Squeezing of Longitudinal Spin Component in Spin Coherent State

Abstract

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.