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We propose and explore the feasibility of a novel Ramsey interferometercreated by a trapped two-state Bose-Einstein condensate (BEC) driven by dipoleoscillations and gravitational sag. The BEC is formed in a pure cigar shapedcompressed magnetic trap (CMT) via a dilute atom cloud of $^{87}Rb$ atoms instate $\vert F=2, m_F=+2 \rangle$ $(\vert +2 \rangle)$ of the $5^2S_{\frac{1}{2}}$ ground state. Here, Rmasey interferometry is performed withstates $\vert F=2, m_F=+1 \rangle$ $(\vert +1 \rangle)$ and $\vert +2 \rangle$.The proposed interferometer utilises the response of atoms to the harmonicoscillator trapping potential and the gravitational sag due to the variation inthe $m_F$ state. Briefly, the state $\vert +1 \rangle$ experiences a shallowerradial trap with a larger gravitational sag; whereas, state $\vert +2 \rangle$experiences a tighter radial trap with a gravitational sag which is half ofstate $\vert +1 \rangle$. Due to this, a superposition between the states$\vert +1 \rangle$ and $\vert +2 \rangle$ experiences multipath propagationresulting in an interference pattern. This may be utilised to measure localgravitational fields and measure inter-sate scattering lengths. Here, atheoretical framework is reported which is developed via the two-level systemin combination with the Gross-Pitaevskii equation (GPE). Further, thedevelopment of a simulation tool via GPELabs in MATLAB that explores the prosedinterferometer is reported along with key insights and findings.

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