Evidence for a Bose–Einstein condensate in liquid 4He from quantum evaporation

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Bose–Einstein condensation (BEC) is a purely quantum phenomenon whereby a macroscopic number of identical atoms occupy the same single-particle state1. Interest in this phenomenon has grown considerably following the direct demonstration of BEC in low-density gases of alkali metal atoms2,3,4. It is therefore worth reconsidering the case of liquid 4He, which is generally accepted to have such a condensate5, but for which similarly direct evidence is lacking6. Nevertheless, theoretical models that depend on the existence of a condensate have proved successful at explaining many of the properties of this system7,8,9, and BEC is considered to underlie the striking phenomena of superfluidity and quantized vorticity observed in liquid 4He. So the current issue is not whether there is a condensate in this system, but how to demonstrate its existence in a clear and simple way. Here I argue that an earlier measurement10 of evaporation from liquid 4He caused by a collimated beam of phonons provides such a demonstration. The calculated angular distribution of evaporated atoms agrees well with that measured if it is assumed that the atoms initially had zero momentum parallel to the surface of the liquid—this is to be expected if the atoms originate from a condensate. This process of quantum evaporation also opens the possibility for creating beams of phase-coherent atoms of short wavelength.

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Figure 1: Properties of 4He.


  1. 1

    Einstein, A. Sitzungsber K. Preuss. Akad. Wiss. 3–14 (1925).

  2. 2

    Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Observation of Bose–Einstein condensation in a dilute atomic vapour. Science 269, 198–201 (1995).

  3. 3

    Davis, K. B. et al. Bose–Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995).

  4. 4

    Bradley, C. C., Sackett, C. A., Tollett, J. J. & Hulet, R. G. Bose–Einstein condensation of lithium: observation of limited condensate number. Phys. Rev. Lett. 78, 985–989 (1997).

  5. 5

    London, F. The λ-phenomenon of liquid helium and the Bose–Einstein degeneracy. Nature 141, 643–644 (1938).

  6. 6

    Sokol, P. E. in Bose–Einstein Condensation (eds Griffin, A., Snoke, D. W. & Stringari, S.) 51–85 (Cambridge, New York, (1995)).

  7. 7

    Bogoliubov, N. On the theory of superfluidity. J. Phys. USSR 11, 23–32 (1947).

  8. 8

    Campbell, C. E. in Excitations in Two-Dimensional and Three-Dimensional Quantum Fluids (eds Wyatt, A. F. G. & Lauter, H. J.) 159 (Plenum, New York, (1991)).

  9. 9

    Griffin, A. Excitations in a Bose-Condensed Liquid (Cambridge, London, (1993)).

  10. 10

    Brown, M. & Wyatt, A. F. G. The surface boundary conditions for quantum evaporation in 4He. J. Phys.: Condens. Matter 2, 5025–5046 (1990).

  11. 11

    Baird, M. J., Hope, F. R. & Wyatt, A. F. G. Quantised evaporation from liquid helium. Nature 304, 325–326 (1983).

  12. 12

    Hope, F. R., Baird, M. J. & Wyatt, A. F. G. Quantum evaporation from liquid 4He by rotons. Phys. Rev. Lett. 52, 1528–1531 (1984).

  13. 13

    Penrose, O. & Onsager, L. Bose Einstein condensation and liquid helium. Phys. Rev. 104, 576–584 (1956).

  14. 14

    Wyatt, A. F. G. Liquid 4He: An ordinary and exotic liquid. J. Phys.: Condens. Matter 8, 9249–9262 (1996).

  15. 15

    Krotscheck, E. Liquid helium on a surface: ground state, excitations, condensate fraction and impurity potential. Phys. Rev. B 32, 5713–5730 (1985).

  16. 16

    Campbell, C. E. Remnants of Bose condensation and off-diagonal long range order in finite systems. J. Low Temp. Phys. 93, 907–919 (1993).

  17. 17

    Griffin, A. & Stringari, S. Surface region of superfluid helium as an inhomogeneous Bose-condensed gas. Phys. Rev. Lett. 76, 259–263 (1996).

  18. 18

    Sears, V. F., Svensson, E. C., Martel, P. & Woods, A. D. B. Neutron-scattering determination of the momentrum distribution and condensate fraction in liquid 4He. Phys. Rev. Lett. 49, 279–282 (1982).

  19. 19

    Sears, V. F. Kinetic energy and condensate fraction of superfluid 4He. Phys. Rev. B 28, 5109–5121 (1983).

  20. 20

    Ceperley, D. M. & Pollock, E. L. Path integral computation of the low-temperature properties of liquid 4He. Phys. Rev. Lett. 56, 351–354 (1986).

  21. 21

    Manousakis, E. Pandharipande, V. R. & Usmani, Q. N. Condensate fraction and momentum distribution of the ground state of liquid 4He. Phys. Rev. B 31, 7022–7028 (1985).

  22. 22

    Whitlock, P. A. & Panoff, R. M. Accurate momentum distributions from computations on 3He and 4He. Can. J. Phys. 65, 1409–1415 (1987).

  23. 23

    Tucker, M. A. H. & Wyatt, A. F. G. Phonons in liquid 4He from a heated metal film: I. The creation of high-frequency phonons. J. Phys.: Condens. Matter 6, 2813–2824 (1994).

  24. 24

    Tucker, M. A. H. & Wyatt, A. F. G. Phonons in liquid 4He from a heated metal film: II The angular distribution. J. Phys.: Condens. Matter 6, 2825–2834 (1994).

  25. 25

    Edwards, D. O. & Saam, W. F. The free surface of liquid helium. Prog. Low Temp. Phys. 7, 283–369 (1978).

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I thank A. Griffin for encouragement and for comments on the draft manuscript; C.Williams and J. Warren for discussions on their results for 3He and allowing me to quote them; C.Williams and M. Brown for the simulation of the peak in Fig. 1; and M. Gibbs for discussions on neutron scattering. This work was supported by the EPSRC.

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Correspondence to Adrian F. G. Wyatt.

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