Skip to main content
SpringerLink
Log in

Squeezed “atomic” states, pseudo-Hermitian operators and Wigner D-matrices

  • Quantum Optics and Quantum Information
  • Published:
The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics Aims and scope Submit manuscript

Abstract.

The states of N two-level atoms can be mapped onto the eigenvectors of angular momentum (with j=N/2) and this system in interaction with a radiation field constitutes a fundamental model in Quantum Optics. There from one may construct “atomic” coherent states and “minimum uncertainty packets”. The “squeezing” of such states is of considerable contemporary interest. We show that the properties of squeezed atomic states are most elegantly and economically expressed in terms of “pseudo-Hermitian” operators and through Wigner D-matrices and their analytical continuation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • F. Bloch, Phys. Rev. 70, 460 (1946)

    Article  ADS  Google Scholar 

  • J.M. Radcliffe, J. Phys. A 4, 313 (1971)

    Article  ADS  MathSciNet  Google Scholar 

  • F.T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, Phys. Rev. A 6, 2211 (1972)

    Article  ADS  Google Scholar 

  • D. Stoler, Phys. Rev. D 1, 3217 (1970); H.P. Yuen, Phys. Rev. A 13, 2226 (1976); C.M. Caves, Phys. Rev. D 23, 1693 (1981)

    ADS  Google Scholar 

  • P.A.M. Dirac, Proc. Roy. Soc. London A 180, 1 (1942); W. Pauli, Rev. Mod. Phys. 15, 175 (1943); S.N. Gupta, Proc. Roy. Soc. London A 63, 681 (1950); K. Bleuler, Helv. Phys. Acta 23, 567 (1950); E.C.G. Sudarshan, Phys. Rev. 123, 2183 (1961); T.D. Lee, G.C. Wick, Nucl. Phys. B 9, 209 (1969)

    Article  ADS  MathSciNet  Google Scholar 

  • C.M. Bender, S. Boettcher, Phys. Rev. Lett. 80, 219 (1998); C.M. Bender, S. Boettcher, Meisenger, J. Math. Phys. 40, 2201 (1999); C.M. Bender, G.V. Dunne, P.N. Meisenger, Phys. Lett. A 252, 272 (1999); C.M. Bender, G.V. Dunne, J. Math. Phys. 40, 4616 (1999)

    MathSciNet  Google Scholar 

  • A. Mostafazadeh, J. Math. Phys. 43, 205, 2814 (2002)

    MATH  ADS  MathSciNet  Google Scholar 

  • C. Aragone, E. Chalbaud, S. Salamo, J. Math. Phys. 17, 1963 (1976); M.A. Rashid, J. Math. Phys. 19, 1391 (1978)

    ADS  Google Scholar 

  • D.A. Varshalovich, A.N. Moskalev, V.K. Khersonskii, in Quantum Theory of Angular Momentum (World Scientific, 1988)

  • M. Kitagawa, M. Ueda, Phys. Rev. Lett. 67, 1852 (1991); Phys. Rev. A 47, 5138 (1993)

    ADS  Google Scholar 

  • R.H. Dicke, Phys. Rev. 93, 99 (1954)

    MATH  ADS  Google Scholar 

  • J. Hald, J.L. Sørensen, C. Schori, E.S. Polzik, Phys. Rev. Lett. 83, 1319 (1999)

    ADS  Google Scholar 

  • D.J. Wineland, J.J. Bollinger, W.M. Itano, F.L. Moore, D.J. Heinzen, Phys. Rev. A 46, R6797 (1992); D.J. Wineland, J.J. Bolinger, W.M. Itano, D.J. Heinzen, Phys. Rev. A 50, 67 (1994)

    ADS  Google Scholar 

  • G.S. Agarwal, R.R. Puri, Phys. Rev. A 49, 4968 (1994); Y. Takahashi, K. Honda, N. Tanaka, K. Toyoda, K. Ishikawa, T. Yabuzki, Phys. Rev. A 60, 4974 (1999); L. Vernac, M. Pinard, E. Giacobino, Phys. Rev. A 62, 063812 (2000); A. Dantan, M. Pinard, V. Josse, N. Nayak, P. Berman, Phys. Rev. A 67, 045801 (2003); C. Genes, P. Berman, A.G. Rojo, Phys. Rev. A 68, 043809 (2003); A. Dantan, M. Pinard, Phys. Rev. A 69, 043810 (2004)

    ADS  Google Scholar 

  • A. Kuzmich, L. Mandel, N.P. Bigelow, Phys. Rev. Lett. 85, 1594 (2000)

    ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Darjeeling Government College, Darjeeling, West Bengal, India

    R. N. Deb

  2. S.N. Bose National Centre for Basic Sciences, Block-JD, Sector-3, Salt Lake City, Kolkata, 700098, India

    N. Nayak & B. Dutta-Roy

Authors
  1. R. N. Deb
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Nayak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Dutta-Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Nayak.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deb, R., Nayak, N. & Dutta-Roy, B. Squeezed “atomic” states, pseudo-Hermitian operators and Wigner D-matrices. Eur. Phys. J. D 33, 149–155 (2005). https://doi.org/10.1140/epjd/e2005-00031-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjd/e2005-00031-y

Keywords

Search

Navigation