Advertisement

Spin Squeezing, Entanglement and Quantum Metrology

  • Christian Groß
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

Spin squeezing is a quantum strategy introduced in 1993 by Kitagawa and Ueda [1] which aims to redistribute the fluctuations of two conjugate spin directions among each other. In 1994 it was theoretically shown that spin squeezed states are useful quantum resources to enhance the precision of atom interferometers [2] and in 2001 the connection between spin squeezing and entanglement was pointed out [3].

Keywords

Spin Length Bloch Sphere Atom Interferometer Bipartite Entanglement Coherent Spin State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Kitagawa M, Ueda M (1993) Squeezed spin states. Phys Rev A 47:5138–5143CrossRefADSGoogle Scholar
  2. 2.
    Wineland D, Bollinger J, Itano W, Heinzen D (1994) Squeezed atomic states and projection noise in spectroscopy. Phys Rev A 50:67–88CrossRefADSGoogle Scholar
  3. 3.
    Sørensen AS, Duan L, Cirac J, Zoller P (2001) Many-particle entanglement with Bose–Einstein condensates. Nature 409:63–6CrossRefADSGoogle Scholar
  4. 4.
    Metcalf H, Van der Straten P (1999) Laser cooling and trapping. Springer, New YorkGoogle Scholar
  5. 5.
    Sakurai J (1994) Modern quantum mechanics. Addison-Wesley, ReadingGoogle Scholar
  6. 6.
    Arecchi FT, Courtens E, Gilmore R, Thomas H (1972) Atomic coherent states in quantum optics. Phys Rev A 6:2211–2237CrossRefADSGoogle Scholar
  7. 7.
    Radcliffe JM (1971) Some properties of coherent spin states. J Phys A Gen Phys 4:313–323MathSciNetCrossRefADSGoogle Scholar
  8. 8.
    Zhang W-M, Feng DH, Gilmore R (1990) Coherent states: theory and some applications. Rev Mod Phys 62:867–927MathSciNetCrossRefADSGoogle Scholar
  9. 9.
    Giovannetti V, Lloyd S, Maccone L (2004) Quantum-enhanced measurements: beating the standard quantum limit. Science 306:1330–1336CrossRefADSGoogle Scholar
  10. 10.
    Lee CT (1984) Q representation of the atomic coherent states and the origin of fluctuations in superfluorescence. Phys Rev A 30:3308–3310CrossRefADSGoogle Scholar
  11. 11.
    Amico L, Fazio R, Osterloh A, Vedral V (2008) Entanglement in many-body systems. Rev Mod Phys 80:517MathSciNetCrossRefzbMATHADSGoogle Scholar
  12. 12.
    Horodecki R, Horodecki P, Horodecki M, Horodecki K (2009) Quantum entanglement. Rev Mod Phys 81:865MathSciNetCrossRefzbMATHADSGoogle Scholar
  13. 13.
    Plenio MB, Virmani S (2007) An introduction to entanglement measures. Quantum Inf Comput 7:1MathSciNetzbMATHGoogle Scholar
  14. 14.
    Benatti F, Floreanini R, Marzolino U (2010) Sub-shot-noise quantum metrology with entangled identical particles. Ann Phys 325:924MathSciNetCrossRefzbMATHADSGoogle Scholar
  15. 15.
    Tóth G, Knapp C, Gühne O, Briegel HJ (2007) Optimal spin squeezing inequalities detect bound entanglement in spin models. Phys Rev Lett 99:250405CrossRefADSGoogle Scholar
  16. 16.
    Tóth G, Knapp C, Gühne O, Briegel HJ (2009) Spin squeezing and entanglement. Phys Rev A 79:042334Google Scholar
  17. 17.
