The Study Of Ultrafast Dynamics In Bose-einstein Condensate

Bose-Einstein condensation(BEC)as a peculiar macroscopic quantum phenomena,since its first realization in dilute alkali atom gas in 1995,it has became an important field of physics research.Due to its intrinsic nonlinearity,overall quantum coherence and highly experimental controllability,it plays an important role in quantum information,many-body physics and complex nonlinear dynamic research.In this thesis,we mainly studied the phase fluctuations induced by time-dependent trapping potential in BEC,the groundstate phase diagram of harmonic potential trapped Rashba spinorbit coupling(SOC)BEC and the related quantum phase transition between different groundstates,the dynamics of soliton in spinor BEC under the influence of spin-orbit coupling interaction.In Chapter 1,we give a brief overview of the theory of BEC,the phase transition of BEC in ideal Bose gas and the mean field theory of dilute interacting Bose gas have been included,the Bogoliubov spectrum of dilute Bose gas has also been calculated.In addition,we also give a brief introduction to the theory of mixed BEC and spinor BEC,the theory and method being used to generate synthetic SOC in BEC were also included.In Chapter 2,we have studied the origin and dynamic evolution of phase fluctuations in one-and two-dimension BEC under the drive of time-varying harmonic potential.By dynamic algebra approach and scale method,the overall dynamics of BEC can be well described.When the inter-particle interaction is absent in the system,the condensate remains coherent all the time,with no phase fluctuations or density fluctuations in the system.When the inter-particle interaction becomes nonzero,under the drive of external potential,the phase of the condensate varies wildly,since the system cannot evolve adiabatically,the wild phase variations lead to phase fluctuations in the condensate,resulting density fluctuations with muti-peak density distribution signature.For the phase induced by external potential can be zero in the dynamic evolution,the condensate is also accompanied with phase coherence revival phenomena.In Chapter 3,we have studied the groundstate phase diagram of harmonic potential trapped two-component BEC with Rashba SOC interaction and analysed the type of phase transition between different groudstates.Because of the influence of SOC interaction,the groundstate of the system gets different forms: striped phase,half vortex state,symmetric skymion state,and the phase similar to plane wave phase,additionally,there also exist square-halo state,triangle-halo state and a strange twisted crossover state.By calculating the corresponding fidelity of the groundstate wavefunction in the system,we can distinguish the phase transition between different groundstates to be continuous or first-order quantum phase transition.In Chapter 4,we briefly introduce the soliton theory in BEC and study the influence of SOC on the dynamics of polar bright soliton in one dimensional spin-1 spinor BEC.When the SOC is weak,the initial soliton structure remains stable,due to the influence exerted by SOC,there are oscillating dark soliton structure appearing in the other two components of the condensate,the oscillating period does not depend on the SOC strength.When the SOC strength becomes comparable to the inter-particle interaction,the initial soliton structure is completely broken,and an additional fastly oscillating behavior induced by SOC arises in the system.By introducing an extra linear Zeeman field into the system,under the influence of SOC,the system changes periodically from polar state to ferromagnetic state,and the oscillating behavior becomes much more complex.In the final Chapter 5,we briefly summarise our works and introduce the prospect of our future research.