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

Abstract

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 ${}^{87}Rb$ atoms in state $|F=2,m_F=+2⟩$ $(|+2⟩)$ of the $5^2{S}_{\frac{1}{2}}$ ground state. Here, Rmasey interferometry is performed with states $|F=2,m_F=+1⟩$ $(|+1⟩)$ 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 $m_F$ 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.

16 pages, 13 figures