Precision measurements in ion traps using slowly moving standing waves

The present paper describes the experimental implementation of a measuring technique employing a slowly moving, near-resonant, optical standing wave in the context of trapped ions. It is used to measure several figures of merit that are important for quantum computation in ion traps and which are otherwise not easily obtainable. Our technique is shown to offer high precision, and also in many cases uses a much simpler setup than what is normally used. We demonstrate here measurements of (i) the distance between two crystalline ions, in units of the standing wave period, (ii) the Lamb-Dicke parameter, (iii) the temperature of the ion crystal, and (iv) the interferometric stability of a Raman setup. The exact distance between two ions, in units of standing wave periods, is very important for motional entangling gates, and our method offers a practical way of calibrating this distance in the typical laboratory situation.