Theory of Heating of the Quantum Ground State of Trapped Ions

Abstract

Using a displacement operator formalism, I analyze the depopulation of the vibrational ground state of trapped ions. Two heating times, one characterizing short time behavior and the other long time behavior, are found. The long time behavior is analyzed for both single and multiple ions, and a formula for the relative heating rates of different modes is derived. The possibility of correction of heating via the quantum Zeno effect, and the exploitation of the suppression of heating of higher modes to reduce errors in quantum computation, is considered.