Impact of the axionlike self-interactions in gravitational atoms for LISA

Ultralight bosons with self-interactions, such as axion-like particles, can form astrophysical Bose--Einstein condensates around stars or compact objects, often referred to as gravitational atoms. In this work, we adopt a recently proposed dynamical formation mechanism for these halos and estimate their impact on extreme- and intermediate-mass-ratio inspirals when present around the primary black hole. We show that, for signal-to-noise ratios 100, LISA can distinguish gravitational waveforms from binaries embedded in such halo overdensities. Our analysis indicates that LISA can probe boson masses mdm~10⁻¹⁷--10⁻¹⁵\,eV and decay constants fₐ~3 × 10¹⁰--6 × 10¹²\,GeV using binaries with total masses M~10⁴--10⁵\,M_, assuming conservative DM densities consistent with the central values of Navarro--Frenk--White profiles. Allowing for higher background densities and different extreme-mass-ratio configurations further extends the accessible parameter space. Moreover, we find that for a binary configuration with M~10⁴M_, ρdm = 10⁴\,GeV/cm³, and signal to noise ratio SNR ~ 20, a particle mass of mdm = 3.2 · 10⁻¹⁵ eV and decay constant of fₐ = 1.6 · 10¹¹ GeV maximize the dephasing due to dynamical friction, enabling the recovery of the particle parameters at the percent level. These results demonstrate that LISA can place constraints on axion-like particle masses and self-interactions without requiring additional couplings to Standard Model fields.