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We present a study of the environments of 17 Lyman-$\alpha$ (Ly$\alpha$)emitting galaxies (LAEs) in the reionisation era ($5.8 < z < 8$) identified byJWST/NIRSpec as part of the JWST Advanced Deep Extragalactic Survey (JADES).Unless situated in sufficiently (re)ionised regions, Ly$\alpha$ emission fromthese galaxies would be strongly absorbed by neutral gas in the intergalacticmedium (IGM). We conservatively estimate sizes of the ionised regions requiredto reconcile the relatively low Ly$\alpha$ velocity offsets ($\Deltav_\text{Ly$\alpha$}<300\,\mathrm{km\,s^{-1}}$) with moderately high Ly$\alpha$escape fractions ($f_\mathrm{esc,\,Ly\alpha}>5\%$) observed in our sample ofLAEs, suggesting the presence of ionised hydrogen along the line of sighttowards at least eight out of 17 LAEs. We find minimum physical `bubble' sizesof the order of $R_\text{ion}\sim0.1$-$1\,\mathrm{pMpc}$ are required in apatchy reionisation scenario where ionised bubbles containing the LAEs areembedded in a fully neutral IGM. Around half of the LAEs in our sample arefound to coincide with large-scale galaxy overdensities seen in FRESCO at $z\sim 5.8$-$5.9$ and $z\sim7.3$, suggesting Ly$\alpha$ transmission is stronglyenhanced in such overdense regions, and underlining the importance of LAEs astracers of the first large-scale ionised bubbles. Considering onlyspectroscopically confirmed galaxies, we find our sample of UV-faint LAEs($M_\text{UV}\gtrsim-20\,\mathrm{mag}$) and their direct neighbours aregenerally not able to produce the required ionised regions based on theLy$\alpha$ transmission properties, suggesting lower-luminosity sources likelyplay an important role in carving out these bubbles. These observationsdemonstrate the combined power of JWST multi-object and slitless spectroscopyin acquiring a unique view of the early Universe during cosmic reionisation viathe most distant LAEs.

Inside the bubble: exploring the environments of reionisation-era Lyman-$\alpha$ emitting galaxies with JADES and FRESCO