Thermodynamics of degenerate Fermi gases has been extensively studied through various aspects such as Pauli blocking effects, collective modes, BCS superfluidity, and more. Despite this, multicomponent fermions with imbalanced spin configurations remain largely unexplored, particularly beyond the two-component scenario. In this Letter, we generalize the thermodynamic study of SU(N) fermions to spin-imbalanced configurations based on density fluctuations. Theoretically, we provide closed-form expressions of density fluctuation across all temperature ranges for general spin population setups. Experimentally, after calibrating the measurements with deeply degenerate ^{173}Yb Fermi gases under spin-balanced configurations (N≤6), we examine the density fluctuations in spin-imbalanced systems. Specifically, we investigate two-species and four-species configurations to validate our theoretical predictions. Our analysis indicates that interaction enhancement effects can be significant even in highly spin-imbalanced systems. Finally, as an application, we use this approach to examine the decoherence process. Our Letter provides a deeper understanding of the thermodynamic features of spin-imbalanced multicomponent Fermi gases and opens new avenues for exploring complex quantum many-body systems.
Thermodynamics of degenerate Fermi gases has been extensively studied through various aspects such as Pauli blocking effects, collective modes, BCS superfluidity, and more. Despite this, multicomponent fermions with imbalanced spin configurations remain largely unexplored, particularly beyond the two-component scenario. In this Letter, we generalize the thermodynamic study of SU(N) fermions to spin-imbalanced configurations based on density fluctuations. Theoretically, we provide closed-form expressions of density fluctuation across all temperature ranges for general spin population setups. Experimentally, after calibrating the measurements with deeply degenerate ^{173}Yb Fermi gases under spin-balanced configurations (N≤6), we examine the density fluctuations in spin-imbalanced systems. Specifically, we investigate two-species and four-species configurations to validate our theoretical predictions. Our analysis indicates that interaction enhancement effects can be significant even in highly spin-imbalanced systems. Finally, as an application, we use this approach to examine the decoherence process. Our Letter provides a deeper understanding of the thermodynamic features of spin-imbalanced multicomponent Fermi gases and opens new avenues for exploring complex quantum many-body systems.
Fermionic matter is ubiquitous in nature, from the electrons in metals and semiconductors or the neutrons in the inner crust of neutron stars, to gases of fermionic atoms, like 40K or 6Li that can be created and studied under laboratory conditions. It is especially interesting to study these systems at very low temperatures, where we enter the world of quantum mechanical phenomena. Due to the Fermi-Dirac statistics, a dilute system of spin-polarised fermions exhibits no interactions and can be viewed as an ideal Fermi gas. However, interactions play a crucial role for fermions of several spin species. This thesis addresses several questions concerning interacting Fermi gases, in particular the transition between the normal and the superfluid phase and dynamical properties at higher temperatures. First we will look at the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. This system is particularly interesting as it exhibits universal behaviour. Due to the strong interactions perturbation theory is inapplicable and no exact theoretical description is available. I will describe the Determinant Diagrammatic Monte Carlo algorithm with which the unitary Fermi gas can be studied from first principles. This algorithm fails in the presence of a spin imbalance (unequal number of particles in the two components) due to a sign problem. I will show how to apply reweighting techniques to generalise the algorithm to the imbalanced case, and present results for the critical temperature and other thermodynamic observables at the critical point, namely the chemical potential, the energy per particle and the contact density. These are the first numerical results for the imbalanced unitary Fermi gas at finite temperature. I will also show how temperatures beyond the critical point can be accessed and present results for the equation of state and the temperature dependence of the contact density. At sufficiently high temperatures a semiclassical description captures all relevant physical features of the system. The dynamics of an interacting Fermi gas can then be studied via a numerical simulation of the Boltzmann equation. I will describe such a numerical setup and apply it to study the collision of two spin-polarised fermionic clouds. When the two components are separated in an elongated harmonic trap and then released, they collide and for sufficiently strong interactions can bounce off each other several times. I will discuss the different types of the qualitative behaviour, show how they can be interpreted in terms of the equilibrium properties of the system, and explain how they relate to the coupling between different excitation modes. I will also demonstrate how transport coefficients, for instance the spin drag, can be extracted from the numerical data.
