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

TL;DR

This paper introduces a simulation tool for a novel trapped two-state Bose-Einstein condensate Ramsey interferometer driven by dipole oscillations and gravitational sag, aiming to measure gravitational fields and inter-state interactions.

Contribution

It develops a theoretical framework combining two-level systems and GPE, and creates a MATLAB-based simulation tool for this new interferometer design.

Findings

Simulation successfully models interferometer behavior.

Interference patterns depend on gravitational sag and trap parameters.

Potential for precise gravitational field measurements.

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 $\vert F=2, m_F=+2 \rangle$ $(\vert +2 \rangle)$ of the $5 ^2S_{\frac{1}{2}}$ ground state. Here, Rmasey interferometry is performed with states $\vert F=2, m_F=+1 \rangle$ $(\vert +1 \rangle)$ and $\vert +2 \rangle$. 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 $\vert +1 \rangle$ experiences a shallower radial trap with a larger gravitational sag; whereas, state $\vert +2 \rangle$ experiences a tighter radial trap with a gravitational sag which is half of state $\vert +1 \rangle$. Due to this, a superposition between the states $\vert +1 \rangle$ and $\vert +2 \rangle$ 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.