# The hidden phase of Fock states; quantum non-local effects

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## Abstract.

We revisit the question of how a definite phase between Bose-Einstein condensates can spontaneously appear under the effect of measurements. We first consider a system that is the juxtaposition of two subsystems in Fock states with high populations, and assume that successive individual position measurements are performed. Initially, the relative phase is totally undefined, and no interference effect takes place in the first position measurement. But, while successive measurements are accumulated, the relative phase becomes better and better defined, and a clear interference pattern emerges. It turns out that all observed results can be interpreted in terms of a pre-existing, but totally unknown, relative phase, which remains exactly constant during the experiment. We then generalize the results to more condensates. We also consider other initial quantum states than pure Fock states, and distinguish between intrinsic phase of a quantum state and phase induced by measurements. Finally, we examine the case of multiple condensates of spin states. We discuss a curious quantum effect, where the measurement of the spin angular momentum of a small number of particles can induce a big angular momentum in a much larger assembly of particles, even at an arbitrary distance. This spin observable can be macroscopic, analogous to the pointer of a measurement apparatus, which illustrates the non-locality of standard quantum mechanics with particular clarity. The effect can be described as the teleportation at arbitrary distances of the continuous classical result of a local experiment. The EPR argument, transposed to this case, takes a particularly convincing form since it does not involve incompatible measurements and deals only with macroscopic variables.

## Keywords

Angular Momentum Relative Phase Macroscopic Variable Standard Quantum Mechanic Spin Angular Momentum## Preview

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## References

- A.S. Davydov,
*Quantum Mechanics*, 2nd edn. (Pergamon press, 1965), p. 130 and following Google Scholar - P. Carruthers, M.M. Nieto, Rev. Mod. Phys.
**40**, 411 (1968) Google Scholar - A.L. Alimov, E.V. Damaskinskii, Teor. Mat. Fizika
**38**, 58 (1979)Google Scholar - R.J. Glauber, Phys. Rev.
**131**, 2766 (1963)Google Scholar - J. Javanainen, Sun Mi Ho, Phys. Rev. Lett.
**76**, 161 (1996)Google Scholar - T. Wong, M.J. Collett, D.F. Walls, Phys. Rev. A
**54**, R3718 (1996)Google Scholar - J.I. Cirac, C.W. Gardiner, M. Naraschewski, P. Zoller, Phys. Rev. A
**54**, R3714 (1996)Google Scholar - Y. Castin, J. Dalibard, Phys. Rev. A
**55**, 4330 (1997)Google Scholar - K. Mølmer, Phys. Rev. A
**55**, 3195 (1997)Google Scholar - K. Mølmer, J. Mod. Opt.
**44**, 1937 (1997)Google Scholar - C. Cohen-Tannoudji, Collège de France 1999-2000 lectures, Chaps. V et VI “Emergence d’une phase relative sous l’effet des processus de détection” http://www.phys.ens.fr/cours/college-de-france/ Google Scholar
- Y. Castin, C. Herzog, C.R. Acad. Sci. IV
**2**, 419 (2001)Google Scholar - C.J. Pethick, H. Smith,
*Bose-Einstein condensates in dilute gases*(Cambridge University Press, 2002), see Chap. 13 Google Scholar - P.W. Anderson, Rev. Mod. Phys.
**38**, 298 (1966)Google Scholar - A.J. Leggett, F. Sols, Found. Phys.
**21**, 353 (1991)Google Scholar - A.J. Leggett, “Broken gauge symmetry in a Bose condensate”, in
*Bose-Einstein condensation*, edited by A. Griffin, D.W. Snoke, S. Stringari (Cambridge University Press, 1995); see in particular pp. 458-459 Google Scholar - P.W. Anderson,
*Basic notions in condensed matter physics*(Benjamin-Cummins, 1984) Google Scholar - P.W. Anderson, “Measurement in quantum theory and the problem of complex systems”, in
*The Lesson of quantum theory*, edited by J. de Boer, E. Dal, O. Ulfbeck (Elsevier, 1986), see Section 3 Google Scholar - K. Mølmer, Phys. Rev. A
**65**, 021607 (2002) Google Scholar - P. Horak, S.M. Barnett, J. Phys. B
**32**, 3421 (1999)Google Scholar - J.S. Bell,
*Speakable and unspeakable in quantum mechanics*(Cambridge University Press, 1987) Google Scholar - F. Laloë, Am. J. Phys.
**69**, 655 (2001)Google Scholar - A.J. Leggett, Found. Phys.
**25**, 113 (1995)Google Scholar - J.A. Dunningham, K. Burnett, Phys. Rev. Lett.
**19**, 3729 (1999)Google Scholar - I. Zapata, F. Sols, A.J. Leggett, Phys. Rev. A
**67**, 021603(R) (2003) Google Scholar - S. Kohler, F. Sols, Phys. Rev. A
**63**, 053605 (2001) Google Scholar - J. Javanainen, J. Phys. B
**33**, 5493 (2000)Google Scholar - E. Siggia, A. Ruckenstein, Phys. Rev. Lett.
**44**, 1423 (1980) Google Scholar - J.S. Bell, “Einstein-Podolsky-Rosen experiments”,
*Proceedings of the Symposium on frontier problems in high energy physics,*Pisa (1976), 33-45; see in particular note 24 Google Scholar - J.S. Bell, “Are there quantum jumps?” in
*Schrödinger, Centenary of a polymath*(Cambridge Univ. Press, 1987), see second sentence of the second paragraph Google Scholar - B. d’Espagnat, Phys. Rev. D
**11**, 1424 (1975), see in particular note 30 Google Scholar - P.H. Eberhard, Nuov. Cim. B
**46**, 392 (1978)Google Scholar - M. Jammer,
*The conceptual development of quantum mechanics*(Mc. Graw Hill, 1966) Google Scholar - A. Einstein, B. Podolsky, N. Rosen, Phys. Rev.
**47**, 777 (1935)CrossRefzbMATHGoogle Scholar - N. Bohr, Phys. Rev.
**48**, 696 (1935)Google Scholar - F. Laloë, J. Phys. Coll.
**1**, C2-1 (1981)Google Scholar - D. Mermin, Am. J. Phys.
**66**, 920 (1998) Google Scholar - B. d’Espagnat,
*Le réel voilé*(Fayard, 1994), § 16-2 Google Scholar - A. Shimony, H. Stein, Am. J. Phys.
**69**, 848 (2001)Google Scholar - H.P. Stapp, Am. J. Phys.
**66**, 924 (1998) Google Scholar