Atomic diffraction through a crystalline membrane

Make it precise

The precision achieved with current atomic and molecular interferometers is quite remarkable. You can resolve the recoil of a single photon onto massive molecules, observe the attraction of a particle to a nearby object and measure local gravity well enough to sense a cloud flying above you. Hence, these apparatuses are often employed where very high precision is needed, such as defining physical constants [1], searching for new physics [2] or looking for the boundary between the realm of quantum-mechanics and classical physics [3]. However, you can also use it for measurements connected to our everyday life, such as the search for natural resources or for navigation.

Make it big. Hence, make it small

One feature that influences how sensitive your interferometer can be, is the separation of the delocalized particles. The larger the better, so you’d like to have beamsplitters which lead to large angle-diffraction. Usually, people use laser gratings, but as discussed in this post, you can also use mechanical diffraction masks. Here we also discussed that a smaller slit width leads to larger diffraction angles, which is what we want.

The big question is now, what is the mechanical grating with the smallest conceivable grating period and thus the largest diffraction angle for atomic or molecular matter-waves. Current nano-machining has a resolution of a few nanometer and the smallest free-standing gratings produced so far have a period of 100 nm.

In the early days of quantum mechanics people diffracted atomic beams from crystalline surface in reflection to test de Broglie’s hypothesis [4]. These gratings offer a period well below a nanometer and also for neutrons you can use such gratings. However, if you try the same thing with atoms, you most likely rather destroy the crystal than observing diffraction in transmission.

Make it unique

So, is it a lost cause to use crystals? Not really, you just have to combine several unique ingredients for this endeavor to be successful [5]:

  • Take the thinnest conceivable crystalline material there is. A good choice is a single-layer graphene consisting of carbon atoms in a hexagonal chicken wire arrangement as it is extremely resistant to forces. However, other 2D materials might also work.
  • Take the smallest atoms you can find: This is atomic hydrogen consisting only of a proton and an electron.
  • Accelerate these atoms to velocity between 30’000 and 120’000 m/s to pass through the membrane without destroying it.

This should allow you to diffract atoms at a grating with a period of 0.246 nm, around 400 times smaller than state-of the-art nano-machined gratings. What you get are diffraction angles on the order of mrad, that is a few mm after a meter, quite a lot compared to what you can do nowadays.

A single sheet of graphite is called graphene. The period of this two-dimensional material illustrated by the arrow is 0.246 nm, 400 times smaller than those of the smallest machined free-standing transmission gratings. As the grating is 2D, so is the diffraction pattern.

So, is this the method of choice to build atom interferometers in the future? This depends very much on what you are interested in. In general, one might object that the resolution also scales with the time the particles spend inside the interferometer, either to the power of 2 or even 3 [6]. As modern interferometers can reach interaction times up to several seconds, fast atoms cannot beat them in this respect.

However, we can have a look at effects which may be hard to study with usual interferometers. These are effects that scale strongly with velocity, such as quantum friction. Here a fast-moving atom is “sensed” by a surface, preventing interference of the atoms [7]. As common atom interferometers use ultra-cold atoms with a velocity well below mm/s, having a look with atoms at 120’000 m/s might be worth a shot.

But it’s not only about fundamental research, but has also real-life applications: You learn a lot about the interaction of fast atoms with two-dimensional membranes, which is interesting for building new electronics, sensors, and capacitors [8].

References

[1] R. H. Parker et al., Measurement of the fine-structure constant as a test of the Standard Model, Science 360 191 (2018)

[2] P. Hamilton et al., Atom-interferometry constraints on dark energy, Science 349 849 (2015)

[3] Y. Fein et al., Quantum superposition of molecules beyond 25 kDa, Nat. Phys. (2019)

[4] I. Estermann and O. Stern, Beugung von Molekularstrahlen, Z. Phys. 61 95 (1930)

[5] C. Brand et al., Coherent diffraction of hydrogen through the 246 pm lattice of graphene, New J. Phys. 21 033004 (2019)

[6] O. Amit et al., T3-Stern-Gerlach Matter-Wave Interferometer, Phys. Rev. Lett. 123 083601 (2019)

[7] J. B. Pendry, Quantum friction–fact or fiction?, New. J. Phys. 12 033208 (2010)

[8] J. Feng et al., Patterning of graphene, Nanoscale 4 4883 (2012)