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Kolmen komponentin välinen pariutuminen ultrakylmissä Fermi-kaasuissa

Nummi, Olli Heikki

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

This master's thesis studies the competition and the coexistence of pairing modes in three-component ultracold Fermi gases. The system is considered to be in a homogeneous potential or in a spherically symmetric harmonic trap. In the homogeneous potential different treatments of chemical potentials lead to qualitatively different pairing schemes. In the harmonic trap, local density approximation gives the thermodynamical limit, but Bogoliubov-de Gennes method takes into account finite size effects. Both methods suggest that the coexistence of several pairing gaps only exists in a symmetric case at the thermodynamical limit. In addition, the population imbalances can lead to qualitatively different, possibly non-BCS pairing schemes. The radio-frequency(RF-) spectroscopy is an experimental method for measuring the pairing gap. The RF-spectra reveal the underlying pairing scheme in the three-component system. The coexistence of two pairing gaps can give rise to novel kind of superfluid current flowing between mutually non-paired components. This anomalous current possesses features similar to the Josephson effect, but the phenomenon is qualitatively different and new.

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Työväentutkimus Vuosikirja•May 28, 2009•0 citations
This master's thesis studies the competition and the coexistence of pairing modes in three-component ultracold Fermi gases. The system is considered to be in a homogeneous potential or in a spherically symmetric harmonic trap. In the homogeneous potential different treatments of chemical potentials lead to qualitatively different pairing schemes. In the harmonic trap, local density approximation gives the thermodynamical limit, but Bogoliubov-de Gennes method takes into account finite size effects. Both methods suggest that the coexistence of several pairing gaps only exists in a symmetric case at the thermodynamical limit. In addition, the population imbalances can lead to qualitatively different, possibly non-BCS pairing schemes. The radio-frequency(RF-) spectroscopy is an experimental method for measuring the pairing gap. The RF-spectra reveal the underlying pairing scheme in the three-component system. The coexistence of two pairing gaps can give rise to novel kind of superfluid current flowing between mutually non-paired components. This anomalous current possesses features similar to the Josephson effect, but the phenomenon is qualitatively different and new.
We in this paper investigate the phase diagram associated with the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC) crossover of a three-component ultracold superfluid Fermi gas of different chemical potentials and equal masses in two dimensions. The gap-order parameter and number densities are found analytically by using the functional-path-integral method. The balance of pairing will be broken in the free space due to the unequal chemical potentials. We obtain the same particle-number density and condensed fraction in the BCS-superfluid phase as those in a recent paper [Phys. Rev. A 83, 033630 (2011)] while the Sarma phase of the coexistence of normal and superfluid Fermi gases is characteristic of an inhomogeneous system. The minimum ratio of the BCS-superfluid phase becomes 1/3 in the BCS limit corresponding to the zero ratio in the two-component system in which the critical point of phase separation is ${\ensuremath{\epsilon}}_{B}/{\ensuremath{\epsilon}}_{F}=2$, but it becomes 3 in the three-component case.
This thesis studies radio-frequency spectroscopy of superfluid alkali Fermi gases. Radio-frequency and laser fields provide a coherent and well understood tool for manipulating atomic gases. However, new phenomena are expected and have already been seen experimentally when the alkali atoms become strongly interacting. Here we use a simple perturbative treatment of the atom-rf-field coupling for studying the spectroscopy of a strongly interacting gas. At ultracold temperatures fermionic atoms become paired in analogy to electrons in superconductors. The resulting binding energy, or the pairing gap, can be observed as a shift in the radio-frequency spectrum. With strong interactions, the fermions begin pairing already above the critical superfluid transition temperature. The radio-frequency spectroscopy grants a way to study these fluctuation effects quantitatively. The inhomogeneous trapping potential of the atom cloud also adds its own flavour, resulting in distinct mesoscopic effects in the radio-frequency spectra. Our theoretical models are in very good agreement with the experimental results. First order perturbation theory provides qualitatively correct lineshapes, and our generalised perturbative approach gives quantitatively correct magnitudes for the transfer rates. The inhomogeneity plays an important part also in more exotic systems in which the simple BCS-type pairing of atoms is prevented by polarising the gas. Superfluidity and phase separation in such spin-imbalanced gases has been experimentally observed. We have suggested the use of radio-frequency spectroscopy for observing exotic polarised superfluid states, present at the edges of the atom cloud.
Superconductivity and superfluidity of fermions require, within the BCS theory, matching of the Fermi energies of the two interacting Fermion species. Difference in the number densities of the two species leads either to a normal state, to phase separation, or---potentially---to exotic forms of superfluidity such as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, Sarma state, or breached pair state. We consider ultracold Fermi gases with polarization, i.e., spin-density imbalance. We show that, due to the gases being trapped and isolated from the environment in terms of particle exchange, exotic forms of superfluidity appear as a shell around the Bardeen-Cooper-Schrieffer (BCS) superfluid core of the gas and, for large density imbalance, in the core as well. We obtain these results by describing the effect of the trapping potential by using the Bogoliubov-de Gennes equations. For comparison to experiments, we calculate also the condensate fraction, and show that, in the center of the trap, a polarized superfluid leads to a small dip in the central density difference. We compare the results to those given by local density approximation and find qualitatively different behavior.
Abstract Experiments with ultracold gases on the lattice give the opportunity to realize superfluid fermionic mixtures in a trapping potential. The external trap modifies the chemical potential locally. Moreover, this trap also introduces non-homogeneity in the superconducting order parameter. There are, among other approaches, two methods which can be used to describe the system of two-component mixtures loaded into an optical lattice: the Local Density Approximation (LDA) and the self-consistent Bogoliubov–de Gennes equations. Here, we compare results obtained within these two methods. We conclude that the results can be distinguishable only in the case of a small value of the pairing interaction.
This is a study of ultra-cold Fermi gases in different systems. This thesis is focused on exotic superfluid states, for an example on the three component Fermi gas and the FFLO phase in optical lattices. In the two-components case, superfluidity is studied mainly in the case of the spin population imbalanced Fermi gases and the phase diagrams are calculated from the mean-field theory. Different methods to detect different phases in optical lattices are suggested. In the three-component case, we studied also the uniform gas and harmonically trapped system. In this case, the BCS theory is generalized to three-component gases. It is also discussed how to achieve the conditions to get an SU(3)-symmetric Hamiltonian in optical lattices. The thesis is divided in chapters as follows: Chapter 1 is an introduction to the field of cold quantum gases. In chapter 2 optical lattices and their experimental characteristics are discussed. Chapter 3 deals with two-components Fermi gases in optical lattices and the paired states in lattices. In chapter 4 three-component Fermi gases with and without a harmonic trap are explored, and the pairing mechanisms are studied. In this chapter, we also discuss three-component Fermi gases in optical lattices. Chapter 5 devoted to the higher order correlations, and what they can tell about the paired states. Chapter 6 concludes the thesis.