# Relativity Doppler Shifts et al

1. Feb 20, 2005

### stunner5000pt

A lithium atom with initial velocity of 1000m/s (x hat direction) will be deflected into a positron cloud by a laser of wavelength 670nm. The laser beam is 1mm high and 15cm long and has an average power of 1mW. As the atoms absorbs each pohoton it is deflected in the yhat direction by a small smount and henece sees the laser with a difference frequency due to the Doppler Shift. The atom in the excited state has a lifetime of 27ns.

a) How many photons will be absorbed as the atom passes through the laser beam.

I can certainly find the raidation pressure using $$\frac{F}{A} = \frac{I}{c}$$ but how do i find hte number of photon absorbed??

b) Find an expression for the classical (1000m/s << c) Doppler Shift of the laser as a function of time during the time the atom is in the laser beam.

I thought there wasnt any trasverse Doppler Shift so what the

c) What is total relaitivistic Doppler Shift at the end of the 15cm laser beam/

First i have to find the amount of deflection (true?) sooo $$\Delta p = \frac{\Delta U}{c}$$ in this case and here Delta U is the power times the time the atom is in the laser beam that is 0.00015s but this is much more than 27ns so the totoal doppler shift is going to be lesser than it should be and since the speed 1000m/s is much lesser than c then the gamma value is almost 1.

d) In order to achieve the maximum delfection from the natural frequency of the laser must be tuned to compensated for the Doppler Shift. Atr what rate Hz/sec must the laser be tuned. (called Chirping the laser)

Im not quite sure how this should be done. So when the Lithium atom is aexcited it will not absorb that same frequency which excited it. SO the laser's wavelength has to be changed. IS this chriping menas??

e) How does the second order term in the relaitivisitic shift (v/c)^2 compare to the tota;l classical Doppler Shift.
i have no idea here whatsoever

ANy help would be greatly appreciated!!

2. Feb 20, 2005

### Staff: Mentor

a) Presumably since the laser photons are deflecting the Li atom in the y-direction, the laser beam is pointing in the y-direction. You need to figure out how long the Li atom is in the laser beam, and then divide that time by the 27 ns (lifetime of excited state in which it will not absorb at that wavelength) and that will give you the number of photons absorbed.

d) The laser has to be tuned every 27 ns, because that is when the Li atom is ready to absorb another photon. So the period equals one excited lifetime.

3. Feb 20, 2005

### stunner5000pt

can anyone else help with b) c) and e) then i understand how a) and d0 are done thanks AStro.

4. Feb 21, 2005

### stunner5000pt

So do i use $$\Delta p = \frac{\Delta U}{c}$$