A recent analysis by one of the authors [ ] has indicated the presence of a 2 \sigma signal of spatially oscillating new force residuals in the torsion balance data of the Washington experiment .
We extend that study and analyse the data of the Stanford Optically Levitated Microsphere Experiment ( SOLME ) [ ] ( kindly provided by the authors of [ ] ) searching for sub-mm spatially oscillating new force signals .
We find a statistically significant oscillating signal for a force residual of the form F ( z ) = \alpha cos ( \frac { 2 \pi } { \lambda } z + c ) where z is the distance between the macroscopic interacting masses ( levitated microsphere and cantilever ) .
The best fit parameter values are \alpha = ( 1.1 \pm 0.4 ) \times 10 ^ { -17 } N , \lambda = ( 35.2 \pm 0.6 ) \mu m .
Monte Carlo simulation of the SOLME data under the assumption of zero force residuals has indicated that the statistical significance of this signal is at about 2 \sigma level .
The improvement of the \chi ^ { 2 } fit compared to the null hypothesis ( zero residual force ) corresponds to \Delta \chi ^ { 2 } = 13.1 .
Private communication with the authors of Ref . [ ] has indicated that this previously unnoticed signal is indeed in the data but is most probably induced by a systematic effect caused by diffraction of non-Gaussian tails of the laser beam .
Thus the amplitude of this detected signal can only be useful as an upper bound to the amplitude of new spatially oscillating forces on sub-mm scales .
In the context of gravitational origin of the signal emerging from a fundamental modification of the Newtonian potential of the form V _ { eff } ( r ) = - G \frac { M } { r } ( 1 + \alpha _ { O } \cos ( \frac { 2 \pi } { \lambda } r + \theta ) ) % \equiv V _ { N } ( r ) + V _ { osc } ( r ) , we evaluate the source integral of the oscillating macroscopically induced force .
If the origin of the SOLME oscillating signal is systematic , the parameter \alpha _ { O } is bounded as \alpha _ { O } < 10 ^ { 7 } for \lambda \simeq 35 \mu m .
Thus , the SOLME data can not provide useful constraints on the modified gravity parameter \alpha _ { O } .
However , the constraints on the general phenomenological parameter \alpha ( \alpha < 0.3 \times 10 ^ { -17 } N at 2 \sigma ) can be useful in constraining other fifth force models related to dark energy ( chameleon oscillating potentials etc ) .