I am trying to learn about Bose–Einstein (BE) condensate, and in doing so I encountered some bizarre phenomena, which is a norm in quantum mechanics. I realized matter would turn into 'waves' and lose their identities close to absolute zero. Moreover, I understand we can never reach absolute zero, because as long as there exists a particle, there exists a movement of the particle, which means there exists heat, which means the absolute zero cannot be reached. I was wondering, IF HYPOTHETICALLY, we could reach absolute zero, would that imply that the particle would become 'non-existent'? I do not have a specific question but I would like someone shed light on BE condensate and explain the significance of it and the meaning of BE condensate as a distinct matter. I am more keen on building an intuition.
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Rob, I second the advice given by @KFGauss in the comments to review quantum mechanics and statistical mechanics first.
But let me dissect your question and analyze the words you use.
I realized matter would turn into 'waves' and lose their identities close to absolute zero.
This poetic language of "losing identity" or "identity crisis" as in the Youtube video refers to the statistics of indistinguishable particles. At high temperature, Maxwell-Boltzmann statistics describe the energy level occupations of thermal atoms. Indistinguishability matters little at high temperature because there are possibly many ways to label/tag atoms and distinguish them (e.g. many different spatial modes, many different velocity groups; many different spin states.)
At low temperature, indistinguishability starts to matter because more and more atoms share the same labels/tags that I described above. And the statistics is described by Bose-Einstein statistics or Fermi-Dirac statistics, depending on whether your matters are made of bosons or fermions.
Finally, it's not like a particle is a billiard ball and it suddenly turns into a wave below certain temperature. The waviness of the particle is described by thermal de Broglie wavelength, and at high temperature, it is extremely short, so the description of a particle as a billiard ball is fine. At low temperature, especially when the thermal de Broglie wavelength becomes longer, approaching or even surpassing the other existent length scales (e.g. length over which external potential varies; inter-particle spacing), the quantum-mechanical description of the particle is required.
because as long as there exists a particle, there exists a movement of the particle, which means there exists heat, which means the absolute zero cannot be reached.
You refer to the zero-point motion of a particle, but that does not mean that a particle has to carry some fundamental quantity of heat. As I said in the comments section, heat is related to the variance in motion, not motion itself. There is a laser cooling technique that can cool atoms to zero temperature in principle ("VSCPT"), but it will require infinitely long time.
If you really want to understand Bose-Einstein condensation, it has to do with the saturation of thermal occupation of excited states. Given the temperature of the system and the energy level distribution, you know the average thermal occupation of excited states. Below certain temperature, you will find that the sum of those occupations is less than the total number of atoms you have in the system. Because of saturation, any extra particle introduced into the system goes into the ground state. And as you go lower and lower in temperature, the population in the ground state grows until almost all of the population is in the ground state.