A new measure of Δα/α at redshift z=1.84 from very high resolution spectra of Q 1101-264

Aims. We probe the evolution of the fine-structure constant a with cosmic time. Methods. Accurate positions of the Fe II lines lambda 1608, lambda 2382, and lambda 2600 are measured in the z(abs) = 1.84 absorption system from a high-resolution ( FWHM similar to 3.8 km s(-1)) and high signal-to-noise ( S/N greater than or similar to 100) spectrum of the quasar Q 1101-264 ( z(em) = 2.15, V = 16.0), integrated for 15.4 h. The Single Ion Differential a Measurement ( SIDAM) procedure and the Delta(2)(chi) method are used to set constraints on Delta alpha/alpha. Results. We have found a relative radial velocity shift between the lambda 1608 and lambda 2382, 2600 lines of Delta v = -180 +/- 85 m s(-1) ( both random and systematic errors are included), which, if real, would correspond to Delta alpha/alpha = ( 5.4 +/- 2.5) x 10(-6) ( 1 sigma C.L.). Considering the strong implications of a such variability, additional observations with comparable accuracy at redshift z similar to 1.8 are required to confirm this result.