  The response of a gravitating object to an external tidal field is encoded in
its Love numbers, which identically vanish for classical blackholes (BHs). Here
we show, using standard time-independent quantum perturbation theory, that for
a quantum BH, generically, the Love numbers are nonvanishing and negative, and
that their magnitude depends on the lowest lying levels of the quantum spectrum
of the BH. We calculate the quadrupolar electric quantum Love number of
nonrotating BHs and show that it depends most strongly on the first excited
level of the quantum BH. We then compare our results to the same Love number of
exotic ultra compact objects and to that of classical compact stars and
highlight their different parametric dependence. Finally, we discuss the
detectability of the quadrupolar quantum Love number in future precision
gravitational-wave observations and show that, under favourable circumstances,
its magnitude is large enough to imprint an observable signature on the
gravitational waves emitted during the inspiral phase of two moderately
spinning BHs.
