  We introduce the Galaxy Intensity Mapping cross-COrrelation estimator
(GIMCO), which is a new tomographic estimator for the gravitational lensing
potential, based on a combination of intensity mapping (IM) and galaxy number
counts. The estimator can be written schematically as
IM$(z_f)\times$galaxy$(z_b)$ $-$ galaxy$(z_f)\times$IM$(z_b)$ for a pair of
distinct redshifts $(z_f,z_b)$; this combination allows to greatly reduce the
contamination by density-density correlations, thus isolating the lensing
signal. As an estimator constructed only from cross-correlations, it is
additionally less susceptible to systematic effects. We show that the new
estimator strongly suppresses cosmic variance and consequently improves the
signal-to-noise ratio (SNR) for the detection of lensing, especially on linear
scales and intermediate redshifts. %This makes it particularly valuable for
future studies of dark energy and modified gravity. For cosmic variance
dominated surveys, the SNR of our estimator is a factor 30 larger than the SNR
obtained from the correlation of galaxy number counts only. Shot noise and
interferometer noise reduce the SNR. For the specific example of the Dark
Energy Survey (DES) cross-correlated with the Hydrogen Intensity mapping and
Real time Analysis eXperiment (HIRAX), the SNR is around 4, whereas for Euclid
cross-correlated with HIRAX it reaches 52. This corresponds to an improvement
of a factor 4-5 compared to the SNR from DES alone. For Euclid cross-correlated
with HIRAX the improvement with respect to Euclid alone strongly depends on the
redshift. We find that the improvement is particularly important for redshifts
below 1.6, where it reaches a factor of 5. This makes our estimator especially
valuable to test dark energy and modified gravity, that are expected to leave
an impact at low and intermediate redshifts.
