Skip to main content
  • 710 Accesses

Abstract

A new and general quantum state reconstruction method is proposed. It can be applied to reconstruct the state of a particle in an arbitrary, time-dependent potential. The state is reconstructed by measuring the position probability distribution at n + 1 different time values. This yields an n-th order Taylor polynomial expansion of the density matrix in the off-diagonal variable.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Bertrand and P. Bertrand, A tomographic approach to Wigner’s function, Found. Phys. 17:397 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  2. K. Vogel and H. Risken, Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase, Phys. Rev. A 40:2487(1989).

    Google Scholar 

  3. D. Smithey, M. Beck, M. Raymer, and A. Faridani, Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum, Phys. Rev. Lett. 70:1244 (1993).

    Article  ADS  Google Scholar 

  4. G. Breitenbach, S. Schiller, and J. Mlynek, Measurement of the quantum states of squeezed light, Nature. 387:471 (1997).

    Article  ADS  Google Scholar 

  5. K. Banaszek and K. Wódkiewicz, Direct probing of quantum phase space by photon counting, Phys. Rev. Lett. 76:4344 (1996).

    Article  ADS  Google Scholar 

  6. S. Wallontowitz and W. Vogel, Unbalanced homodyning for quantum state measurements, Phys. Rev. A 53:4528 (1996).

    Article  ADS  Google Scholar 

  7. D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, Experimental determination of the motional quantum state of a trapped atom, Phys. Rev. Lett. 77:4281 (1996).

    Article  ADS  Google Scholar 

  8. Special issue on’ Quantum State Preparation and Measurement”, J. Mod. Opt. 44:2021, No. 11/12 (1997).

    ADS  Google Scholar 

  9. M. G. Raymer, M. Beck, and D. F. McAlister, Complex wave-field reconstruction using phasespace tomography, Phys. Rev. Lett. 72:1137 (1994).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. U. Leonhardt and M. G. Raymer, Observation of moving wave packets reveals their quantum state, Phys. Rev. Lett. 6:1985 (1996).

    Article  MathSciNet  ADS  Google Scholar 

  11. D. S. Krähmer and U. Leonhardt, State reconstruction of one-dimensional wave packets, Appl. Phys. B 65:725 (1997).

    Article  ADS  Google Scholar 

  12. U. Leonhardt, T. Kiss, and P. J. Bardroff, State reconstruction of wave packets moving in time-dependent potentials and the existence of Wronskian pairs, submitted to J. Phys. A.

    Google Scholar 

  13. L. M. Johansen, Hydrodynamical quantum state reconstruction, Phys. Rev. Lett. 80:5461 (1998).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  14. H. M. Nussenzweig, “Introduction to Quantum Optics”. Gordon & Breach Science Publishers, London (1973).

    Google Scholar 

  15. W. Band and J. L. Park, Quantum state determination: Quorum for a particle in one dimension, Am. J. Phys. 47:188 (1979).

    Article  ADS  Google Scholar 

  16. A. Wünsche, Reconstruction of operators from their normally ordered moments for a single boson mode, Quantum Opt. 2:453 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  17. C. T. Lee, Moment problem for a density matrix and a biorthogonal set of operator bases, Phys. Rev. A 46:6097 (1992).

    Article  MathSciNet  ADS  Google Scholar 

  18. J. E. Moyal, Quantum mechanics as a statistical theory, Proc. Cambridge Philos. Soc. 45:99 (1949).

    Article  MathSciNet  MATH  Google Scholar 

  19. J. V. Lill, M. I. Haftel, and G. H. Herling, Semiclassical limits in quantum-transport theory, Phys. Rev. A 39:5832 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  20. J. V. Lill, M. I. Haftel, and G. H. Herling, Mixed state quantum mechanics in hydrodynamical form, J. Chem. Phys. 90:4940 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  21. L. M. Johansen, Nonclassical evolution of a free particle, m “Fifth International Conference on Squeezed States and Uncertainty Relations”, D. S. Han, J. Janszky, Y. S. Kim, and V. I. Man’ko, eds., NASA Goddard Space Flight Center, Greenbelt, Maryland (1998).

    Google Scholar 

  22. E. Madelung, Quantentheorie in hydrodynamischer form Z. Phys. 40:322 (1926).

    MATH  ADS  Google Scholar 

  23. D. Hilbert, Begründung der kinetischen gastheorie, Matematische Annalen, 72:562 (1912).

    Article  MathSciNet  MATH  Google Scholar 

  24. L. M. Johansen, Nonrecursive hydrodynamical quantum state reconstruction, submitted to Phys. Rev.A.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Kluwer Academic Publishers

About this chapter

Cite this chapter

Johansen, L.M. (2002). Hydrodynamical Quantum State Reconstruction. In: Kumar, P., D’Ariano, G.M., Hirota, O. (eds) Quantum Communication, Computing, and Measurement 2. Springer, Boston, MA. https://doi.org/10.1007/0-306-47097-7_22

Download citation

  • DOI: https://doi.org/10.1007/0-306-47097-7_22

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-46307-5

  • Online ISBN: 978-0-306-47097-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics