carlo simulations of two-component gases of fermions in two dimensions with hard-core interactions. We have determined the gross features of the zero-temperature phase diagram by investigating the relative stabilities of paramagnetic and ferromagnetic fluids and crystals. We have also examined the effect of including a pairwise, long-range ${r}^{\ensuremath{-}3}$ potential between the particles. Our most important conclusion is that there is no region of stability for a ferromagnetic fluid phase, even if the long-range interaction is present. We also present results for the pair-correlation function, static structure factor, and momentum density of two-dimensional hard-core fluids.
We investigate the temperature effects in an imbalanced superfluid atomic Fermi gas. We consider a bilayer system of two-component dipolar fermionic atoms with one layer containing atoms of one component and the other layer the atoms of other component with an imbalance between the populations of the two components. This imbalance results in uniform and nonuniform superfluid phases such as phase-separated BCS, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma and normal Fermi liquid phases for different system parameters. Using the mean-field BCS theory together with the superfluid mass-density criterion we classify different phases in thermodynamic phase diagram. Our results indicate that for a dipolar Fermi system the Sarma phase is stable for large imbalance at finite temperature below the critical temperature, and the FFLO phase is stable for intermediate imbalance on the BCS side of a BCS-BCE crossover. The phase diagram in the temperature and population imbalance plane indicate three Lifshitz points: one corresponding to coexistance of BCS, FFLO and normal Fermi liquid phase while the other two correspond to the coexistance of the Sarma phase, FFLO phase and normal Fermi phase for dipolar interactions.
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.