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This might be a very naive question. But since gravitational effects in the "quantum world" are of great interest, caused by the fact that there is no theory which unifies gravity with the other three fundamental forces of nature, I recently asked myself are there any observations of gravitational effects in quantum experiments? Or is there theoretical work done showing that such an observation is impossible to be seen because of the immensely small contribution of gravitational force to quantum systems on these scales?

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Have a look here :

Physicists have observed quantized states of matter under the influence of gravity for the first time. Valery Nesvizhevsky of the Institute Laue-Langevin and colleagues found that cold neutrons moving in a gravitational field do not move smoothly but jump from one height to another, as predicted by quantum theory. The finding could be used to probe fundamental physics such as the equivalence principle, which states that different masses accelerate at the same rate in a gravitational field

Note that gravity here is treated as an extra potential affecting the neutron, it is not quantization of gravity which is still and effective theory used in cosmology where there exist exchange gravitons analogous to exchanged photons for electromagnetsm.

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