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.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Prakash H, Kumar R (2005) Simultaneous squeezing of two orthogonal spin components. J Opt B Quantum Semiclass Opt 7:S757

    ADS  MathSciNet  Article  Google Scholar 

  2. 2.

    Walls DF, Zoller P (1981) Reduced fluctuation in resonance fluorescence. Phys Rev Lett 47:709

    ADS  CAS  Article  Google Scholar 

  3. 3.

    Kitagawa M, Ueda M (1993) Squeezed spin states. Phys Rev A 47:5138

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Wineland DJ, Bollinger JJ, Itano WM, Moore FL (1992) Spin squeezing and reduced quantum noise. Phys Rev A 46:R6797

    ADS  CAS  Article  Google Scholar 

  5. 5.

    Sorensen A, Duan LM, Cirac JI, Zoller P (2001) Many particle-entanglement with Bose–Einstein condensates. Nature 409:63

    ADS  CAS  Article  Google Scholar 

  6. 6.

    Prakash H, Kumar R (2007) Atomic squeezing in assembly of two two-level atoms interacting with a single mode coherent radiation. Eur Phys J D 42:475

    ADS  CAS  Article  Google Scholar 

  7. 7.

    Raghavan S, Pu H, Meystre P, Bigelow N (2001) Generation of arbitrary Dicke states in spinor Bose Einstein condensates. Opt Commun 188:149

    ADS  CAS  Article  Google Scholar 

  8. 8.

    Ma J, Wang X, Sun CP, Nori F (2011) Quantum spin squeezing. Phys Rep 509:89

    ADS  MathSciNet  CAS  Article  Google Scholar 

  9. 9.

    Polzik ES (2008) Quantum physics—the squeeze goes on. Nature 453:45

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Hammerer K, Sorensen AS, Polzik ES (2010) Quantum interface between light and atomic ensembles. Rev Mod Phys 82:1041

    ADS  CAS  Article  Google Scholar 

  11. 11.

    Banerjee A (1996) Generation of atomic squeezed states in an optical cavity with an injected squeezed vacuum. Phys Rev A 54:5327

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Kuzmich A, Molmer K, Polzik ES (1997) Spin squeezing in an ensemble of atoms illuminated with squeezed light. Phys Rev Lett 79:4782

    ADS  CAS  Article  Google Scholar 

  13. 13.

    Esteve J, Gross C, Weller A, Giovanazzi S, Oberthaler MK (2008) Squeezing and entanglement in a Bose Einstein condensate. Nature 455:1216

    ADS  CAS  Article  Google Scholar 

  14. 14.

    Hald J, Sorenson J, Polzik ES (1999) Spin squeezed atoms: a macroscopic entangled ensemble created by light. Phys Rev Lett 83:1319

    ADS  Article  Google Scholar 

  15. 15.

    Horodecki R, Horodecki P, Horodecki M, Horodecki K (2009) Quantum entanglement. Rev Mod Phys 81:865

    ADS  MathSciNet  CAS  Article  Google Scholar 

  16. 16.

    Agarwal GS, Scully M (1996) Ramsey spectroscopy with nonclassical light source. Phys Rev A 53:467

    ADS  CAS  Article  Google Scholar 

  17. 17.

    Bigelow N (2009) Squeezing entanglement. Nature 409:27

    ADS  Article  Google Scholar 

  18. 18.

    Walls DF, Zoller P (1981) Enhanced sensitivity of a gravitational-wave detector. Phys Lett A 85:118

    ADS  Article  Google Scholar 

  19. 19.

    Redcliffe JM (1971) Some properties of coherent spin states. J Phys A 4:313

    ADS  MathSciNet  Article  Google Scholar 

  20. 20.

    Arrechi FT, Courtens E, Gilmore R, Thomas H (1972) Atomic Coherent states in quantum optics. Phys Rev A 6:221

    ADS  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Pankaj Kumar.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kumar, R., Kumar, P. & Prakash, H. Squeezing of Longitudinal Spin Component in Spin Coherent State. Natl. Acad. Sci. Lett. (2021). https://doi.org/10.1007/s40009-020-01025-8

Download citation

Keywords

  • Two-level atoms
  • Spin coherent states
  • Spin squeezing