We consider imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mix-tures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species both occupying only a single hyperfine state. In both cases, the number of atoms for each component is allowed to be differ-ent, which leads to a spin imbalance, or spin polarization. Two different atomic species also lead to a mass imbalance. Imbalanced Fermi gases are relevant to condensed-matter physics, nuclear physics and astroparticle physics. They have been studied intensively in recent years, following their experimental realization in ultracold atomic Fermi gases. The experimental control in such a system allows for a systematic study of the equation of state and the phase diagram as a function of temperature, spin polarization and interaction strength. In this re-view, we discuss the progress in understanding strongly-interacting imbalanced Fermi gases, where a main goal is to describe the results of the highly controlled experiments. We start by discussing Feshbach resonances, after which we treat the imbalanced Fermi gas in mean-field theory to give an introduction to the relevant physics. We encounter several unusual superfluid phases, including phase-separation, gapless Sarma superfluidity, and supersolidity. To obtain a more quantitative description of the experiments, we review also more sophisti-cated techniques, such as diagrammatic methods and the renormalization-group theory. We end the review by discussing two theoretical approaches to treat the inhomogeneous imbalanced Fermi gas, namely the Landau-Ginzburg theory and the Bogoliubov-de Gennes approach. Key words:
It is quite common that several different phases exist simultaneously in a system of trapped quantum gases of ultra-cold atoms. One example is the strongly interacting Fermi gas with two imbalanced spin species, which has received a great deal of attention owing to the possible occurrence of exotic superfluid phases. By using novel numerical techniques and algorithms, we self-consistently solve the Bogoliubov–de Gennes equations, which describe Fermi superfluids in the mean-field framework. From this study, we investigate the novel phases of spin-imbalanced Fermi gases and examine the validity of local density approximation (LDA), which is often invoked in the extraction of bulk properties from experimental measurements within trapped systems. We show how the validity of the LDA is affected by the trapping geometry, the number of atoms and the spin imbalance.
The induced intraspecies interactions among the majority species, mediated by the minority species, is computed for a population-imbalanced two-component Fermi gas. Although the Feshbach-resonance mediated interspecies interaction is dominant for equal populations, leading to singlet s-wave pairing, we find that, in the strongly imbalanced regime, the induced intraspecies interaction leads to p-wave pairing and superfluidity of the majority species. Thus, we predict that the observed spin-polaron Fermi-liquid state in this regime is unstable to p-wave superfluidity, in accordance with the results of Kohn and Luttinger, below a temperature that, near unitarity, we find to be within current experimental capabilities. We present possible experimental signatures of the p-wave state using radiofrequency spectroscopy as well as density-density correlations after free expansion.
In this chapter the recent theoretical work on phase transition in imbalanced fermion superfluids is reviewed. The imbalanced systems are those in which the two fermionic species candidate to form pairing have different Fermi surfaces or densities. We consider systems subjected to weak interactions. In this scenario two distinct phase transitions are predicted to occur. A thermodynamical phase transition, induced by the temperature (T), and a quantum phase transition as a function of the increasing chemical potentials asymmetry, that takes place at zero temperature. We also briefly discuss some recent experimental work at non-zero T with imbalanced Fermi gases in cold atomic traps.
Strongly coupled quantum matter displays a rich phenomenology including phase transitions and often unexpected collective behavior. Remarkable advances in experiments with ultracold Fermi gases allow us to gain deep insight into these intriguing systems. Their theoretical description, however, is often challenging as exact analytic solutions are available only in a few special cases, and approximate techniques such as mean-field or perturbation theory are of limited use. Numerical treatment with Monte Carlo (MC) methods has led to profound success in this regard. Unfortunately, for many systems - and especially for asymmetric quantum gases - the infamous sign problem slows progress due to an exponentially scaling of the computational effort with inceasing system size. In this thesis, we set out to explore the rich physics of two-component Fermi gases in the presence of finite spin polarization and/or mass imbalance. To surmount an arising sign problem, we learn from methodological advances made in the field of quantum chromodynamics and further develop these lattice approaches in the context of nonrelativistic Fermi gases. An extensive overview of the numerical methods is presented, including several toy problems to detail the capabilities and shortcomings of the developed approaches. With these tools in hand, we perform extensive benchmarks of the hybrid Monte Carlo method with imaginary asymmetries (iHMC) and the complex Langevin (CL) method, which is based on a complex version of stochastic quantization. Both approaches are shown to yield excellent results for the ground-state energy equation of state of mass-imbalanced Fermi gases in one spatial dimension. Due to its great versatility, the CL method is subsequently employed to study pairing in one-dimensional Fermi gases, for which suitable two-body correlations are computed, revealing unexpected pairing patterns for spin- and mass-imbalanced systems. Another major system of interest in this thesis is the paradigmatic unitary Fermi gas which is investigated at finite temperature and spin polarization. A precise determination of the density equation of state in the normal phase enables us to explore a broad range of thermodynamic properties. We infer valuable information on the finite-temperature phase diagram, such as a flat phase boundary of the normal-to-superfluid transition near the balanced limit and indications for the absence of an extensive pseudogap phase above this transition. The presented results provide experimentally testable ab initio predictions for a range of previously inaccessible thermodynamic quantities.