    Korbicz J et al (2006) Generalized spin-squeezing inequalities in N-qubit systems: theory and experiment. Phys Rev A 74:52319MathSciNetCrossRefADSGoogle Scholar
  18. 18.
    Korbicz JK, Cirac JI, Lewenstein M (2005) Erratum spin squeezing inequalities and entanglement of N qubit states. Phys Rev Lett 95:259901CrossRefADSGoogle Scholar
  19. 19.
    Korbicz JK, Cirac JI, Lewenstein M (2005) Spin squeezing inequalities and entanglement of N qubit states. Phys Rev Lett 95:120502CrossRefADSGoogle Scholar
  20. 20.
    Wang X, Sanders B (2003) Spin squeezing and pairwise entanglement for symmetric multiqubit states. Phys Rev A 68:12101CrossRefADSGoogle Scholar
  21. 21.
    Chaudhury S, Smith A, Anderson BE, Ghose S, Jessen PS (2009) Quantum signatures of chaos in a kicked top. Nature 461:768–771CrossRefADSGoogle Scholar
  22. 22.
    Bennett CH, DiVincenzo DP, Smolin JA, Wootters WK (1996) Mixed-state entanglement and quantum error correction. Phys Rev A 54:824–3851MathSciNetGoogle Scholar
  23. 23.
    Cohen-Tannoudji C, Diu B, Laloe F (2005) Quantum mechanics. Wiley-VCH, New YorkGoogle Scholar
  24. 24.
    Ghose S, Stock R, Jessen P, Lal R, Silberfarb A (2001) Chaos, entanglement, and decoherence in the quantum kicked top. Phys Rev A 78:042318MathSciNetCrossRefADSGoogle Scholar
  25. 25.
    Sørensen AS, Mølmer K (1949) Entanglement and extreme spin squeezing. Phys Rev Lett 86:4431–4434CrossRefGoogle Scholar
  26. 26.
    Ramsey NF (1949) A new molecular beam resonance method. Phys Rev 76:996Google Scholar
  27. 27.
    Ramsey NF (1950) A molecular beam resonance method with separated oscillating fields. Phys Rev 78:695–699CrossRefADSGoogle Scholar
  28. 28.
    Santarelli G et al (1999) Quantum projection noise in an atomic fountain: a high stability cesium frequency standard. Phys Rev Lett 82:4619–4622CrossRefADSGoogle Scholar
  29. 29.
    Wasilewski W, Jensen K, Krauter H, Renema JJ, Polzik ES (2010) Quantum noise limited and entanglement assisted magnetometry. Phys Rev Lett 104:133601CrossRefADSGoogle Scholar
  30. 30.
    Cronin AD, Schmiedmayer J, Pritchard DE (2009) Optics and interferometry with atoms and molecules. Rev Mod Phys 81:1051CrossRefADSGoogle Scholar
  31. 31.
    Kasevich M, Chu S (1992) Measurement of the gravitational acceleration of an atom with a light-pulse atom interferometer. Appl Phys B 54:321–332CrossRefADSGoogle Scholar
  32. 32.
    Gustavson TL, Bouyer P, Kasevich MA (1997) Precision rotation measurements with an atom interferometer gyroscope. Phys Rev Lett 78:2046–2049CrossRefADSGoogle Scholar
  33. 33.
    Pezzé L, Smerzi A (2009) Entanglement, nonlinear dynamics, and the Heisenberg limit. Phys Rev Lett 102:100401MathSciNetCrossRefADSGoogle Scholar
  34. 34.
    Leibfried D et al (2004) Toward Heisenberg-limited spectroscopy with multiparticle entangled states. Science 304:1476–1478CrossRefADSGoogle Scholar
  35. 35.
    Roos CF, Chwalla M, Kim K, Riebe M, Blatt R (2006) ‘Designer atoms’ for quantum metrology. Nature 443:316CrossRefADSGoogle Scholar
  36. 36.
    Nagata T, Okamoto R, O’Brien JL, Sasaki K, Takeuchi S (2007) Beating the standard quantum limit with four-entangled photons. Science 316:726–729CrossRefADSGoogle Scholar
