Extreme emission line galaxies (EELGs) exhibit large equivalent widths (EW) in their rest-optical emission lines ([OIII]$\lambda5007$ or H$\alpha$ rest-frame EW$ > 750\r{A}$) which can be tied to a recent upturn in star formation rate, due to the sensitivity of the nebular line emission and the rest-optical continuum to young ($<10$Myr) and evolved stellar populations, respectively. By studying a sample of 85 star forming galaxies (SFGs), spanning the redshift and magnitude interval $3 $ M$_{UV}>-21$, in the JWST Advanced Deep Extragalactic Survey (JADES) with NIRSpec/prism spectroscopy, we determine that SFGs initiate an EELG phase when entering a significant burst of star formation, with the highest EWs observed in EELGs with the youngest mass-weighted ages ($<5$ Myr old) and the highest burst intensity (those with the highest proportion of their total stellar mass formed in the last 10 Myr). We spectroscopically confirm that a greater proportion of SFGs are in an EELG phase at high redshift in our UV-selected sample ($61\pm4\%$ in our $z>5.7$ high-redshift bin, compared to $23^{+4}_{-1}\%$ in our lowest-redshift bin $35.7$ have observed Lyman-$\alpha$ emission, potentially lying within large ionised regions. The high detection rate of Lyman-$\alpha$ emitters in our EELG selection suggests that the physical conditions associated with entering an EELG phase also promote the escape of Lyman-$\alpha$ photons.
Comment: 26 pages, 14 figures