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We develop approximate ``analytic-kludge" waveforms to describe the inspiralof a stellar-mass compact object into a supermassive compact object in anextreme mass ratio inspiral (EMRI) scenario. The deformability of thesupermassive compact object is characterized by a dimensionless quantity calledthe tidal Love number (TLN). Our analysis shows that, up to the leading orderof the mass ratio, the conservative dynamics of the EMRI are not affected bytidal interaction, and the tidal effect is only present in the inducedquadrupole moment. We calculate the energy and angular momentum fluxes andobtain leading order corrections to the orbital evolution equations. Bycomparing the waveforms with and without tidal interaction, we demonstrate thateven a small TLN can produce significant differences in the waveforms, whichcan be detected by space-borne detector LISA. Finally, using the Fisherinformation matrix method, we perform parameter estimation for the TLN and findthat the precision can reach the level of $10^{-4}$ in suitable scenarios.

Probing the Tidal Deformability of the Central Object in an Extreme Mass Ratio Inspiral with Analytic Kludge Waveforms