# Bragg diffraction of polyatomic molecules

Diffracting light at crystals

When you illuminate a crystalline sample with light of a single color, you observe bright stripes at certain angles. These depend on the wavelength of the light and the crystal you use. This technique, called Bragg diffraction, is a standard method to investigate matter. The idea is depicted in Fig. 1: A sample is illuminated under an angle θ and the light is reflected at each atom (blue and red dots). As shown, this happens not only at the outermost layer but also at layers deeper inside the crystal. From the sketch it is also apparent that the lower part of the beam has to travel longer to reach the detector further to the right. The path difference is drawn in a broken line and amounts to 2 d×sin(θ).

Whenever this value is an integer n of the wavelength λ, the waves interfere constructively and you observe a bright spot for that angle.

n λ = 2 d×sin(θ)

So, as you know λ and θ, Bragg diffraction gives you information on the spacing of the crystal planes d.

Diffracting matter at crystals made of light

However, you can also turn things around: instead of diffracting light at matter, you can diffract matter at light. The first diffraction of atoms at light gratings has been done in 1983 [1] and the technique has been refined ever since. With respect to Bragg diffraction this has some major advantages:

First of all, you get only two beams: the transmitted and the reflected one. Hence, you get more atoms or molecules per diffraction order, leading to a more efficient beam splitter. In atomic diffraction, the level of control is so high that you can determine the fraction of particles that are reflected and transmitted. This allows you to realize even mirrors, reflecting nearly all the atoms.

Going from atoms to molecules

Molecules are intrinsically more complex than atoms: they vibrate and rotate. Moreover, they may change their shape within a split-second, altering their response to the laser radiation. Hence, the interaction of the laser grating is less well-defined than for the atoms.

However, in spite of these apparent challenges, Bragg diffraction of molecular matter-waves is rather robust. We tested it for two organic molecules, a dye and an antibiotic (Fig. 3) [2].

The molecules used to investigate molecular Bragg diffraction: The dye molecule phthalocyanine on the left and the antibiotic ciprofloxacin on the right.

For both species we observe the main features of Bragg diffraction, that is, only two beams and a shift of intensity from one beam to the other.

In the case of the dye, even the absorption of light from the grating did not destroy the pattern. This is remarkable, as for atoms the absorption of light prevents the observation of a pattern unless special measures are taken [3].

In the future, this technique might be valuable for building new molecular interferometers operating in the optical far-field regime. Here you can manipulate each arm of the interferometer separately. It would be very interesting to do this with particles with different structures or chirality.

References

[1] P. E. Moskowitz, P. L. Gould, S. R. Atlas, and D. E. Pritchard “Diffraction of an Atomic Beam by Standing-Wave Radiation” Phys. Rev. Lett. 51, 370-373 (1983)

[2] C. Brand, F. Kiałka, S. Troyer, C. Knobloch, K. Simonović, B. A. Stickler, K. Hornberger, and M. Arndt “Bragg diffraction of large organic molecules” Phys. Rev. Lett. 125, 033604 (2020)

[3] M. S. Chapman et al. “Photon Scattering from Atoms in an Atom Interferometer: Coherence Lost and Regained” Phys. Rev. Lett. 75, 3783 (1995)