This thesis studies the theory of quantum gases. We focus on fermionic superfluidity in systems in which the control over the spin degree of freedom has a central role. \nWe explain the microscopic origin of the spin-asymmetric Josephon effect, and propose methods for realizing this effect experimentally in quantum gases. \nWe investigate the phenomenon of fermionic superfluidity in the presence of spin-polarization, with our main focus on the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase. We show that the FFLO pairing mechanism leads to an anisotropic speed of sound which can be used to identify the state in experiments. Using real-space dynamical mean field theory (DMFT), we compute the phase diagram of a trapped, spin-polarized Fermi gas in a dimensional crossover from a 1D to a 3D optical lattice. We find that the FFLO state is realized in a broad region of parameters throughout the crossover while the shell structure of the Fermi gas preceding the transition to the full FFLO state shows a strong dependence on the dimensionality. Finally, we utilize the cluster DMFT method to show that the FFLO state is stable against non-local quantum fluctuations even though these fluctuations do affect the critical temperature of the state.
This thesis studies the theory of quantum gases. We focus on fermionic superfluidity in systems in which the control over the spin degree of freedom has a central role. \nWe explain the microscopic origin of the spin-asymmetric Josephon effect, and propose methods for realizing this effect experimentally in quantum gases. \nWe investigate the phenomenon of fermionic superfluidity in the presence of spin-polarization, with our main focus on the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase. We show that the FFLO pairing mechanism leads to an anisotropic speed of sound which can be used to identify the state in experiments. Using real-space dynamical mean field theory (DMFT), we compute the phase diagram of a trapped, spin-polarized Fermi gas in a dimensional crossover from a 1D to a 3D optical lattice. We find that the FFLO state is realized in a broad region of parameters throughout the crossover while the shell structure of the Fermi gas preceding the transition to the full FFLO state shows a strong dependence on the dimensionality. Finally, we utilize the cluster DMFT method to show that the FFLO state is stable against non-local quantum fluctuations even though these fluctuations do affect the critical temperature of the state.
This is a study of the theory of ultracold atomic Fermi gases, especially in optical lattices, ie. periodic potentials created with laser light. Superfluidity is studied especially in the case of spin population imbalanced Fermi gases and phase diagrams are calculated from mean field theory. The Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase is shown to occupy a larger region of the phase diagram than previously predicted for purely harmonically trapped systems. Methods for detecting the FFLO phase are suggested. As another topic, excitations in a superfluid Fermi gas, their signatures and use in sensor applications are studied. The thesis is divided in chapters in the following way: Chapter 1 is an introduction to the research field of ultracold quantum gases, including references to some of the most important experiments done with the fermionic isotopes. Chapter 2 is an introduction to optical lattices and their major experimental characteristics. Chapter 3 deals with extensions of BCS-theory, mainly the FFLO and the detection of the phases predicted by the extensions. In chapter 4 I discuss excitations in BCS-like states and their applications in sensing electro-magnetic fields. Chapter 5 contains the conclusions.
The Fulde-Ferrell Larkin-Ovchinnikov (FFLO) type superconductor is an exotic form of matter known as a supersolid because it simultaneously supports superfluid and magnetic order. In both condensed matter and ultracold atomic gases, this phase has yet to be conclusively observed despite long interest in both theory and experiment. In one-dimension (1D), unlike expectations for higher dimensions, the FFLO phase is found in a large region of the phase diagram [1]. The effect of quantum and thermal fluctuations, however, are expected to be reduced in higher dimensions. These considerations motivated the proposal to search for FFLO near the 1D-3D dimensional crossover [2], which we have identified and characterized [3]. We confine a spin-imbalanced Fermi gas of lithium 6 to an array of 1D tubes using a 2D optical lattice. We bring the system into the dimensional crossover by increasing the inter-tube tunneling rate and using a Feshbach resonance to tune interactions. The periodicity of these domain walls, which depends on the magnitude of the polarization, is a definitive signature of the FFLO phase. In this work, we develop new experimental and analytical methods to extract periodic signals that, if they indeed are domain walls, lay the foundation for full confirmation of the FFLO phase. [1] Y. A. Liao, A. S. C. Rittner, T. Paprotta, W. Li, G. B. Partridge, R. G. Hulet, S. K. Baur, and E. J. Mueller, “Spin-imbalance in a one-dimensional Fermi gas,” Nature 467, 567 (2010). [2] M. M. Parish, S. K. Baur, E. J. Mueller, and D. A. Huse, “Quasi-One- Dimensional Polarized Fermi Superfluids,” Phys. Rev. Lett. 99, 250403 (2007). [3] M. C. Revelle, J. A. Fry, B. A. Olsen, and R. G. Hulet, “1D to 3D Crossover of a Spin-Imbalanced Fermi Gas,” Physical Review Letters 117 (2016).
The recent development of experimental techniques in ultracold atomic Fermi gases is extremely helpful in the progress of the realization of the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase in quasi-one dimensional systems (Liao et al 2010 Nature 467 567). Due to a Fermi surface nesting, which is enhanced in 1D, the low-dimensional systems are particularly good candidates to find the FFLO phase stable. We investigate the influence of a dimensional crossover (from one dimension (1D) to two dimensions (2D) or three dimensions (3D)) on the stability of the FFLO state in the spin-imbalanced attractive Hubbard model.
Leveraging cutting-edge numerical methodologies, we study the ground state of the two-dimensional spin-polarized Fermi gas in an optical lattice. We focus on systems at high density and small spin polarization, corresponding to the parameter regime believed to be most favorable to the formation of the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. Our systematic study of large lattice sizes, hosting nearly 500 atoms, provides strong evidence of the stability of the FFLO state in this regime, as well as a high-accuracy characterization of its properties. Our results for the density correlation function reveal the existence of density order in the system, suggesting the possibility of an intricate coexistence of long-range orders in the ground state. The ground-state properties are seen to differ significantly from the standard mean-field description, providing a compelling avenue for future theoretical and experimental explorations of the interplay between spin imbalance, strong interactions, and superfluidity in an exotic phase of matter.
We show that the combination of spin-orbit coupling and in-plane Zeeman field in a two-dimensional degenerate Fermi gas can lead to a larger parameter region for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases than that using spin-imbalanced Fermi gases. The resulting FFLO superfluids are also more stable due to the enhanced energy difference between FFLO and conventional Bardeen-Cooper-Schrieffer (BCS) excited states. We clarify the crucial role of the symmetry of Fermi surface on the formation of finite momentum pairing. The phase diagram for FFLO superfluids is obtained in the BCS-BEC crossover region and possible experimental observations of FFLO phases are discussed.
We review the concepts and the present state of theoretical studies of spin-imbalanced superfluidity, in particular the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in the context of ultracold quantum gases. The comprehensive presentation of the theoretical basis for the FFLO state that we provide is useful also for research on the interplay between magnetism and superconductivity in other physical systems. We focus on settings that have been predicted to be favourable for the FFLO state, such as optical lattices in various dimensions and spin-orbit coupled systems. These are also the most likely systems for near-future experimental observation of the FFLO state. Theoretical bounds, such as Bloch's and Luttinger's theorems, and experimentally important limitations, such as finite-size effects and trapping potentials, are considered. In addition, we provide a comprehensive review of the various ideas presented for the observation of the FFLO state. We conclude our review with an analysis of the open questions related to the FFLO state, such as its stability, superfluid density, collective modes and extending the FFLO superfluid concept to new types of lattice systems.