Deterministic nuclear spin squeezing and squeezing by continuous measurement using vector and tensor light shifts

We study the joint effects of vector and tensor light shifts in a set of large spin atoms, prepared in a polarized state and interacting with light. Depending on the ratio \epsilon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ϵ</mml:mi> </mml:math> between tensor and vector coupling and a measurement rate \Gamma <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Γ</mml:mi> </mml:math> , we identify a regime of quantum non-demolition measurement squeezing for times shorter than (\sqrt{\epsilon}\Gamma)^{-1} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:msqrt> <mml:mi>ϵ</mml:mi> </mml:msqrt> <mml:mi>Γ</mml:mi> <mml:msup> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , and a deterministic squeezing regime for times longer than (\epsilon \Gamma)^{-1} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mi>ϵ</mml:mi> <mml:mi>Γ</mml:mi> <mml:msup> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . We apply our results to fermionic isotopes of strontium, ytterbium, and helium, which are atoms with purely nuclear spin in their ground state, benefiting from very low decoherence. For ytterbium 173, with a cavity such as that of [J. A. Muniz et al., Phys. Rev. Res. 3, 023152 (2021)], it would be possible to achieve an atomic spin variance reduction of 0.03 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mn>0.03</mml:mn> </mml:math> in \simeq 50 \rm ms .