Below a temperature of 2.17 K, liquid 4He undergoes a phase transition to a new state of matter with superfluid properties. It has long been accepted that a Bose-Einstein condensate is responsible, namely that a macroscopic number of atoms occupy the same quantum state. Direct evidence for this condensate has eluded our best efforts for many decades, but finally, as reported on page 56 of this issue by Wyatt1, a macroscopic fraction of atoms with zero momentum has been observed in liquid 4He. A Bose condensate of Cooper pairs also underlies superfluidity in superconductors and liquid 3He.
Wyatt used high-energy phonons generated in the bulk liquid to knock atoms from the free surface of superfluid 4He (Fig. 1, overleaf), and then measured their kinetic energy and momentum2. In the new analysis1, Wyatt finds that all the evaporated atoms initially had zero momentum parallel to the liquid surface. These results end a long and sometimes controversial search in low-temperature physics, and development of the technique opens up the exciting possibility of producing a phase-coherent beam of 4He atoms, a kind of ‘atom laser’.
Recalling a little history should make the significance of these results clear. Within weeks of the discovery of the superfluid properties of liquid 4He in 1938, Fritz London3 suggested that they were a consequence of the fact that 4He atoms have zero spin, and hence obey Bose statistics. (Bosons are particles with integer spin 0, 1, 2, ⃛; fermions have spin 1/2, 3/2, ⃛.) In particular, London argued that superfluidity was related to the occurrence of Bose-Einstein condensation (BEC) in a liquid, similar to that predicted in an ideal gas a decade earlier by Einstein4 in a paper that had fallen into disfavour. London's colleague Tisza5 quickly developed a two-fluid model, in which the superfluid component had its origin in the macroscopic occupation of atoms of a single quantum state. The superfluid component is a new, coherent, collective degree of freedom which moves without resistance.
It took many years to properly develop this BEC picture of London and Tisza, and it was overshadowed by the phenomenological theory developed in 1941 by L. D. Landau, who derived the two-fluid equations of motion describing superfluidity without any explicit reference to a Bose condensate. However, by about 1960, it was generally agreed that the Landau theory could be understood as a consequence of a condensate described by a macroscopic wavefunction (for a review, see ref. 6). The superfluid velocity is given by the gradient of the phase of this condensate wavefunction.
The superfluid fraction can be easily measured, but in a Bose liquid it is not simply related to the underlying condensate (in contrast to a Bose gas), as shown by the fact that the entire liquid forms the superfluid at zero temperature. In spite of this, the condensate fraction and its temperature dependence have been accurately determined by indirect methods over the past two decades. Computer simulations7 show consistently that it is about 9% at absolute zero, and vanishes at the superfluid transition temperature of 2.17 K. That agrees with inelastic neutron-scattering experiments, which allow one to extract the atoms’ momentum distribution. Although the condensate peak at zero momentum is masked by finite energy resolution and final-state effects, it is possible instead to find the number of atoms with finite momentum (the non-condensate fraction)6,8, and thus obtain the condensate fraction.
Those studying liquid helium could only look on with envy, three years ago, when Bose condensation was clearly observed in alkali atoms in magnetic traps9. But now Wyatt's evaporation experiment has finally provided direct evidence for a condensate in liquid 4He at 100 mK, where the liquidis essentially in its ground state. The large number of atoms that emerge near the expected angle of 20° to the vertical (after absorbing mono-energetic phonons) means there must be macroscopic occupation of the state with zero momentum parallel to the liquid surface. In contrast, the flux of evaporated atoms initially in states with finite momentum leads to a broad angular spread of low intensity. Before we can estimate the condensate fraction, measurements of greater sensitivity are needed to detect the evaporation from the non-condensate atoms.
Crucial to the success of the new quantum evaporation experiment is the ability to produce a narrow mono-energetic beam of long-lived, high-energy (10.15 K) phonons. The remarkable physics of the anharmonic up-scattering phonon processes which gives rise to this beam was clarified only a few years ago10.
The observation that the evaporated atoms have absorbed a single high-frequency phonon implies that these atoms come from the region very close to the liquid surface, otherwise there would be energy losses via collisions before the atom evaporates. That limits Wyatt's technique to the study of 4He atoms in the surface region — perhaps a blessing in disguise, as the zero-temperature condensate fraction is predicted to go from 9% in the bulk liquid to 100% in the low-density surface tail (due to lack of collisions)11,12. Future evaporation experiments promise to give detailed information about the profile of the inhomogeneous Bose condensate at liquid 4He surfaces.
Wyatt's experiment has put the Bose condensate in liquid 4He back into the spotlight, 60 years after it was suggested by London3. As an agreeable side-benefit, this quantum evaporation technique might be adapted to produce a phase-coherent mono-energetic beam of 4He atoms, as they all come from the same initial quantum state. This would be similar to the beam produced in 1997 by allowing a Bose-condensed gas of 23Na atoms to leak out of a trap13 — another type of ‘atom laser’.
Wyatt, A. F. G. Nature 391, 56–59 (1998).
Brown, M. & Wyatt, A. F. G. J. Phys. Cond. Matter 2, 5025–5046 (1990).
London, F. Nature 141, 643–644 (1938).
Einstein, A. Sitzungsber Berlin Preuss. Akad. Wiss. 3-14 (1925).
Tisza, L. Nature 141, 913 913 (1938).
Griffin, A. Excitations in a Bose-Condensed Liquid (Cambridge Univ. Press, 1993).
Ceperley, D. M. & Pollock, E. L. Phys. Rev. Lett. 56, 351–354 (1986).
Sokol, P. E. in Bose-Einstein Condensation (eds Griffin, A., Snoke, D. W. & Stringari, S.) 51-85 (Cambridge Univ. Press, 1995).
Anderson, M. H.et al. Science 269, 198–201 (1995).
Tucker, M. A. H. & Wyatt, A. F. G. J. Phys. Cond. Matter 6, 2813-2824; 2825-2834 (1994).
Lewart, S. D., Pandharipande, V. R. & Pieper, S. C. Phys. Rev. B 37, 4950–4964 (1988).
Griffin, A. & Stringari, S. Phys. Rev. Lett. 76, 259–263 (1996).
Andrews, M. R.et al. Science 275, 637–641 (1997).
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Physical Review B (2002)
Comptes Rendus de l'Académie des Sciences - Series IV - Physics (2001)
Biochemical and Biophysical Research Communications (2000)
Physical Review A (2000)
Physical Review Letters (1999)