Related spectroscopic probes of ultracold fermi gases and high temperature superconductors

In this thesis, we present a unified understanding of two related but different spectroscopic techniques in two very different strongly correlated systems: radio frequency (RF) spectra in cold Fermi gases and tunneling spectra in the cuprates. These two techniques can probe density of states and measure the energy gap of single particle excitations.;We presume the BCS-BEC crossover theory is applicable both to the cuprates and to ultracold gases. This approach captures the short coherence length physics of the cuprates. Fortunately, experiments in cold gases are able to test the crossover physics in great detail and thereby shed light on the cuprates. BCS theory describes the superfluidity in fermionic systems due to weak attraction. When the attraction is strong, fermions can form tightly bound pairs which behave like composite bosons. At low temperature these tightly bound pairs form a Bose-Einstein condensate (BEC) similar to that in bosonic systems. The BCS-BEC crossover theory provides a smooth connection between these two limits. At finite temperature, the onset of pairing T* and onset of condensation Tc is different due to strong attraction. In this thesis, the contributions of non-condensed pairs or the pairing fluctuations are considered in a manner consistent with the BCS ground state. This will give rise to a pseudogap phase which is important to both cold gases and high temperature superconductivity.;In addition to a comparison between cold gases and the cuprates, in this thesis we present a systematic overview of the theory of RF spectroscopy which has been so successful for the ultracold Fermi gases. This theory also makes it possible to measure the pairing gaps, which are generally different from order parameters. We discuss applications to topical issues such as the effects of traps, population imbalance, final state interactions over the entire range of temperatures, most notably in the context of recent tomographic scans in the population imbalanced gases. We show that this broad range of phenomena can be accommodated within the BCS-Leggett description of BCS-BEC crossover. We discuss a way of exploiting a sum rule to extract the pairing gap from RF spectra.;RF spectroscopy in cold gases is very similar to tunneling spectra in the cuprates except that the former is s-wave pairing and the latter is d-wave pairing. Another closely related condensed matter technique is scanning tunneling microscopy (STM). It can reveal detailed electronic structure of the underlying superconductor. The resulting spatial modulation caused by impurity scattering, also known as quasi-particle interference (QPI) pattern, poses mysterious question such as the dichotomy of the nodal and anti-nodal behavior and the origin of the pseudogap. Our calculations based on crossover theory naturally explain this dichotomy. Our study on the finite temperature evolution of QPI pattern shows that the pseudogap comes from preformed pairs. Furthermore, we find that the intensity of the QPI peaks is profoundly sensitive to superfluid coherence.;We note that the key themes which have emerged in cold gases and cuprates studies involve characterization of the effects of superconducting coherence (in passing from above to below the superfluid transition temperature, Tc). We discuss the possibility to distinguish superfluid coherence through non phase sensitive experiments such as RF and tunneling spectra. In general, there are slope discontinuities in the spectral intensity around Tc, which may be related to the thermodynamic jumps at the transition point.