Interferometry With Bose-Einstein Condensates: Fill & Download for Free

“Has the double slit experiment ever been actually performed with a single atom/electron?”Atom, yes – the wavelength is too small for a practical experiment except from a Bose-Einstein condensate. Atom Interferometry with Bose-Einstein Condensates in a Double-Well PotentialElectron, yes – Is there a real-life video of the electron double slit experiment?

Ingenuity is a good one, which is helped by having some intuition for the system you're modeling. It also depends on what problems you're trying to solve. For instance, if you are working with Bose-Einstein condensates you might be looking to use one as some kind of sensor on the account of it basically being a massive particle with quantum properties (in other words, it can be robust against decoherence). This means that if you're an experimentalist, you're trying to localize the constituent particles to reduce measurement errors, which makes a theorist tasked with modeling the system much easier.You can gain some intuition for your problem by running full 3D simulations or 1D/2D toy simulations to get a handle on how a BEC behaves in certain situations. For example, you'll see some scattering if you start with a moving wavepacket that hits a sharp barrier, so multiplying your trial wavefunction with a trigonometric function makes a lot of sense since it has to be able to model that property. You can extend this to much more complicated situations where you're in 3D and you have some sources of disturbances (the laser/BEC equivalent of putting a stick in water and moving it around, for example).This is only slightly related, but sometimes you can get away with doing only half of a variational method when you're unsure of what other parts of the system might behave. A so-called "hybrid" variational method was the subject of this paper (N.B. I'm an author, also my advisor had a tendency for writing pedagogically so it may be accessible to you). Briefly, the situation is such that you have some confinement of a BEC in one direction that is easy to model, but in the other two directions it's more difficult. You can compute the variational approximation and include it in a numerical scheme for direct integration (similar in spirit to split-step methods for solving general PDEs). This is ~1000 times faster than simulating in 3D, and you can peruse the figures to see how well it worked (spoiler: very well). The reason this was at all possible was because the experimentalists didn't want any fluctuations in the z-direction, so a (blue-detuned) laser sheet was employed to keep the condensate in the plane.I think modeling BECs is a pretty good place to start if you want to play around with variational methods. The reason is that a BEC's wavefunction is basically the same as a single-particle wavefunction which is a solution to a nonlinear Schrodinger equation (in the limit of dilute condensates, zero temperature, etc.). Numerical simulation is quite simple as well, and 1D and 2D simulations can run on your laptop between a couple of seconds and maybe an hour or two. If you are interested in doing this, I've written some code to do direct simulation. Then you can follow the "Lagrangian variational method" prescription and derive systems of ODEs to approximate the dynamics of your simulations. Some helpful links: (1) Lagrangian variational method (original paper with test cases, analysis of toy problems, numerics), and (2) another paper that came from my (former) group that has a similar pedagogical style which might be helpful in framing the problem in the context of interferometry (the other paper I linked does released toroidal condensates whose dynamics may be harder to intuit).cc: Brandon Benton who actually did all these LVM calculations.

The luminiferous aether is a conjecture without experimental evidence just as is supersolid dark matter. Light does not require a medium to propagate so no one is seriously looking for LA, but the interferometry technology that was advanced to search for LA, more than a century ago, has been updated and reused in LIGO to detect gravity waves. A supersolid is a “spatially ordered material with superfluid properties.” The super solid state of matter was discovered in Bose-Einstein condensates in 2017. Bose-Einstein condensates form at ultra-low temperatures, a small fraction of a degree above absolute zero, while the temperature of outer-space is very much higher at 2.7K. So if SSDM is strongly interacting, as is claimed, then it should be too hot to be a super-solid.