search

DanielSank / theory

Physics, math and other theory
22 stars 8 forks source link

Typo in asymmetric coupling section of qubits 101 #37

Open amopremcak opened 5 years ago

amopremcak commented 5 years ago

Equation (86) (the flux quantization condition) and the definition of \delta_L in terms of \delta in the line that follows are inconsistent with equation (87) (dc current through the SQUID in terms of \delta). The expression for \delta_R would equal \delta + (3/2)*\phi as opposed to \delta - \phi/2 as equation (87) suggests.

amopremcak commented 5 years ago

Also, I am having difficulties reproducing equation (88). To zeroth order in \phi, I can derive an expression which differs by yours by a factor of -1/2. The minus sign is because I used \delta_L = \delta - \phi/2 (which is what I think you meant to do). The factor of 1/2 is because only one of the terms in my expression for dI/d\phi contributes in a zeroth order expansion of \phi. In general, my expression for dI/d\phi is given below

equation_for_dan
DanielSank commented 5 years ago

Working through this myself again, I get

image

amopremcak commented 5 years ago

Sounds like we gotta beer bet this one. Below is a pdf of my derivation of the equation abover. Perhaps I am messing up a sign or something: dc_squid_drive.pdf