| The realization of Bose-Einstein condensation (BEC) in dilute atomic gases has enabled numerous fascinating experiments in which fundamental quantum mechanics is studied in a macroscopic and accessible system. Especially the tunability of the strength of the interaction between fermions via Feshbach resonance allows the study of the crossover from a weakly paired Bardeen-Cooper-Schrieffer (BCS) superfluidity to a strongly paired diatomic molecular Bose-Einstein condensate (BEC). There is a general belief that the study of BCS-BEC crossover in the ultracold fermi gases is expected to be helpful for the understanding of pseudogap phenomenon of high-Tc cuprates.To find a theory for BCS-BEC crossover, which can describe the entire regime from the BCS to the BEC limit, is a hot issue of physics for a long time. After the pioneering work of Eagles and Leggett, Nozieres and Schmitt-Rink (NSR) developed a diagrammatic method at finite temperature in the normal phase in 1985. NSR’s success lies in the including particle-particle pairing fluctuation, but there is another type of fluctuation, which is from particle-hole channel first considered by Gorkov-Melik-Barkhudarov (GMB) and also called induced interaction. In the most of studies, the induced interaction in ultracold Fermi gases were confined to the lowest-order. Yu and co-workers went beyond the lowest order and considered the induced interactions from all particle-hole ladder diagrams. However, they considered the extended GMB approximation in the NSR framework which is equivalent to expanding the fermion propagator to the lowest order in self-energy when one calculates the number equation via the fermion propagator. With the belief of the importance of the fluctuation cor-rections in the BCS-BEC crossover region, the non-self-consistent T-matrix approxi-mation (nTMA) framework might be a better choice. In this thesis, we generalize the extended GMB approximation from NSR framework to nTMA framework and calcu-late physical quantities on the basis of this approximation.First, we calculate the transition temperature for the entire BCS-BEC crossover and compare our results with othes. Our result is between that of Yu et al. and that of Tsuchiya et al. based on nTMA framework without considering the induced interac-tion. At unitarity the transition temperature obtained by us is 0.218TF, which is about 90% of that of Tsuchiya et al. without the effect of the extended GMB approxima-tion. In the Bardeen-Cooper-Schrieffer (BCS) limit, the critical temperature is about 0.45TcBCS which is the same as the result of the usual Gorkov and Melik-Barkhudarov (GMB) correction. In the Bose-Einstein condensate (BEC) limit, the effect of the in-duced interaction can be neglected.Secondly, we studied the behavior of single-particle spectral function through which one can calculate almost all important physical quantities. Theorists have antic-ipated that the single-particle spectral function exhibits pseudogap phenomenon above Tc. However, there exists confliction about the existence of pseudogap in strongly in-teracting Fermi gases in experiment recently. In this thesis, we present the spectral function and hence density of states in the normal phase at unitarity including the ex-tended GMB approximation in the nTMA framework. In the numerical results of the spectral weight function in the energy-momentum plane, there are two energy branches near Tc which merge into a single upward branch with increasing temperature. From the results of A(k,ω) vs ω for a given set of wave vectors near kF at Tc, the double-peak structure is found clearly at the transition temperature. A clear depletion is also to be found in DOS around ω= 0. All these indicate the existence of pseudogap phenomenon including the induced interaction.We also obtained the momentum-resolved RF spectra of homogeneous Fermi gas-es and the energy of the Fermi gas at unitarity above Tc with the effect of the induced interaction. The RF spectroscopy experiments on ultracold Fermi gases can provide valuable information on the spectral function. In this thesis, the RF spectrum is ob-tained with the extended GMB approximation in the nTMA framwork. The obtained rf spectra for a homogeneous system show a single peak, which is consistent with ex-periments. Furthermore, compared with experiments, we obtain a more satisfactory result without slightly overestimating the width of the peak. We find there exists up-ward and downward dispersion branches and the downward branch is dominant near Tc. The downward branch indicates the existence of the pseudogap contribution. With increasing temperature, there is only an upward branch left indicating the disappear of pseudogap phenomenon.The energy and the chemical potential of a unitary Fermi gas is also been obtained including the extend-ed GMB approximation within the nTMA framework. Compare-ing with the other theoretical predictions and experimental data, we predicts a higher energy at low temperature, but our result obtains a good agreement with Tokyo experi-ment for temperature between 0.6TFand 0.8TF. |
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