How do composite bosons behave in a Bose-Einstein condensate?

In summary: B) How did they detect the position of the condensate? Can the wavefunction^2 be measured?The position of the condensate can be detected using various imaging techniques such as absorption imaging or fluorescence imaging. These techniques rely on the interaction of light with the atoms in the condensate, and the resulting images can be analyzed to determine the position of the condensate.As for measuring the wavefunction squared, this is not possible as the wavefunction is a complex-valued function and cannot be directly measured. However, by performing multiple measurements and analyzing the results statistically, we can infer the behavior of the wavefunction.
  • #1
jet10
36
0
A few questions about BEC:

A) When these bosons condensate, many particles fill the ground state. I read from textbooks that this would imply that they occupy the same position.
-1- experiments are done with Rb atoms, which consist of protons, neutrons and electrons. Wouldn't the electrons and protons in the atoms repel each other respectively? Can the particles really occupy the same position?
-2- what happens to the electromagnetic and strong interaction? Wouldn't the particles form molecules or different nucleus if the particles are so close to each other?

B) How did they detect the position of the condensate? Can the wavefunction^2 be measured?
 
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  • #2
jet10 said:
A few questions about BEC:

A) When these bosons condensate, many particles fill the ground state. I read from textbooks that this would imply that they occupy the same position.
-1- experiments are done with Rb atoms, which consist of protons, neutrons and electrons. Wouldn't the electrons and protons in the atoms repel each other respectively? Can the particles really occupy the same position?
-2- what happens to the electromagnetic and strong interaction? Wouldn't the particles form molecules or different nucleus if the particles are so close to each other?

B) How did they detect the position of the condensate? Can the wavefunction^2 be measured?

First of all, condensing into the "same state" need not necessarily imply the "same position".

Secondly, what you are asking for is the situation for a composite boson. This require a bit more in-depth study on not just the bosonic state, but also the fermionic state that make up the composite boson. The easiest way to illustrate this is using the Cooper pairs that make up the supercurrent condensate.

Each Cooper pair naively can be describe via a singlet spin-up and spin-down pair, but with opposite momentum, i.e. something like this:

[tex]|k_1, up> - |-k_1, down>[/tex]

However, in the Fermi sea, you can have almost an infinite set of these k's. So another pair may have

[tex]|k_2, up> - |-k_2, down>[/tex]

etc...

Now, the composite pair may all condensed into a single BE state, but each of the electrons making up all of those pairs will have some unique momentum state. So the electrons still obey the FD statistics, even when they are part of a bosonic conglomerate.

Similar description applies to LH3 and the systems you described.

Zz.
 
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  • #3
I am not very familiar with theory of Cooper pairs. Maybe I just have to read it up. It is a little hard for me to imagine it.

About a composite boson: Let's say you have [tex]|k_1, up> - |-k_1, down>[/tex] and [tex]|k_2, up> - |-k_2, down>[/tex]. They are two bosons or Cooper pairs made up of 2 electrons respectively. The second boson is in the same state as the first only if k2 = k1, am I right? In order to do that, I will need another pair of electrons that have k1 and -k1. But the Pauli Principle would forbid the existence of an additional pair of these states in the system. How can I get two Cooper pairs to be in the same state then?
 
  • #4
jet10 said:
I am not very familiar with theory of Cooper pairs. Maybe I just have to read it up. It is a little hard for me to imagine it.

About a composite boson: Let's say you have [tex]|k_1, up> - |-k_1, down>[/tex] and [tex]|k_2, up> - |-k_2, down>[/tex]. They are two bosons or Cooper pairs made up of 2 electrons respectively. The second boson is in the same state as the first only if k2 = k1, am I right? In order to do that, I will need another pair of electrons that have k1 and -k1. But the Pauli Principle would forbid the existence of an additional pair of these states in the system. How can I get two Cooper pairs to be in the same state then?

Ah. You are confusing "single-particle" states with "two-particle states".

What I wrote for the states of the fermions are single-particle states. So each fermion must occupy a unique single-particle states. However, once you form a pair of anything (not just bosons) and they are now coupled together, you can no longer treat each particle individually. You now have to do a 2-particle state. This has to be solved differently and depends on what situation you are dealing with.

In the superconductivity case, you can naively construct a wavefunction that is a linear combination of all the pairs, i.e. you sum up all the k's. This is the "single state", because you have one coherent wavefunction.

Zz.
 
  • #5
jet10 said:
A few questions about BEC:

A) When these bosons condensate, many particles fill the ground state. I read from textbooks that this would imply that they occupy the same position.
-1- experiments are done with Rb atoms, which consist of protons, neutrons and electrons. Wouldn't the electrons and protons in the atoms repel each other respectively? Can the particles really occupy the same position?
-2- what happens to the electromagnetic and strong interaction? Wouldn't the particles form molecules or different nucleus if the particles are so close to each other?
A condensate of alkali metal atoms (like Rb) is a condensate of "composite bosons". Each atom is made up of an even number of fermions, making it "look" like a boson to another atom that is far away from it. If the atoms get close enough to each other that they can "distinguish" the individual fermions in the other atom, then we are no longer in the limit of a weakly-interacting Bose gas.

In most experiments done with alkali atoms, the density of the gas is actually very small (several orders of magnitude less dense than air at STP), and the individual atoms are pretty far away from each other (as expected).
 

What is Bose Einstein condensate?

Bose Einstein condensate (BEC) is a state of matter that occurs at extremely low temperatures, near absolute zero. It is formed when a group of boson particles, such as atoms or particles of light, lose their individual identities and behave as a single coherent entity.

What are the properties of Bose Einstein condensate?

BEC is characterized by its superfluidity, meaning it has zero viscosity and can flow without any resistance. It also exhibits quantum coherence, where all particles in the condensate behave in a coordinated manner. BEC also has a high degree of spatial coherence, meaning the wavefunctions of the particles are all in phase with each other.

How is Bose Einstein condensate created?

BEC is typically created by cooling a gas of boson particles, such as rubidium or sodium atoms, to extremely low temperatures, usually below 100 nanokelvins. This is achieved using techniques such as laser cooling and evaporative cooling. As the temperature decreases, the particles become more and more confined to the lowest energy state, leading to the formation of BEC.

What are the potential applications of Bose Einstein condensate?

BEC has potential applications in fields such as quantum computing, precision measurements, and quantum simulations. It has also been used in the development of new types of atomic clocks and interferometers. Research is ongoing to explore the potential uses of BEC in various fields of physics and technology.

What are the challenges in studying Bose Einstein condensate?

One of the main challenges in studying BEC is the extremely low temperatures required, which can be difficult and expensive to achieve. Additionally, the delicate nature of BEC makes it sensitive to external disturbances, making it challenging to manipulate and study. The properties and behavior of BEC also require a deep understanding of quantum mechanics, making it a complex subject for study.

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