Temperature is ignored when calculating state lifetime and transition rate in Cell

[JacksonPhoong]

I noticed that when initialising Cell, the functions _add_state_lifetimes() and _add_decoherence_rates() do not accept an argument for temperature. Instead, the default temperature of 0 K is used. This means that the values would be inaccurate when modelling a system at, say, room temperature.

Also related, both of the functions above utilise the ARC package and the values returned according to their docs are in units of s and s^-1 respectively. I see that these values are then converted within the functions into unit of MHz. My question is that why aren't these values converted to unit of Mrad/s?

[dihm]

Thank you for bringing this up. This was actually a conscious decision (which we haven't documented, oops). The short of it is we decided to not support it at this time because the more accurate lifetimes generated don't meaningfully change results for many problems, making the difficulties supporting it not really worth it for most people. We do plan to incorporate something in the near future though. Below are the specific issues:

• While the underlying ARC functions for state lifetimes and decoherence rates do take a temperature parameter, they also require defining a maximum n to include in the calculations (since ARC is convolving the black-body spectrum with the transition frequencies to weight stimulated emissions to other states into the effective lifetime). What n to use for these calculations is obviously very dependent on the state (ie you don't want to calculate transitions up to n=50 when getting the lifetime of the n=10 excited state of Rb). Coming up with some heuristic is possible, but just as likely to be wrong for any given person's situation.
• Including all these extra states makes the calculations themselves very slow (even a moderately complex Cell could take 10s of seconds to create, especially if the ARC cache is being populated for the first time).
• The temperature dependent lifetimes, while fractionally large for Rydberg states, often are irrelevant for thermal ensembles since transit and Doppler effects dominate the lifetimes anyway.

As for the units, some care is needed. To begin, we aren't defining lifetimes in MHz, but rather $\mu s^{-1}$. This matters because, when it comes to lifetimes, $s^{-1}$ is basically equivalent to rad/s. There are a number of ways to prove that to yourself, but I like to start from an insight I heard from Bill Phillips: dephasing is not a periodic process, so defining lifetimes in units of Hz is somewhat nonsensical. So what does it actually mean?

[JacksonPhoong]

Thanks @dihm for the clear explanations. It has helped me understand more about this. You're right that the temperature doesn't meaningfully change the results. I had an issue where I was simulating 5P3/2 and 5D5/2 states of Rb-87 but there was no gamma_mismatch. I mistakenly thought the issue was with rydiqule because the issue disappears when I computed the lifetime manually with the temperature parameter. It turned out that the issue was with ARC and it's resolved when I updated it to v3.10.0 or above.

That's a great insight about the units as well. Thanks for sharing, I am quite new to this field so I am still trying to understand a lot of things.