Study Of Higgs Mode And Quantum Transport In BCS-BEC Crossover

Recent years the huge progress in ultracold atoms has make it be the ideal platform for studying varies quantum phenomenon.Especially,using the magnetic Feshbach resonance technique one can control the attractive interaction between two atoms,thus the crossover from condensation of large scaled Cooper pair to Bose-Einstein condensation of the tight-bound molecular.Based on the symmetry analysis,the effective theory of the BCS limit has the lorentz invariance,while the opposite limit,the theory is Galilean invariance.In many body physics,the Higgs mode which is analogy of Higgs boson in high energy physics will emerge in the theory with lorentz invariance after spontaneous symmetry broken.Therefore,the BCS-BEC crossover can be taken as a natural platform to investigate the behavior of Higgs mode during the lost of the lorentz invariance.Furthermore,we can also study the quantum transport between two reservoirs filled with degenerate fermi gas through quantum point contact.So the main purpose of the thesis are to reveal the observability of Higgs mode and transport property in the BCS-BEC crossover at zero and finite temperature.In 2017,Esslinger group report an anomalous conductance in the BCS-BEC crossover via wide Feshbach resonance on PANS.Aa a consequence,three theory group attack this problem independently.Boyang Liu and Ueda all give their sup-port for the preformed pair,the difference is that Boyang's calculation is based on the narrow Feshbach resonance where there is bound state in the close channel.Another explanation is given by Demler,arguing that the multiple Andreev reflec-tion occur in the superfluid region should be responsible for the anomaly.Thus as warm up,we will recalculate the conductance in the BCS-BEC crossover at above transition temperature,showing how the fluctuation do impact on it.Due to the debate on whether the fluctuation or the multiple Andreev reflection is dominant below but near transition temperature,only above transition temperature case is discussed.Esllinger group study the thermoelectricity in the weak and strong interaction fermi gas in 2013 and 2018 respectively.They observed that the figure of merit ZT,measuring the efficiency of energy conversion,would increase when the system is tuned from the ballistic transport to diffusive transport.Following this work,the same group investigate the thermoelectricity in the unitary fermi gas,finding the violation of Wiedemann-Franz law obeyed by Landau-Fermi liquid in low temperature.Actually,our calculation on the lorentz number also reveal the law broken in the strong fluctuation region.Our method is similar with that in chapter three.The violation of the Wiedemann-Franz law hint the behavior of non-fermi liquid.Fixed the temperature ratio T/T₀=1.1 where T₀is transition temperature at unitary,the figure of merit grows monotonously from BCS to BEC.The behavior of Higgs mode in BCS-BEC crossover is reported in chapter five.At zero temperature,the signal of it becomes weaker and weaker,and finally it will diminish in the BEC region,lost in the two-fermion continuum.The interaction strength is chosen at 1/a_sk_F,where the current ultracold atoms experiments can reach,and our calculation shows the signal of Higgs mode can be detected.