Questions regarding the random recoil

[Xin Wang]

Hi,

Thanks very much for your fancy work!

I have two questions regarding the random events in evolve_motion  in rate eq method and Bloch eq method.

1. I found for each random recoil, two random velocity were added on the atom. I wonder why 2 velocity vector were added instead of 1? SInce the radiation force has already been taken into account by equation evolution, each decay there will only be 1 photon emitted, is that correct?

2.The random_force in rate eq is not clear for me. The only difference of random force from random recoil is that one random velocity from emission was replaced by the one from photon kick. May I ask the physical picture of the random force and random velocity?  From what I understand, the random kick did the same thing with the radiation force while evolving, is that correct?

I'm looking forward to your reply, thanks again

Best

Xin Wang

[Lajos Palanki]

Hi All,

I wanted to piggyback off this question as there has not been an answer. I am especially interested in the first question of the two random vectors being added together to form the recoil. Is there some statistical or physical reason behind this?

Best,

Lajos

[Eckel, Stephen P. (Fed)]

Hi Lajos and Xin Wang,

Sorry for the delayed reply to these questions. Note that the subtle difference between the two calculations is related to calculating and applying the average force to the atoms.

1. When you apply the average force to the motion of the atom, you need to also take into account the randomness of the absorption process [see the discussion after equation (23) in the pylcp paper. It is also mentioned in https://journals.aps.org/pra/pdf/10.1103/PhysRevA.91.023426 and in Foote’s Atomic Physics, page 188, section 9.3.1]. The intuition here is that, when you have multiple beams that you can scatter from, you cannot be sure which laser was the one that excited the atom. For a typical 3D molasses or MOT, this is almost like getting second random kick in addition to the random kick from the spontaneous emission. This approximation is really only applicable for cases where you have multiple laser beams in a 3D geometry and the atom’s Doppler and/or Zeeman shifts are not large enough to preferentially scatter from one single beam; this is indeed the case for a typical MOT or molasses. This approximation probably overestimates the momentum diffusion in the case of a single beam.

2. During development, we wanted to check that this second random kick was indeed self-consistent. In the rate equations, you can ignore the average force entirely and just calculate a probability that an atoms scatters from a given laser beam. (More specifically, one need not consider the average force because each laser is considered separately and without coherence to the other laser beams.) If a scattering event happens, you apply a momentum kick from the beam doing the scattering and then a random momentum kick for the subsequent spontaneous emission event. This scenario is probably more accurate for single-beam geometries, or cases where the atom’s Doppler and/or Zeeman shifts are large enough to preferentially scatter from a single beam in a multiple-beam geometry.

It turns out that these two approximations give the same answers for molasses and 3D MOT geometries under the rate equations. These are rather crude approximations, so take any estimate you get for temperatures, etc. with a grain of salt.

Let me know if you have further questions or if that was not clear.

-Steve

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Dr. Stephen Eckel
Physicist
Sensor Sciences Division
Fundamental Thermodynamics Group
100 Bureau Drive, Stop 8364
Gaithersburg, MD 20899-8364
(301) 975-8571

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