Zeeman Degenerate Sideband Cooling in $^{176}$Lu$^+$

TL;DR

This paper introduces a degenerate Raman sideband cooling method in $^{176}$Lu$^+$ that efficiently reduces motional quanta in fewer cycles by coupling Zeeman states, achieving near ground-state cooling with minimal pulses.

Contribution

The work demonstrates a novel degenerate Raman sideband cooling technique that couples Zeeman states for efficient motional ground-state preparation in trapped ions.

Findings

Near ground-state cooling achieved with ~10 pulses from an initial average phonon number of 6.

Method reduces the number of cooling cycles compared to traditional sideband cooling.

Theoretical model applicable to any hyperfine level F, showing broad applicability.

Abstract

We explore degenerate Raman sideband cooling in which neighboring Zeeman states of a fixed hyperfine level are coupled via a two-photon Raman transition. The degenerate coupling between $|F,m_F\rangle\rightarrow |F,m_F-1\rangle$ facilitates the removal of multiple motional quanta in a single cycle. This method greatly reduces the number of cooling cycles required to reach the ground state compared to traditional sideband cooling. We show that near ground state cooling can be achieved with a pulse number as low as $\bar{n}$ where $\bar{n}$ is the average phonon number in the initial thermal state. We demonstrate proof-of-concept in $^{176}\mathrm{Lu}^+$ by coupling neighboring Zeeman levels on the motional sideband for the $F=7$ hyperfine level in $^3D_1$. Starting from a thermal distribution with an average phonon number of 6, we demonstrate near ground-state cooling with $\sim10$ pulses. A theoretical description is given that applies to any $F$ level and demonstrates how effective this approach can be.