This thesis presents my research on spin-mixing and interferometry in an all-optically generated spinor Bose-Einstein condensate (BEC) of sodium atoms. The sodium atoms are loaded from a magneto-optical trap into a crossed optical dipole trap and are subsequently evaporatively cooled down to quantum degeneracy by ramping down the laser power. With our setup, we obtained nearly pure sodium BECs with atoms number of approximately 20,000 to 40,000.

We study the spin-mixing dynamics in the F=1 sodium spinor system. I present experiments on a resonant coupling between spin and spatial degrees of freedom beyond the single-mode approximation (SMA) during non-equilibrium dynamics in our sodium spin-1 BEC. These quench-induced spin oscillation experiments rely on microwave dressing of the F=1 hyperfine states, where F denotes the total angular momentum of the Na atoms. Our data show a slow baseline drift of the coherent spin population oscillation between mF=0 and mF=±1 pairs when the effective quadratic Zeeman shift q is tuned via microwave dressing to certain values. The baseline drifting indicates spin dynamics beyond the SMA. Our data agree well with the recent theory based on a q-dependent, resonant coupling between spin and spatial degrees of freedom. We further explore these effects by scanning q around the point of maximum baseline drift to map out this new resonance phenomenon as a function of q.

I also present the result of our spin-mixing atom interferometer experiments. We experimentally demonstrate two new types of interferometry based on different initial states: single-sided seeding and double-sided seeding interferometers. The entangled probe states of the interferometers are generated via spin-exchange collisions in F=1 spinor BECs, where two atoms with the magnetic quantum number mF=0 collide and change into a pair with mF=±1. Our results show that our spin-mixing interferometers beat the standard quantum limit with a metrological gain of 3.96 dB in the single-sided atom interferometer with spin-mixing time t = 10 ms and 4.77 dB in the double-sided atom interferometer with spin-mixing time t = 8 ms. Our research on spin-mixing interferometry is useful for future quantum technologies such as quantum-enhanced microwave sensors and quantum parametric amplifiers based on spin-mixing. Our work paves the way for future light-pulse atom interferometry experiments, which involve the coupling between the spin and momentum degrees of freedom, and are useful for quantum-enhanced inertial sensing and gravimetry with BECs.