In a laser cooling experiment

1. A beam of 87Rb atoms is to be slowed down using a Zeeman slower with laser light tuned to the 52s1/2 − 52p3/2 transition with F = 2,mF = 2 → F ′ = 3,mF ′ = 3 (λ=780 nm). The nuclear spin is I = 3/2. The atoms escape from an oven with most probable velocity v0 = 400 m/s. The lifetime of the excited state is 26 ns.

(a) Determine the stopping distance L0.

(b) Calculate the maximum possible scattering force.

(c) Calculate the number of scattering events that takes place during the time the atom slows down.

(d) After Zeeman slowing, the atoms are loaded into an optical molasses. What is the shortest possible damping time in the absence of heating due to fluctuations if the laser intensity is I=0.1 mW/cm2?

(e) Calculate the Doppler cooling limit and the recoil limit temperatures for laser cooling using this transition and wavelength

[15 marks]

2. The treatment of Doppler cooling given in the lectures assumes a two-level atom but in real experiments with the optical molasses technique, or the magneto-optical trap, any hyperfine structure of the ground state causes complications.

(a) The 87-isotope of rubidium has a nuclear spin I=3/2. Draw an energy level diagram of the hyperfine structure of the 52s1/2 and 5

2p3/2 transitions and indicate the allowed electric dipole transitions.

(b) In a laser cooling experiment, the transition 52s1/2, F = 2 to 5 2p3/2, F

′ = 3 is excited by light that has frequency detuning δ = Γ/2. Selection rules dictate that the excited state decays back to the initial state so there is a nearly closed cycle of absorption and spontaneous emission, but there is some off-resonant excitation to the F ′ = 2 hyperfine level which can decay to F = 1 and be ’lost’ from the cycle. The F ′ = 2 level lies about 45Γ below the F ′ = 3 level. Estimate the average number of photons scattered by an atom before it falls into the lower hyperfine level of the ground state configuration. Assume I = ISAT and that the transitions have similar strengths.

(c) To counteract the leakage out of the laser cooling cycle, experiments use an ad- ditional laser beam that excites atoms out of the 52s1/2, F = 1 level so that they eventually decay back to the 52s1/2, F = 2 level. Suggest a suitable transition for this ’re-pumping’ process and comment on the intensity required.

[15 marks]

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