Quadrupole shift cancellation using dynamic decoupling

TL;DR

This paper introduces a radio-frequency pulse sequence to cancel quadrupole shifts in optical ion clocks, enabling multi-ion operation and reducing frequency uncertainty, while also addressing other tensorial shifts and Zeeman effects.

Contribution

The authors develop and experimentally validate a dynamic decoupling method that cancels quadrupole and tensorial shifts in multi-ion optical clocks, improving spectral resolution and stability.

Findings

Quadrupole shift difference reduced to ~20 mHz

Method cancels tensorial shifts including ac Stark shifts

Zeeman shift effects also mitigated using RF dynamic decoupling

Abstract

We present a method that uses radio-frequency pulses to cancel the quadrupole shift in optical clock transitions. Quadrupole shifts are an inherent inhomogeneous broadening mechanism in trapped ion crystals, limiting current optical ion clocks to work with a single probe ion. Cancelling this shift at each interrogation cycle of the ion frequency allows the use of $N>1$ ions in clocks, thus reducing the uncertainty in the clock frequency by $\sqrt{N}$ according to the standard quantum limit. Our sequence relies on the tensorial nature of the quadrupole shift, and thus also cancels other tensorial shifts, such as the tensor ac stark shift. We experimentally demonstrate our sequence on three and seven $^{88}\mathrm{Sr}^{+}$ ions trapped in a linear Paul trap, using correlation spectroscopy. We show a reduction of the quadrupole shift difference between ions to $\approx20$ mHz's level where other shifts, such as the relativistic 2$^{\mathrm{nd}}$ order Doppler shift, are expected to limit our spectral resolution. In addition, we show that using radio-frequency dynamic decoupling we can also cancel the effect of 1$^{\mathrm{st}}$ order Zeeman shifts.