Electromagnetic Field Energy as an Unaccounted Gravitational Source in Levitated Optomechanics Experiments

Recent advances in levitated optomechanics have enabled experiments probing gravitational interactions at unprecedented scales, with the goal of detecting quantum signatures of gravity. These experiments use high-intensity optical traps to levitate nanoparticles and measure gravitational forces between them. We demonstrate that the electromagnetic field energy density in these optical traps constitutes a gravitational source through the stress-energy tensor T^{mu nu}, yet this contribution is not accounted for in current experimental analyses. Using the linearized Einstein field equations, we calculate the gravitational potential and field arising from concentrated laser fields at experimentally relevant power densities (~10^15 W/m^2). We find that the electromagnetic field gravitational contribution can be comparable to or exceed the gravitational effects being measured between particle masses, potentially constituting a systematic error of order 10^-2 to 10^0 in current experiments. We propose calibration protocols to detect and characterize this effect, including power-scaling tests and field geometry variations that can discriminate electromagnetic field gravity from particle-particle gravitational interactions.