  37. 37.
    Meyer V et al (2001) Experimental demonstration of entanglement-enhanced rotation angle estimation using trapped ions. Phys Rev Lett 86:5870–5873CrossRefADSGoogle Scholar
  38. 38.
    Schleier-Smith MH, Leroux ID, Vuletic V (2010) Reduced-quantum-uncertainty states of an ensemble of two-level atoms. Phys Rev Lett 104:73604CrossRefADSGoogle Scholar
  39. 39.
    Leroux ID, Schleier-Smith MH, Vuletic V (2010) Implementation of cavity squeezing of a collective atomic spin. Phys Rev Lett 104:73602CrossRefADSGoogle Scholar
  40. 40.
    Fernholz T et al (2008) Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement. Phys Rev Lett 101:073601CrossRefADSGoogle Scholar
  41. 41.
    Kuzmich A, Mandel L, Bigelow NP (2000) Generation of spin squeezing via continuous quantum nondemolition measurement. Phys Rev Lett 85:1594–1597CrossRefADSGoogle Scholar
  42. 42.
    Hald J, Sørensen JL, Schori C, Polzik ES (1999) Spin squeezed atoms: a macroscopic entangled ensemble created by light. Phys Rev Lett 83:1319–1322CrossRefADSGoogle Scholar
  43. 43.
    Appel J et al (2009) Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit. Proc Natl Acad Sci USA 106:10960–10965CrossRefADSGoogle Scholar
  44. 44.
    Goda K et al (2008) A quantum-enhanced prototype gravitational-wave detector. Nat Phys 4:472–476CrossRefGoogle Scholar
  45. 45.
    Vahlbruch H et al (2008) Observation of squeezed light with 10 dB quantum-noise reduction. Phys Rev Lett 100:033602CrossRefADSGoogle Scholar
  46. 46.
    Estève J, Gross C, Weller A, Giovanazzi S, Oberthaler M K (2008) Squeezing and entanglement in a Bose–Einstein condensate. Nature 455:1216–1219CrossRefADSGoogle Scholar
  47. 47.
    Giovannetti V, Lloyd S, Maccone L (2006) Quantum metrology. Phys Rev Lett 96:010401MathSciNetCrossRefADSGoogle Scholar
  48. 48.
    Lee H, Kok P, Dowling J (2003) A quantum Rosetta stone for interferometry. J Mod Opt 49:2325–2338MathSciNetCrossRefADSGoogle Scholar
  49. 49.
    Bouyer P, Kasevich MA (1997) Heisenberg-limited spectroscopy with degenerate Bose–Einstein gases. Phys Rev A 56:R1083–R1086CrossRefADSGoogle Scholar
  50. 50.
    Dowling JP (1998) Correlated input-port, matter-wave interferometer: Quantum-noise limits to the atom-laser gyroscope. Phys Rev A 57:4736–4746MathSciNetCrossRefADSGoogle Scholar
  51. 51.
    Bollinger JJ, Itano WM, Wineland DJ, Heinzen DJ (1996) Optimal frequency measurements with maximally correlated states. Phys Rev A 54:R4649–R4652CrossRefADSGoogle Scholar
  52. 52.
    Pezzé L, Collins LA, Smerzi A, Berman GP, Bishop AR (2005) Sub-shotnoise phase sensitivity with a Bose–Einstein condensate Mach–Zehnder interferometer. Phys Rev A 72:043612CrossRefADSGoogle Scholar
  53. 53.
    Pezzé L, Smerzi A, Khoury G, Hodelin JF, Bouwmeester D (2007) Phase detection at the quantum limit with multiphoton Mach–Zehnder interferometry. Phys Rev Lett 99:223602CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg  2012

Authors and Affiliations

  • Christian Groß
    • 1
  1. 1.University of HeidelbergHeidelbergGermany

Personalised recommendations