In the present paper, we have shown that any component \( S_{{{\hat{\mathbf{n}}}}} = {\mathbf{S}} \cdot {\hat{\mathbf{n}}} \) of atomic spin operator \( {\mathbf{S}} \) along unit vector \( {\hat{\mathbf{n}}} \) except transverse spin component is squeezed for spin coherent state \( \left| {S,S ,{\hat{\mathbf{n}}}_{ 0} } \right\rangle \) for given unit vector \( {\hat{\mathbf{n}}}_{0} \), defined by \( ({\mathbf{S}} \cdot {\mathbf{S}} )\left| {S,S,{\hat{\mathbf{n}}}_{\text{0}} } \right\rangle = S(S + 1 )\left| {S,S,{\hat{\mathbf{n}}}_{\text{0}} } \right\rangle \) and \( S_{{{\hat{\mathbf{n}}}_{\text{0}} }} \left| {S,S,{\hat{\mathbf{n}}}_{\text{0}} } \right\rangle = S\left| {S ,S ,{\hat{\mathbf{n}}}_{\text{0}} } \right\rangle \), for \( {\hat{\mathbf{n}}} \, \cdot \, {\hat{\mathbf{n}}}_{\text{0}} \, \ne \, 0 \), as per the Prakash and Kumar criterion (J Opt B Quantum Semiclass Opt 7:S757, 2005) obtained by generalization of Walls and Zoller (Phys Rev Lett 47:709, 1981) definition of atomic squeezing. We have obtained perfect squeezing for longitudinal spin component in spin coherent state.

在本文中，我们证明了任何成分\（S _ {{{\ hat {\ mathbf {n}}}}} = {\ mathbf {S}} \ cdot {\ hat {\ mathbf {n}}}沿着单位向量\（{\ hat {\ mathbf {n}}} \）的原子自旋算符\（{\ mathbf {S}} \）的\）除外，将横向自旋分量压缩为自旋相干态\（\ left |给定单位向量的{S，S，{\ hat {\ hatbf {n}}} _ {0}} \ right \ rangle \）\（{\ hat {\ mathbf {n}}} _ {0} \），由\（（{{mathbf {S}} \ cdot {\ mathbf {S}}}）\ left | {S，S，{\ hat {\ mathbf {n}}} __ {\ text {0}}定义} \ right \ rangle = S（S + 1）\ left | {S，S，{\ hat {\ mathbf {n}}} _ {\ text {0}}} \ right \ rangle \）和\（S _ {{{\ hat {\ mathbf {n}}} _ {\ text {0}}}} \ left | {S，S，{\ hat {\ mathbf {n}}} __ \ text { 0}}}} \ right \ rangle = S \ left | {S，S，{\ hat {\ mathbf {n}}} _ {\ text {0}}} \ right \ rangle \）为\（{根据Prakash和Kumar，帽子{\ mathbf {n}}} \，\ cdot \，{\ hat {\ mathbf {n}}} _ {\ text {0}} \，\ ne \，0 \）通过对Walls and Zoller（Phys Rev Lett 47：709，1981）的定义的一般化获得的标准（J Opt B Quantum Semiclass Opt 7：S757，2005）。我们已经获得了自旋相干状态下纵向自旋分量的完美压缩。