Simulation of Broad Transition MOTs

[Lufter Reis]

Hi All,

I noticed that the Recoil-limited MOT example agrees very well with the published Strontium MOT on narrow transition (7 kHz). So I am wondering if this model from PyLCP still works for the broad transition (32 MHz). One problems pops up immediately is that even a single atom trajectory takes tens of minutes to run. The program will need to calculate 1e7 solutions for a 50ms free-run simulation by default using rate equation as governing equation. Comparing to the Recoil-limited MOT example, 50ms simulation only needs a few thousands of solutions by default. I assume this is because there are 1000 more scattering events within this 50ms simulation time. But is there a way to reduce the calculation time of the broadMOT example (A small example code attached) for more practical use?

Best,

Lufter

[Barker, Daniel S. (Fed)]

Hi Lufter,

 

One limitation of the rate equation governing equation is that it needs to re-diagonalize the Hamiltonian when the direction of the magnetic field changes (since that defines the rate equation quantization axis). In a MOT simulation, this happens at every timestep in evolve motion, making the simulation very slow (even when random recoil is false).

 

My first suggestion is to remove max_step=1 from the call to evolve_motion and use max_scatter_probability (=0.1 is default) to control the step size instead. That might give you a marginal improvement in speed (particularly if you investigate higher values of max_scatter_probability). You could also reduce the solver precision using the rtol and atol arguments of the underlying call to scipy’s solve_ivp (though this may lead to nonsense results, I typically need to increase the precision from the pylcp defaults).

 

Another possibility is to switch to the OBE governing equation. The OBE always uses the z axis as the quantization axis, so there’s no repetitive Hamiltonian diagonalization. Because bosonic alkaline-earths only have 4 state Hamiltonians, the simulations might be faster than the rate equations. But, I have not tested this myself. (Please let me know how it goes if you try it).

 

Finally, my intuition is that the broad line dynamics may be faster than the narrow line dynamics. You might be able to run shorter simulations once you figure out when the MOT reaches steady state.

 

Let us know if you have any more questions,

 

Daniel

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