Velocity-comb modulation transfer spectroscopy

Sub-Doppler laser spectroscopy is crucial for laser-frequency stabilization, playing a significant role in atomic physics and precision measurement. However, despite decades of development, inefficient atomic utilization remains a widespread issue. Most existing methods rely on single-frequency lasers, and due to the Doppler effect, only a small fraction ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mo><</a:mo> <a:mn>1</a:mn> <a:mi mathvariant="normal">%</a:mi> </a:math> ) of atoms with near-zero longitudinal velocities are utilized, severely limiting improvements in the spectral signal-to-noise ratio ( <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>S</d:mi> <d:mo>/</d:mo> <d:mi>N</d:mi> </d:math> ). Here, we propose a velocity-comb modulation transfer spectroscopy (VC-MTS) solution that leverages the velocity-selective resonance of modulated <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi>N</f:mi> </f:math> -frequency lasers, seeming as an optical comb, to enhance the utilization of nonzero-velocity atoms, which optimizes the spectral amplitude and frequency instability by <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>N</h:mi> </h:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msqrt> <j:mi>N</j:mi> </j:msqrt> </j:math> times, respectively. Unlike traditional MTS, in this work, each pair of counterpropagating lasers interacts with atoms from different longitudinal velocity groups, independently contributing to the amplitude and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi>S</l:mi> <l:mo>/</l:mo> <l:mi>N</l:mi> </l:math> . Preliminary proof-of-principle results show that the frequency stability of the triple-frequency laser is improved by <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msqrt> <n:mn>3</n:mn> </n:msqrt> </n:math> times compared to the single-frequency laser. With more frequency components, VC-MTS stabilized lasers are expected to achieve order-of-magnitude breakthroughs in frequency stability, taking an essential step toward next-generation compact optical clocks. This method also applies to quantum systems with wide velocity distributions, offering an innovative perspective on laser spectroscopy and inspiring further intriguing applications.