Atomic and molecular absorption at high redshift

Strong constraints on possible variations in fundamental constants can be derived from HI 21-cm and molecular rotational absorption lines observed towards quasars. With the aim of forming a statistical sample of constraints we have begun a program of systematic searches for such absorption systems. Here we describe molecular rotational searches in 25 damped Lyman-α systems where, in many cases, we set optical depth limits an order of magnitude better than that required to detect the 4 known redshifted millimeter-wave absorbers. We also discuss the contributory factors in the detectability of HI 21-cm absorption, focusing on possible biases (e.g. low covering factors) in the currently known sample of absorbers and non-detections.