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Which paper introduced the concept of the "Bloch sphere"?

Physics Asked by Yuji on June 6, 2021

Everyone loves Bloch sphere, but which paper of Bloch was it introduced? The Wikipedia article on Bloch sphere (here), as of 17/May/2021 links to this paper of Bloch “Nuclear Induction” but it doesn’t seem to discuss the Bloch sphere!

I would appreciate if you could point me to the right reference.

2 Answers

The names "Bloch state" and "Bloch sphere" were introduced in Ref.[1]. Section III of Ref.[2] says "A very elegant and convenient representation was independently proposed by Radcliffe and by ACGT in terms of what ACGT have called Bloch states."

[1] F. T. Arecchi, E. Courtens, B. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972)

[2] L. M. Narducci, C. A. Coulter, and C. M. Bowden, Phys. Rev. A 9, 829 (1974)

Correct answer by Shintaro on June 6, 2021

The wikipedia page cites Bloch's paper "Nuclear induction" in 1946 where he wrote down Bloch's equation for nuclear magnetization. It seems that Bloch didn't explicitly say anything about "his sphere", or anything about geometric representation of quantum states of spin-1/2. He went straight to the equation of motion for the magnetization vector. So it seems it's not that Bloch actually introduced the sphere himself, perhaps his name was attached because of his equations. Then there is a paper in 1957 by Feynmann, Venon and Hellwarth titled "Geometrical Representation of the Schrodinger Equation for Solving Maser Problems", which clearly presented the idea of Bloch sphere but didn't cite Bloch (for the geometric representation).

Answered by Meng Cheng on June 6, 2021

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