Developing a simulation tool to investigate a novel trapped two-state Bose-Einstein condensate Ramsey interferometer driven by dipole oscillations and gravitational sag

We propose and explore the feasibility of a novel Ramsey interferometer created by a trapped two-state Bose-Einstein condensate (BEC) driven by dipole oscillations and gravitational sag. The BEC is formed in a pure cigar shaped compressed magnetic trap (CMT) via a dilute atom cloud of 87Rb atoms in state |F=2,mF=+2⟩ (|+2⟩) of the 52S12 ground state. Here, Rmasey interferometry is performed with states |F=2,mF=+1⟩ (|+1⟩) and |+2⟩. The proposed interferometer utilises the response of atoms to the harmonic oscillator trapping potential and the gravitational sag due to the variation in the mF state. Briefly, the state |+1⟩ experiences a shallower radial trap with a larger gravitational sag; whereas, state |+2⟩ experiences a tighter radial trap with a gravitational sag which is half of state |+1⟩. Due to this, a superposition between the states |+1⟩ and |+2⟩ experiences multipath propagation resulting in an interference pattern. This may be utilised to measure local gravitational fields and measure inter-sate scattering lengths. Here, a theoretical framework is reported which is developed via the two-level system in combination with the Gross-Pitaevskii equation (GPE). Further, the development of a simulation tool via GPELabs in MATLAB that explores the prosed interferometer is reported along with key insights and findings.