Spin squeezing

Spin squeezing is a quantum process that decreases the variance of one of the angular momentum components in an ensemble of particles with a spin. The quantum states obtained are called spin squeezed states. Such states can be used for quantum metrology, as they can provide a better precision for estimating a rotation angle than classical interferometers.

Spin squeezed states for an ensemble of spins have been defined analogously to squeezed states of a bosonic mode. A quantum state always obeys the Heisenberg uncertainty relation

${\displaystyle (\Delta J_{x})^{2}(\Delta J_{y})^{2}\geqslant {\frac {1}{4}}|\langle J_{z}\rangle |^{2},}$

where ${\displaystyle J_{l}}$ are the collective angular momentum components defined as ${\displaystyle J_{l}=\sum _{n}j_{l}^{(n)},}$ and ${\displaystyle j_{l}^{(n)}}$ are the single particle angular momentum components. The state is spin-squeezed in the ${\displaystyle x}$-direction, if the variance of the ${\displaystyle x}$-component is smaller than the square root of the right-hand side of the inequality above

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