Superfluid helium is a Bose Einstein condensate



 

The Superfluidity or Superfluid (English: superfluidity, often wrongly called superfluidity or superfluid) in physics describes the state of a liquid in which it loses all internal friction. Superfluidity was discovered in 1937 by Pyotr Leonidovich Kapitsa, John F. Allen, and Don Misener. The branch of physics that deals with superfluidity is quantum hydrodynamics.

description

Helium and lithium 6 are the only elements for which this phenomenon has been observed so far. They go into the superfluid state when their temperature exceeds the so-called lambda point (this is the critical temperature of superfluidity, TSf ) falls below. At 3He is around 2.6 mK (that is a very low temperature, but by far not one of the ultra-low temperatures of 10-7 K and less, in which one would observe Bose-Einstein condensation of certain gases in atomic traps); at 4Hey lies TSf much higher, namely at 2.17 K.

In the superfluid phase one can observe unusual phenomena:

  • Almost ideal thermal conductivity of the liquid due to the effect of the second sound.
  • As excited states when the liquid rotates, quantized mechanical eddies form (similar to the magnetic flux eddies in the superconductor or eddies in the bathtub). If the vortex density is sufficiently high, these are arranged in a regular hexagonal grid.
  • The so-called fountain effect: fountains cannot be stopped in a superfluid.
  • He levels are the same in neighboring vessels due to the Rollin film (film creeping) (Onnes effect).

Superfluids 4He is also known as Helium-II, in contrast to normal fluid (liquid) Helium-I.

Explanatory approaches

So far, the superfluidity cannot be fully explained theoretically. However, there are various approaches that describe the properties of superfluid helium at least qualitatively.

Two fluid model

The two-fluid model (also known as the 'two-fluid model') to explain superfluidity goes back to Lew Dawidowitsch Landau. Since helium exhibits both superfluid and viscous properties in the temperature range from 1K to the lambda point, it is assumed that the total density of the liquid is made up of a normal portion, which becomes increasingly smaller as the temperature drops, and a superfluid portion. However, excitations in the superfluid part can also be generated, which act like a viscosity of superfluid helium. For example, if you pull a floating body over superfluid helium, it will feel it up to a certain limit speed (the so-called Landau criterion) no friction. Above this speed, however, rotons can be excited and, at even higher speeds, phonons can be excited, which acts like friction on the body. Mathematically, this results in a limit speed of approx. 60 cm / s. In fact, it is found that the limit speed is well below 1 cm / s. The cause is the excitation of quantized eddies in the superfluid, so-called vortices. This phenomenon is comparable to the excitation of quantized circulating currents in superconductors. The vortices must not be confused with the rotons, since the latter represent a macroscopic excitation of the superfluid.

Quantum mechanical approach

Superfluid can be well understood in the Bose-Einstein condensation model. According to this model, a macroscopic part of all bosons occupies the same quantum state. This means that all He particles that have condensed into this ground state can be described by a single wave function. The superfluid phase, like the laser, the quantum Hall effect and the superconducting phase, is a macroscopic quantum state. The critical temperature for the phase transition to superfluid helium is 3.1 K, which is qualitatively correct, but is significantly higher than the measured 2.17 K. Furthermore, at T = 0 Kelvin, only 8% of the atoms are in the ground state , not 100% as the Bose-Einstein theory model predicts. The cause of these discrepancies is the atomic interaction of the He atoms, which is set to zero in the Bose-Einstein model. In contrast, in the case of the Bose-Einstein condensation of rubidium and sodium gases in atomic traps (mentioned in the special article), the interaction of the atoms involved is actually negligible.

For He liquids, the Bose-Einstein condensation model only applies qualitatively, and also quantitatively for the gases mentioned.

It should be noted that the Bose-Einstein condensation does not contradict the two-fluid model. The proportion of particles that is condensed in the ground state depends on the temperature. Below a critical temperature (lambda point at 4He) more and more particles occupy the ground state, the lower the temperature. The condensed portion can be viewed as superfluid helium, while the remaining particles are normal liquid helium.

In contrast to the Bosonian 4He atoms are the atoms of the seldom occurring in nature 3Hey about fermions. The Bose-Einstein statistics do not apply to these, but the Fermi-Dirac statistics. For the 3The Bose-Einstein condensation model cannot therefore be applied to He atoms. Nevertheless, one also observes at 3He superfluid properties. However, this is not a contradiction in terms, considering the superfluidity of 3He does not start from isolated atoms, but from the coupling of two atoms, so that, analogous to Cooper pair formation in electron superconductivity, bosonic 3He pairs with spin 1 are obtained (one can understand that, because of the weakness of this coupling, the transition temperature is about 1000 times lower than for 4Hey is). Two 3He atoms can assume a somewhat lower (and therefore somewhat more probable) state in terms of energy if their nuclear magnetic moments (nuclear spins) are aligned (magnetic states) or in the opposite direction (non-magnetic state).

Technical applications

In physics and chemistry it becomes superfluid 4He used in spectroscopy. The sample is surrounded by liquid helium in a cryostat. By pumping out the gaseous helium, the temperature is lowered below the lambda point and the helium becomes superfluid. The temperature depends on the pressure and can in practice be set between 1.1 K and 2.1 K by pumping at different levels.

A far more complex technique is called Superfluid Helium Droplet Spectroscopy (SHeDS) or. Helium Nano Droplet Isolation (HeNDI) Called spectroscopy. The helium droplets used for this are produced in an adiabatic expansion of helium in a vacuum apparatus and have a temperature of only 370 mK. Molecules or clusters that appear in superfluid 4He are dissolved can in fact rotate freely as if they were in a vacuum.

Category: quantum physics