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When liquid helium are cooled (see cooling) to 2.2o K, it would not enter the solid phase but instead goes into a third phase called helium II. Liquid helium II exhibits some remarkable phenomena under the name of superfluidity. At temperature below TC = 2.2oK, the helium atoms
Helium II State Helium-4 Phase Diagram banded together to form a coherent whole - the superfluid. In an ideal Bose-Einstein Condensate (BEC) at T = 0oK, all particles are in the lowest energy level. In practice, some particles would occupy exited states as shown in Figure 13-05c with the ratio of N(E=0)/N(E0) ~ 13%. At finite temperatures, thermal excitations move more particles to the states in normal fluid (helium I). Superfluidity disappears beyond the lambda point (Figure 13-05d1). All those peculiar properties are related to the inert and coherent nature

Figure 13-05c Helium II State [view large image]

Figure 13-05d1 Helium-4

of the entity. The whole thing can move about in near frictionless condition. The small friction is attributed to the excited helium II atoms.
Useful technical applications of superfluidity in daily life is very limited as it is quite difficult - and therefore expensive - to reach the low temperatures necessary for helium to become superfluid. The two practical examples above are either very expensive or elaborated scientific projects. On the other hand, the two conjectures about natural phenomena seems to be a reasonable explanation, but also cost a lot of money to observe or prove. In short, superfluidity is not cheap to come by.

Footnote on Cooling :

The throttling process refers to gas expansion at high pressure seeping through a tiny opening adiabatically and irreversibly (rapidly) into a region of lower pressure. Temperature is lowered in this process since the gas uses its internal energy to do work during the expansion. The temperature change accompanying a throttling process is know as the Joule-Kelvin effect. If a liquid about to vaporize undergoes a throttling process, a cooling effect accompanied by partial vaporization always occurs (such as applying rubbing alcohol to the skin). With a gas, however,
Cooling Laser Cooling cooling occurs only if the initial pressure and temperature lie inside a curve called the inversion curve (see upper left diagram in Figure 13-05m for hydrogen gas). Ordinary tap water is sufficient for nitrogen gas, but liquid nitrogen (< 70K) must be used to cool hydrogen gas, and liquid hydrogen (< 20K) to cool helium gas. As shown in the upper right diagram of Figure 13-05m for a typical liquefying apparatus, the gas is pre-cooled to a temperature within the inversion curve, and run through the heat exchanger repeatedly until the gas is liquefied. The drawing in lower Figure 13-05m is the schematic diagram of a liquefying plant for mass-produce liquid helium.

Figure 13-05m Cooling
[view large image]

Figure 13-05n Laser Cooling [view large image]

    Small scale cooling by laser can lower temperature to 10-9 K :

  1. The incoming laser beam is tuned slightly below the resonance absorption of a stationary atom (or ion) so that only those moving toward the beam would absorb the photon.
  2. The velocity of the atom is reduced by an amount : v = p/m, where p = h/ is the momentum of the photon, and m the mass of the atom. For D-line laser beam and sodium atom ~ 589 nm, and m ~ 3.7x10-23gm, v ~ 3 cm/sec, which seems to be very little comparing to the average speed of the atoms about 6x104 cm/sec at room temperature.
  3. However, a laser can induce on the order of 107 absorptions/sec so that an atom could be stopped in a matter of 10-3 sec.
  4. The atoms re-emit the photon in random directions. Since the initial momentum loss was opposite to the direction of motion, while the subsequent momentum gain was in a random direction, the overall result of the absorption and emission process is to reduce the speed of the atom (provided its initial speed was larger than the recoil speed from scattering a single photon, see Figure 13-05n).
  5. In practice, laser cooling involves millions of atoms, which are held together by magnetic field and bombarded by multiple laser beams to reduce the temperature to 10-6 K or even lower.

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