Can Singlets be Prepared with a Preferred Direction?

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In summary, Professor Susskind explained that the expectation value of all three sigma operators acting on a singlet pair is zero, meaning that a singlet pair cannot be prepared in a preferred direction. This is because the singlet state is spherically symmetric and has no preferred direction. However, this does not cause any difficulty in preparing a singlet state, as seen in the example of hydrogen atoms.
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anorlunda
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Professor Susskind said that the expectation value of all three sigma operators acting on a singlet pair are zero. Does that mean that a singlet pair can not be prepared in a preferred direction?
 
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I assume you are talking about the singlet (total L = 0) state of two spin-1/2 particles? This state has no preferred direction: it is spherically symmetric (this is true of any L = 0 state, no matter how complicated).

This causes no particular trouble in preparing a singlet state of two spin-1/2 particles. For example, the ground state of hydrogen (which consists of two spin-1/2 particles, the proton and the neutron) is the spin singlet state, so hydrogen atoms naturally fall into this state. If the singlet state were actually an excited state, though, we could still easily prepare hydrogen atoms in the singlet state by exciting them to the appropriate energy level with e laser.
 
  • #3
There is no preferred direction with a singlet spin state.
 

FAQ: Can Singlets be Prepared with a Preferred Direction?

Can singlets be prepared in a laboratory setting?

Yes, singlets can be prepared in a laboratory setting through various methods such as chemical synthesis or physical processes like vapor deposition or molecular beam epitaxy.

Are there any limitations or challenges in preparing singlets?

Yes, there are limitations and challenges in preparing singlets as they are highly reactive and short-lived species. This makes it difficult to isolate and study them, and requires specialized equipment and techniques.

What are the potential applications of singlets?

Singlets have potential applications in fields such as materials science, organic chemistry, and quantum computing. They can also be used as intermediates in chemical reactions and as probes for studying reaction mechanisms.

How are singlets different from other electronic states?

Singlets are different from other electronic states because they have two electrons with opposite spins, resulting in a total spin of 0. This makes them more stable and less reactive compared to other electronic states with unpaired electrons.

Can singlets be observed or detected?

No, singlets cannot be directly observed or detected due to their short-lived nature. However, their presence and properties can be inferred through spectroscopic techniques and theoretical calculations.

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