The Hubble Space Telescope has identified a series of low-velocity Ly alpha absorption lines in the direction of 3C 273. We have investigated a recent claim (Williams and Schommer 1993) that there is diffuse Ha emission with surface brightness 1.2 x 10(-18) ergs cm(-2) s(-1) arcsec(-2) at a radial velocity within 130 km s(-1) of one of these Ly alpha features, The observations were made with the TAURUS-2 imaging Fabry-Perot interferometer and a Tek 1024(2) CCD at the 3.9 m Angle-Australian Telescope. We do not detect Ha emission at the claimed wavelength lambda 6600.3 down to a 3 sigma upper limit of 4 x 10(-19) ergs cm(-2) s(-1) arcsec(-2) (E(m) approximate to 0.2 cm(-6) pc), nor do we detect emission at the absorption-line velocity. We show that the Jacquinot advantage of spectroscopic interferometers makes 3 sigma detection thresholds as low as E(m)(H alpha) = 0.02 cm(-6) pc quite feasible. Even at this very deep limit, it is unlikely that Ly alpha absorbers irradiated by the UVX background will be detectable in optical line emission at any redshift. However, our sensitivity limit now brings other important detections into the realm of possibility for the first time, in particular, the detection of ionized disks beyond the H I truncation radius in spiral galaxies.