Stabilization of ion-trap secular frequencies for a quantum phase transition study

TL;DR

This paper demonstrates active stabilization of ion trap secular frequencies using feedback control, significantly improving stability and enabling precise studies of structural phase transitions like the linear-to-zigzag transition.

Contribution

It introduces a method for active RF voltage feedback stabilization in ion traps, achieving sub-5 ppm stability over 200 seconds, enhancing the precision of phase transition experiments.

Findings

Achieved better than 5 ppm stability of trap frequencies over 200 seconds.

Suppressed short-term noise affecting the zigzag mode decoherence.

Identified temperature sensitivity of equipment as a key stability limitation.

Abstract

An array of ions in a linear radio-frequency (RF) Paul trap is a good candidate for investigating structural phase transitions, such as the linear-to-zigzag (LZ) transition, due to the convenient control provided by modification of the trap confinement strength. In such studies, the trap secular frequencies are a key factor that limits the stability of the critical point (CP). In this paper, we implement secular-frequency stabilization, including active feedback stabilization of the RF voltage near the trap electrodes, and achieve a stability of better than 5~ppm over 200~s for both transverse and axial potentials. To evaluate the combined long-term stability of the trap potential in both directions, we measure the zigzag (ZZ) mode frequency near the CP, where the effect of instability in both trap directions is substantially amplified. The short-term noise within a limited spectral window is also suppressed by this scheme, as inferred from decoherence rates of the ZZ mode measured at different frequencies with Ramsey fringes. We also identify that the limitation of the secular frequency stability is mainly from the imperfect temperature insensitivity of voltage dividers and RF detectors, and as a result improvement of lab temperature stability is of great help for stabilizing the trap frequency.