Space-time curvature caused by electromagnetic fields - an experimental results In the article How Current Loops and Solenoids Curve Space-time, the author proposed experiment how to verify a that electromagnetic fields cause gravitational effects.
The experiment is based on measuring phase shift between two beams of light going through Michelson interferometer. While the first beam goes across strong magnetic field (around 20 T), the second one is not influenced by the field. Since an electromagnetic field has an energy, it causes space-time curvature and as a result the light beam going through it travel different distance. Eventually phase shift should appear. 
Despite very strong magnetic field produced by superconducting magnets, the space-time curvature is very weak and hardly measureable. To overcome this, the author proposed to let light beams go through Fabry-Perot cavity for 200 days to travel long distance and to amplify the effect. Ultimately, the phase shift should be similar to one recorded in gravity wave observatories.
My question are:


*

*Is there any article on results of such experiment as the paper is theoretical and only proposed the experiment.

*Do you know about other experiment how to show that electromagnetic fields cause gravitational effects?

*Not connected with electromagnetic field gravitational effect. According to my knowledge, a gravity field should create gravitational effects as well. Is there any experiment to show such effect?

 A: The paper requires a Fabry-Perot cavity that can store light for 200 days, and then measure the phase to a trillionth of a wavelength.  This is far beyond the state of the art.  With 100 meter-long arms, it would require mirrors that lose less than a quadrillionth of the light with each bounce.  To maintain relative coherence between the two arms, you would need to have exactly zero atoms of residual atmosphere in the beam paths, and the two arms would have to be equal in length and stable to about 10^-33 m (about a hundred Planck lengths).
This experiment has not been done.
However, you can show that electromagnetic fields have gravitational effects.  A small but significant (calculable, measurable) fraction of the mass-energy of an atom is due to the EM fields in the nucleus and between the nucleus and electrons.  If this field mass-energy did not have gravitational effects, then the gravitational mass (measured by weight) of an atom would be different from its inertial mass, which is not the case to as accurately as anyone has been able to measure.  (Any discrepancy would be an instant Nobel.  Google 'Equivalence Principle' for more information.)
For your third question, gravitational waves are an example of gravitational fields having gravitational effects, in the same way as EM waves are an effect of the electric field having magnetic effects and vice versa.
Also, the precession of Mercury can be thought of as gravitational fields having gravitational effects. When Mercury is closest to the Sun, there is less gravitational field within the sphere with radius of the Sun-Mercury separation.  Since gravitational field energy is negative (surprising but true), this means that Mercury feels more gravitational pull close in than would be predicted by a Newtonian 1/r^2 field, leading to orbital precession.
Another example is given by a gravitational wave detection that was also seen in electromagnetic radiation (a hard X-ray/gamma burst).  The gravitational field along the path, caused by clusters of galaxies, etc., results in significant propagation delays for electromagnetic radiation compared to the Euclidean light speed calculation.  (We know that this effect is real and consistent with theory for EM waves, because that's how gravitational lenses like the Einstein cross work.) The EM and GW detections were ~simultaneous, indicating that GWs are delayed in exactly the same way as EM waves.
A: *

*I don't know of an article commenting on this paper, but certainly the experiment proposed there is well beyond current technology and therefore has not been attempted, and I would not expect anyone to plan such an experiment at the moment. In addition to the issue of getting the losses small enough, there is the issue that turning on a 20 Tesla field in any lab is going to cause many electromagnetic effects (since the screening of such a large field is never perfect), and these are liable to swamp any gravitational effect. For example, the field might slightly change the length of the Fabry-Perot cavity. I think this part of the paper needs much more qualification by such considerations in order to pass a peer review.

*DMPalmer's answer is good here IMO: the equivalence principle already tests such effects, because the contribution of electromagnetic energy to the mass of atoms and molecules is much larger than the sensitivity of existing equivalence principle tests.

*I would say the most convincing evidence of this is the overall success of General Relativity as a description of gravity. G.R. has been tested now over a wide range of parameter values, from weak to strong fields, and in some respects to exquisite precision. 
