22.51 Quantum Theory of Radiation Interactions, 2011 Midterm

22.51 Quantum Theory of Radiation Interactions, 2010 Midterm

Consider an isolated electron with spin1 , placed in a large magnetic f eld ~ B = Bz~z at zero temperature. The spin is 2 in the state ψ = c0 + c1 where |↑〉 ≡ |S = + | 〉 |↑〉 |↓〉 z 〉 (|↓〉 ≡ |S ~ z = − 〉) represents the spin state aligned (anti-aligned) with the vertical z-axis. 2 2 We now assume that we can measure the magnetic dipole ~ ~μ = γS = γ σ~ ~ of this single spin (with γ the gyromagnet...

22.51 Quantum Theory of Radiation Interactions, 2010 Final

22.51 Quantum Theory of Radiation Interactions, 2009 Final

22.51 Quantum Theory of Radiation Interactions, 2012 Midterm

In this mid-term we will study the dynamics of an atomic clock, mF which is one of the applications of David Wineland’s research (No­ bel prize in physics 2012). We consider a simplified (and sometime inaccurate) model of a vapor-cell atomic clock . Light from a lamp passes through a vapor of rubidium atoms housed in a glass cell and is detected by a photodiode. The light intensity transmitted ...

22.51 Quantum Theory of Radiation Interactions, 2009 Midterm

where we used the fact that (σ 2 z) = 1 . In general e−iφfn·fσ = 1 cos(φ)− in · nσ sin(φ) Now we consider a system composed of two subsystems H = H1 ⊗H2, each being a two-level system. To describe operators on the two subsystems we normally use the shorthanded notations A ≡ A ⊗ 1 2 and B ≡ 1 1 ⊗B2 and AB ≡ A ⊗B2 . a) What is (σσ) z z ? b) Consider the operator U = e− 1 iσ iσ φ⊗ z e− z : to whic...