Polariton Spectrum Of Ultra-cold Fermi Gas In The Optical Cavity

The ultra-cold atom quantum gas is an important research direction in the field of atomic molecule and optical physics.Here,the ultra-cold boson atoms which obey Bose-Einstein quantum statistics,can occur phase transition at low temperature and form a Bose-Einstein condensation?BEC?;the ultra-cold Fermi atom gas,obeying Fermi-Dirac statistics,forms Fermi quantum degeneracy at low temperature.In the past twenty years,due to the introduction of Feshbach resonance technology,the scattering length between atoms can be controlled con-tinuously from zero to infinity.The ultra-cold Fermi gas with strong interaction is well studied.Especially for the unitary Fermi gas,whose scattering length is infinity,the atomic spacing becomes the only scale of length.It is of great significance for studying the theory of low temperature and many-body physics of atoms.Moreover,the Fermi gas is an ideal experimental platform for studying high-temperature superconductivity?HTS?,simulating quark-gluon plasma and many-body dynamics due to the controllable properties of temperature,interac-tion between atoms and potential.On the other hand,the study of the interaction between light and matter in quantum optics is usually based on the cavity quantum electrodynamics.By reducing the mode volume of the optical or microwave cavity,the coupling of light field and matter can be greatly enhanced.When the coupling is larger than the dissipation of the material and the cavity,the system achieves the regime of strong coupling.This leads to a series of new quantum effects,such as spontaneous radiative inversion,quantum entanglement,nonclassical field,single photon switch,quantum memory and quantum computation.During the last ten years,the combination of ultra-cold atom gas and cavity quantum electrodynamics has opened up a fascinating field of quantum systems.At such the ultralow temperatures,quantum effects of both the light and the atomic matter field become important.In such a system,the role of the photon is dual.First,it mediates an interaction between the atoms producing new phases of matter,whose dynamics,in turn,backact on the photon field itself.Second,the photon output serves as a nondestructive probe of optical properties such as refraction and absorption of the underlying atomic medium.At present,the combination of Bose-Einstein condensates and cavity QED is realized in experiment and the researches are about the Dicke quantum phase transformation of the superfluid gas in the optical cavity,the self-organization structure of atoms in the optical cavity,and optomechanics,etc.Because of the different quantum statistics and the stability of the strong interaction,the ultra-cold Fermi atom gas with cavity QED can be used to study the Fermi-Hubbard model and the novel phase transition.Although some theorists have done some researches on such systems,such as studying the long-range interaction between atoms,the equilibrium phase diagram of the system and the Fermi radiation jump,etc.The combination of ultra-cold Fermi gas and cavity QED is just beginning in the experiment,and it is very promising to study the novel physics with the system.The main purpose of this thesis is to construct a system of⁶Li degenerate Fermi gas and cavity QED,and to study the dynamics of the system under strong interaction by using feshbach resonance.The main implements are as follows:1.An experimental platform of generated Fermi gas of⁶Li is built.The system includes MOT capture laser system,ultra-high vacuum system(10^-11torr),precision controllable Feshbach magnetic field system,high-power far-detuning dipole trapping system?FORT?and imaging system.We first capture a large number of atoms in a magneto-optical trap.After the cooling phase and optical repumping phase,the atoms are cooled close to the Doppler cooling limit.Then we load atoms in the far-detuning dipole trap.By force evaporation,we finally get a strongly interacting generated Fermi gas.2.We have designed a high fineness FP cavity and completed the locking of frequency chain of the system.The cavity used in the experiment is a macroscopic symmetrical confocal cavity with length 7.5 cm.It is formed by two mirrors and the reflection rate of mirror is 0.9996.The system consists of two cavities.One is in vacuum chamber used to trap atoms so we call it as scientific cavity.The other one is placed outside which we call it as transfer cavity.The method of the frequency chain locking is that we first lock the frequency of laser to the reflection spectrum of scientific cavity to keep the laser resonance with one cavity longitudinal mode.And then we lock the length of science cavity to the transfer cavity.Thus,we not only maintain the stability of the cavity length,but also can adjust the cavity and the atom detuning.3.We study the propagation dynamics of a wavepacket through an optical cavity.Narrow-band and quasi-percussional excitations of a cavity field by a wavepacket are studied.When the spectral width of an incident wavepacket is wider compared with the cavity linewidth in the time domain,the transmitted pulse is adiabatically followed the time evolution of the incoming pulse.For the quasi-percussional excitation of very short pulse in time,the cavity is excited on the time duration of the incoming pulse.The falling edge of the wavepacket loses its original information and experiences a characteristic decay determined by the intracavity photon lifetime.The measured time delay of the pulse peak,in contrast to the constant delay predicted,greatly depends on the pulse width of the incoming wavepacket.We also examine the cavity high-reflected transient spike of optical precursors at the excitation of a step-modulated pulse.4.We realize the combination of ultra-cold Fermi gas and cavity QED.The most important step in the experiment is to transfer the degenerate Fermi gas in the free space into the cavity standing potential.We use the way to transfer.The atom is first prepared in the center of the cavity,then the standing potential is slowly opened.Thus,we load the atom in an optaical cavity.In this paper,we use the classical method of vacuum Rabi splitting to measure the dressed states of the system and study the relationship between splitting peaks and atomic density.In addition,the superradiance phenomenon of Fermi atoms in optical cavity is preliminarily studied by using this system.5.We calculate all-optical control of three-photon spectra and time asym-metry in a strongly coupled cavity polariton system.Manipulating the nature of photons emission is one of the basic tasks in quantum optics and photonics.The ever growing list of quantum applications requires a robust means of controlling the strongly coupled coherent interaction of photons and matter.Here,we inves-tigate three-photon transmission spectra in a strongly coupled cavity polariton system and show that the correlation functions and transmitted photon stream can be optically manipulated.We have achieved strong coupling between the ultra-cold Fermi atom gas and the optical cavity.We studied the Rabi splitting in the cavity quantum electrodynamics,and find that its splitting is not only related to the number of atoms,but also to its density.We also studied the Fermi superradiance phe-nomenon,which lays an important foundation for the realization of optical cavity Fermi superfluid,Fermi-Hubbard model and other novel phase transition in the future.