Where does this solid angle come from?

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SUMMARY

The discussion centers on the analysis of a quantum interferometer featuring two arms, each equipped with half-wave plates (HWPs) set at angles theta1 and theta2. The user references a paper from arXiv (quant-ph/0412216) and questions the representation of the Bloch sphere in relation to the paths taken by mixed states through the interferometer. The inquiry specifically addresses the significance of the angles of the HWPs and their implications when set equal, indicating a deeper exploration of quantum state manipulation.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly quantum state representation.
  • Familiarity with interferometry and its components, specifically half-wave plates (HWPs).
  • Knowledge of the Bloch sphere and its application in visualizing quantum states.
  • Basic grasp of mixed states in quantum systems.
NEXT STEPS
  • Study the implications of angle settings in quantum interferometers, focusing on HWPs.
  • Research the mathematical representation of the Bloch sphere and its vectors.
  • Examine the effects of equal angles (theta1 = theta2) on quantum state evolution.
  • Explore the paper referenced (quant-ph/0412216) for detailed insights on mixed states and interferometry.
USEFUL FOR

Quantum physicists, researchers in quantum optics, and students studying quantum mechanics who seek to understand the dynamics of quantum interferometers and the role of HWPs in state manipulation.

Heidi
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TL;DR
interferometry prblem (with mixed states)
I found this paper
https://arxiv.org/abs/quant-ph/0412216
We have an interferometer with to arms. The firsr has a couple of HWP's inclened by an angle theta
and the second has the crossed couple. A mixed state is in input.
i look to the figure withe the Bloch sphere. i see 2 paths on it. one down and one up. i suppose
that it corresponds to the arms and that that at the end of the two curves they meet when the arms merge. Is it really the Bloch spere in the figure ? i do not see the r vector into it. or is it a sphere into it with a radius length r?
thanks
 
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I am looking to the picture of the interferometer. There are two HWPs on each arm. on the upper arm the first is labelled by theta1 and the 2nd by theta2. what are these angles? what happens when they are equal?
 

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