Question

In classical optics, the double slit experiment show interference of light. The spacing of the fringes at a distance z

from the slits is given by
w≈zλ/d,
where d is the slit distance, and λ the light wavelength. Moreover, I think one has to remember that for this interference to happen the width of the slits needs to be of order (or smaller than) λ. The Wiki page cited above sys If the width of the slits is small enough (much less than the wavelength of the laser light), the slits diffract the light into cylindrical waves. which is needed for interference to occur.

In quantum mechanics, according to wave-particle duality, a particle of mass m
moving at speed v
is associated to a de Broglie wavelength of
λ_dB=h/mv,
where h is the Planck constant, and therefore can also interfere in a double slit experiment.

Questions I have:

Considering what we have said so far, I'm not sure I understand how it was possible to observe interference of fullerene with λ_dB=2.5
pm using a grating with 50 nm slits with 100 nm period (see the paper). There are four order of magnitude difference between wavelength and width, so they are not really comparable.

What is the longitudinal/transversal coherence, and how does it play a role?

Fullerene has a diameter of 1 nm, so it can pass through relatively small slits. But its size is already three orders of magnitude larger than λ_dB
. For compounds of even larger masses, this ratio between size and wavelength is going to be even smaller. Therefore, what is the limit in scaling up such an experiment, if one considers that at some point the object will not be able to pass anymore through the slits (that need to be comparable to λ_dB).

Answer 1

The observation of interference of fullerene with a de Broglie wavelength of 2.5 pm using a grating with 50 nm slits raises questions about the significant difference in scale. The scaling limit in experiments involving larger masses, like fullerene, passing through slits much smaller than their size needs clarification.

Step-by-step explanation:

In classical optics, the interference pattern is dictated by the spacing of the fringes, which depends on the slit distance, wavelength, and slit width. However, in quantum mechanics, the de Broglie wavelength associates particles with interference in a double-slit experiment.

The discrepancy in scale between the fullerene's size and its de Broglie wavelength prompts inquiries about the limits of scaling up such experiments, especially considering the potential hindrance when the object size approaches or exceeds the slit dimensions.

The challenges and considerations in reconciling classical optics with quantum mechanics in experiments involving particles of significant mass and their interference patterns.