Fermionic condensate: properties, applications and examples

A Fermi condensate is, in the strictest sense, a very dilute gas formed by fermionic atoms that have been subjected to a temperature close to absolute zero. In this way, and under appropriate conditions, they pass to a superfluid phase, forming a new state of matter aggregation.

The first fermionic condensate was obtained on December 16, 2003 in the United States, thanks to a team of physicists from several universities and institutions. The experiment used about 500,000 potassium-40 atoms subjected to a variable magnetic field and a temperature of 5 x 10 -8 Kelvin.

This temperature is considered close to absolute zero and is much lower than the temperature of intergalactic space, which is approximately 3 Kelvin. It is understood by the absolute zero of the temperature reached 0 Kelvin, which is equivalent to -273.15 degrees Celsius. So 3 Kelvin corresponds to -270.15 degrees Celsius.

Some scientists believe that fermionic condensate is the state of sexual matter. The first four states are most familiar to everyone: solid, liquid, gas and plasma.

Previously, a fifth state of matter had been obtained when a condensate of bosonic atoms was reached. This first condensate was created in 1995 from a very dilute rubidium-87 gas, cooled to 17 x 10 -8 Kelvin.

The importance of low temperatures

Atoms behave very differently at temperatures close to absolute zero, depending on the value of their intrinsic angular momentum or rotation.

This divides particles and atoms into two categories:

– Bosons, which are those with complete rotation (1, 2, 3, …).

– Fermions, which are those that have spin semi-entero (1/2, 3/2, 5/2, …).

Bosons are unrestricted, in the sense that two or more of them can occupy the same quantum state.

On the other hand, fermions fulfill the Pauli exclusion principle: two or more fermions cannot occupy the same quantum state, or in other words: there can only be one fermion per quantum state.

This fundamental difference between bosons and fermions makes it more difficult to obtain ​​fermionic condensates than bosonic ones.

For the fermions to occupy all the lower quantum levels, it is necessary that they are previously aligned in pairs, to form the so-called “ Cooper pairs ” that have bosonic behavior.

istory, fundamentals and properties

In 1911, when Heike Kamerlingh Onnes studied the resistance of mercury subjected to very low temperatures using liquid helium as a coolant, he found that when the temperature reached 4.2 K (-268.9 Celsius), the resistance dropped drastically to zero.

The first superconductor had been found unexpectedly.

Without knowing it, HK Onnes managed to put all conducting electrons at the lowest quantum level, a fact that in principle is not possible because electrons are fermions.

The electrons have been passed to the superfluid phase within the metal, but because they have an electrical charge, they cause an electrical charge flow with zero viscosity and, consequently, zero electrical resistance.

HK Onnes himself, in Leiden, Holland, found that the helium he used as a coolant became superfluid when the temperature of 2.2 K (-270.9 Celsius) was reached.

Unconsciously, HK Onnes managed, for the first time, to place the helium atoms with which he cooled mercury to its lowest quantum level. In passing, he also noticed that when the temperature was below a certain critical temperature, helium transitioned into the superfluid phase (zero viscosity).

The theory of superconductivity

Helium-4 is a boson and behaves as such, so it was possible to go from the normal liquid phase to the superfluid phase.

However, none of them is considered a fermionic or bosonic condensate. In the case of superconductivity, fermions, like electrons, were within the mercury crystal lattice; and in the case of superfluid helium, it went from the liquid phase to the superfluid phase.

The theoretical explanation of superconductivity came later. It is the well-known BCS theory developed in 1957.

The theory states that electrons interact with the crystal lattice forming pairs that, instead of repelling, attract each other, forming “Cooper pairs” that act like bosons. In this way, the electrons as a whole can occupy the lowest energy quantum states, as long as the temperature is low enough.

How to produce a fermion condensate?

A legitimate condensate of fermions or bosons must start from a very dilute gas composed of fermion or bosonic atoms, which is cooled in such a way that its particles pass into the lower quantum states.

As this is much more complicated than obtaining a boson condensate, it has only recently been possible to create these types of condensates.

Fermions are particles or conglomerates of particles with full rotation of rotation. The electron, proton and neutron are particles with ½ spin.

The helium-3 nucleus (two protons and one neutron) behaves like a fermion. The neutral potassium atom-40 has 19 protons + 21 neutrons + 19 electrons, which add up to the odd number 59, so it behaves like a fermion.

Particle mediation

Interaction mediating particles are bosons. Among these particles, we can mention the following:

– Photons (mediators of electromagnetism).

– Gluon (mediators of strong nuclear interaction).

– Z and W bosons (weak nuclear interaction mediators).

– Graviton (mediators of gravitational interaction).

composite bosons

Among the composite bosons are the following:

– Deuterium nucleus (1 proton and 1 neutron).

– helium-4 atom (2 protons + 2 neutrons + 2 electrons).

Whenever the sum of protons, neutrons and electrons of a neutral atom results in an integer, the behavior will be boson.

How a fermionic condensate was obtained

A year before reaching the fermion condensate, the formation of molecules with fermionic atoms that formed tightly coupled pairs that behaved like bosons was achieved. However, this is not considered a pure fermionic condensate, but rather a bosonic condensate.

But what was achieved on December 16, 2003 by a team consisting of Deborah Jin, Markus Greiner and Cindy Regal of the JILA laboratory in Boulder, Colorado, was the formation of a condensate of pairs of individual fermionic atoms in a gas.

In this case, the pair of atoms does not form a molecule, but rather moves in a correlated fashion. So, together, the pair of fermionic atoms acts like a boson; therefore, its condensation has been achieved.

To achieve this condensation, the JILA team started with a gas with 40 atoms of potassium (which are fermions), confined in an optical trap of 300 nanokelvin.

The gas was then subjected to an oscillating magnetic field to alter the repulsive interaction between atoms and make it an attractive interaction, using a phenomenon known as “Fesbach resonance”.

Properly adjusting the magnetic field parameters allows atoms to form Cooper pairs instead of molecules. It then continues to cool to obtain the fermionic condensate.

Applications and examples

The technology developed to obtain ​​fermionic condensates, in which atoms are practically manipulated almost individually, will allow the development of quantum computing, among other technologies.

It will also improve the understanding of phenomena such as superconductivity and superfluidity, allowing for new materials with special properties. It was also found that there is an intermediate point between the superfluidity of molecules and the conventional one through the formation of Cooper pairs.

The manipulation of deep-frozen atoms will allow us to understand the difference between these two ways of producing superfluids, which will certainly result in the development of superconductivity at high temperature.

In fact, today there are superconductors that, while they don’t work at room temperature, work at the temperature of liquid nitrogen, which is relatively cheap and easy to obtain.

Extending the concept of ​​fermionic condensates beyond the atomic gases of fermions, numerous examples can be found in which fermions collectively occupy low energy quantum levels.

The first, as already mentioned, is electrons in a superconductor. These are fermions that align in pairs to occupy the lowest quantum levels at low temperatures, exhibiting collective bosonic-type behavior and reducing viscosity and zero resistance.

Another example of fermionic grouping in low energy states is the ​​condensates of quarks. The helium-3 atom is also a fermion, but at low temperatures it forms Cooper pairs of two atoms that behave like bosons and exhibit superfluid behavior.

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