- The initial \(t=0\) Bose gas momentum space distribution \(n_{|k\rangle}(t=0)\) is sharply peaked at some \(k=k_0\), with the low-energy bosons of \(k<k_0\) in the so-called IR regime and the high-energy bosons of \(k>k_0\) in the UV regime.
- The strongly interacting regime corresponds to bosons with \(k\xi\ll 1\) with \(\xi\propto a^{-1/2}\) the healing length, whereas the weakly interacting regime is \(k\xi\gg 1\).
- In the UV regime, if it starts weakly interacting then it will remain like that because \(k\) just grows, pushing further into weakly interacting.
- In the IR regime, there is a transition from strongly to weakly interacting, so more interesting to study.
- Gevorg’s speed limit paper showed that the coherent coarsening dynamics as quantified by the speed limit \(3\hbar/m\) is, after an initial transient, independent of the (dimensionless) interaction strength \(1/(k\xi)\).
- WWT applies to the weakly interacting \(k\xi\gg 1\) regime.
- # the wiggles at the end are due to diffraction off the BEC, not the sinc momentum space contribution from the BEC which is approximately (need to crop them from the data)
- # a homogeneous top hat in real space.
- # Each experimental cycle lasts about 30 seconds, the first 25 seconds is just the standard steps (MOT, evaporation, Sisyphus cooling, molasses, etc.), the last 5 seconds
- # only like a few seconds is actually the physics.
- # Right now, Gevorg & Simon decided to have 15 increasing TOFs, in order to probe the momentum space distribution n_k of the BEC.
- # The idea is that you measure a 2D momentum space distribution of the BEC along your line of sight, then inverse Abel transform (involves a derivative)
- # it to get the 3D momentum space distribution. But also, the only part you can reliably inverse Abel transform is the part that is not diffracted
- # off the BEC and doesn’t saturate the optical density OD at 3, so can only reliably measure in sort of the “outskirt” regions of the cylinder so to speak
- # where the BEC is not too dense (i.e. OD < 3). Also this is why it’s hard to measure the low-k part of the momentum space distribution, b/c the BEC is so dense
- # there (OD > 3) that it saturates the imaging system.
- # Numerical differentiation is much less robust than numerical integration (Gevorg gave example of a monotonic function like exp(x)),
- # so it’s much harder to get the 3D momentum space distribution. In the case of the inverse Abel transform, you have to differentiate by subtracting the
- # of neighbouring pixels.
- # Need to be on the Cambridge VPN to “SSH” into the VNC viewer to see Analysis GpUI (imaging computer), Cicero, Origin, or any of the office computers
- # each of the lab computers has a IP address, and you can only access them from the Cambridge network. Also a remote Toptica software for
- # relocking the laser if it drifts/unlocks overnight (somehow not so easy to just automate this b/c need to manually play with the current and piezo voltage in the AOMs).
- # Ground state wavefunction of BEC in k-space is not exactly a sinc, rather a Bessel b/c it’s a cylinder.
- # one-body loss, evaporative loss, usually temperatures too high cf. box trap depth, in that case lose a lot of energy but not many particles
- # b/c only particels you lose are the high-energy ones, so you lose a lot of energy but not many particles
- # another worry is counting worry, the n_rad_k distributions might overestimate or underestimate the number of particles
- # e.g. the 350000 atoms seems too high…truncate integrals as well to avoid the noisy region at high-k.
- # for n_k use log-log, for k**2*n_k or k**4*n_k use lin-lin maybe? or log-lin… advantage of lin-lin is that area you visually see is proportional to the
- # integral of the function and for k**2 and k**4 this is nice to see.
- #try playing around with some different definition of “speed of thermalization”, see if they give a monotonic thing or not
- # also compare with the GPE & WWT theory of the paper (which plots k**2*n_k) see if it matches…
- # change energy to temperature scale (nK), also get E/N for each set
"I think I can safely say that nobody understands quantum mechanics" Richard Feynman
