Dynamical Properties Of Cavity-assisted Heteronuclear Photoassociation Of Bose-Einstein-condensed Atoms

Compared to atoms, molecules possess morecomplex energy levels. Therefore, molecular BEC has been paid attention to owing to its important application inultraprecise spectroscopy measurement. Photoassociation is an effective way to create molecular BEC. It is more applicable than Feshbach Resonance. Optical cavity provides an access toquantized optical field. Photoassociation assisted by optical cavity has the advantage of selecting photons of particular modes and inhibiting dissociation of molecules. Unlike the homonuclear counterparts which are bosonic, heteronuclear diatomic molecules can either be bosons or fermions. The long-range dipole interaction between heteronuclear molecules have potential application in the field of quantumcomputation.Based on theseadvantages, we proposed cavity-assisted photoassociation of heteronuclear molecular Bose-Einstein condensate in the thesis, investigating thevariation of steady-state solutions of atomic population when experimental parameters are tuned, such as collisional parameter, two-photon detuning and population imbalance between the two atomic components. We found that for zero collision and two-photon detuning, steady-state population for molecules decreases with the increase of cavity driving strength; When driving exceedsa critical value, the system losesits stability. At zero collision, atomic steady-state population declines as the absolute value of two-photon detuning increases; For a relative large collision parameter, opitcal bistability can be triggered by tuning two-photon detuning.We also exhibited the bistable region in the parameter space. Population imbalance between the two atomic components can effectively reduce the unstable region.At the same time, we apply mean-field method to simulate the dynamical process based on the results of steady-state solutions and the final state of evolution agrees with the results of steady-state. To investigate the efficiency of the mean-field method, we introducedtwo other methods, which contain high-order correlation. One is Quantum Self-consistent Method, which contains vacuum fluctuation of cavity and effectively describes the evolution of system without cavity driving.We compared the three methods with zero collision and two-photon detuning, and found that for big atom population, imbalance between the two atomic components, mean-field method is convergent to those high-correlation methods, which means that it is a good approximation.