Fermions & Bosons - How Do They Interact?

[topside]

there's a little confusion in my mind as of late.

How can fermions be made to act like bosons allowing it to bypass the Pauli's exclusion principle?

Example: The rubidium atom they used to make the first BEC was a bosonic atom.

Also, if anyone could lend some insight as to how they recently got fermionic atoms to form into condensates?

 

[ZapperZ]

Originally posted by topside
there's a little confusion in my mind as of late.

How can fermions be made to act like bosons allowing it to bypass the Pauli's exclusion principle?

Example: The rubidium atom they used to make the first BEC was a bosonic atom.

Also, if anyone could lend some insight as to how they recently got fermionic atoms to form into condensates?

The fermions themselves didn't turn into bosons. They PAIR UP so that the composite entity is a boson. For example, a pair of electrons can pair up in opposite direction so that they form an entity with a net spin of 0 - thus, a composite boson with spin 0 (as in conventional superconductors). Or, they can pair up parallel and form an entity with net spin of 1 - thus a composite boson of spin 1, as in the ruthenates superconductors, etc.

Zz.

 

[mstrachan]

The fermionic condensate is acheived the same way as it would be with a bosonic condensate. By supercooling the material to within a fraction of a degree above absolute zero. Techniques used to do this include a form of stimulated immissions involving lasers operating at resonant frequencies of the material basically they hit the atoms with photons that go in rhythm with oscillations of the molecules, which triggers a release of a photon at a higher energy level - basically kicked off at the resonant frequency - the quantization of the energy levels allows energy to be pulled out of the substance in a way that drops its energy.

essentially, spin adds. So, 1/2 spin fermions add to have spin 1 groups, which are therefore bosons and obey boson statistics. You cool the fermions down enough, and they condense the same way.

You just have to have a chemical structure that is able to drop into low enough energy states that it obeys the statistical mechanics. Basically, we have the math to calculate when the phase change can occur based on the properties of the molecules.

Now, the question I have is: What type of lie groups/algebras/ mathematical model of particle physics is it where you can show why spin adds?

Twistors? Quantum Chromodynamics SU(3)? I would really like to know why this works and what mathematical model you need to look at to see how fermion wavefunctions can be 'added' in the formulation that describes spin, so that the wavefunctions connect and become a single wavefunction. I cannot find a single reference to this in the literature. The only thing I can find is the experimental evidence that it occurs--i.e the bose einstein condensate.

I'll settle for a non-relativistic treatment of this, but someone please show me the math that describes spin, and the algebraic connection of wavefunctions in that space that allows condensates to occur.

If I'm thinking the right way, we have a lie group to describe a 4 dimensional space time, and then we have a fibration of additional lie group dimensions that describe further properties of particles, of which spin is described by quaternions. Depending on which mathematical model you are using (QED, QCD, superstrings, M-Theory) the number of dimensions of the fibrated space changes. I don't understand if fibration is disconnected - i.e. a fibration at each point where there is a particle, or if fibration is a continuous space, covering the 4 dimensional space time, and partitioned by particle as described by a wavefunction in the 4 dimensional space time. I really want to find someone who can help me understand this stuff, so if you are this person, please email me at mark@codesource.la.

-Mark

 

[Haelfix]

'Now, the question I have is: What type of lie groups/algebras/ mathematical model of particle physics is it where you can show why spin adds?'

This is an elementary process in quantum mechanics, and yes it does have to with lie groups. Its treated in nearly every textbook on the subject.

Rather than spell it out, google for Clebsch-Gordan coefficients, and you will probably find a nice spiel written out.

 

[Mk]

What does the fermionic condensate have to do with high-temperature superconductors?

 

[loandbehold]

What does the fermionic condensate have to do with high-temperature superconductors?

I'm assuming by "fermionic condensates" you're talking about the experiments with ultracold atoms? If so, I've taken a stab at answering the question below. If not, then I hope you find it interesting anyway...

Basically, to see the connection you need to understand something called the BCS-BEC crossover.

As mentioned in one of the previous posts, in order for fermionic atoms to Bose condense, they must pair up to form composite bosons with integer spin. There's actually different ways to do this, but for the purposes of the discussion I'll first consider two extreme examples. One is analogous to the process in conventional superconductors, where electrons with equal and opposite spin and momentum form Cooper pairs below a critical temperature. The theory of how this pairing leads to superconductivity was first proposed by Bardeen, Cooper and Schrieffer, and therefore one can name the system of Cooper pairs the BCS state. However, another possibility, which can occur when the interactions between the atoms are strong, is for pairs of atoms to bind together to form bosonic molecules. If the temperature is low enough, these molecules can then form a Bose condensate very similar to those found for bosonic atoms. This can be termed the BEC state.

There's actually a continium between these two extremes- your system can lie somewhere between the BEC or BCS states. This is the case for high-temperature superconductors- one difference (among many others) between high Tc superconductors and conventional superconductors is that the interactions between the electrons are strong enough so that one is no longer in the BCS regime, but on the other hand not so strong that one is in BEC regime either. So studying this regime, the so-called BEC-BCS crossover problem, is relevant to understanding high-Tc superconductors, among other systems where these kinds of pairing phenomena occur (such as liquid helium-3).

Now here's where ultracold atoms come in. One thing that's nice about these experiments is that one can use something called a Feshbach resonance. I won't explain what this is, but the important thing about this resonance is that you can very precisely tune the interactions between the atoms. So, in principle, if you have a system of fermionic atoms, you can continously tune the system from the BEC regime, where one has the Bose condensate of molecules, all the way to the BCS regime, where one has a Bose condensate of Cooper pairs. In practice, even though extremely low temperatures can be reached in these experiments, they can't reach low enough to study the BCS regime. However, the transition temperature increases as one increases the interactions (just like in a high Tc superconductor) so that the BEC regime, and even more importantly, some of the cross-over region, can be studied. The experiments have formed BECs of molecules, and more recently pairs in this crossover region, and are currently trying to understand these systems. In particular, they're studying superfluidity (which is the analoguous to superconductivity, but for neutral atoms) as well as testing theories of this crossover, which are highly non-trivial and, as I mentioned above, are important in other systems too.