Context : The formation and evolution of the Galactic bulge and its relationship with the other Galactic populations is still poorly understood .

Aims : To establish the chemical differences and similarities between the bulge and other stellar populations , we performed an elemental abundance analysis of \alpha - ( O , Mg , Si , Ca , and Ti ) and Z-odd ( Na and Al ) elements of red giant stars in the bulge as well as of local thin disk , thick disk and halo giants .

Methods : We use high-resolution optical spectra of 25 bulge giants in Baade ’ s window and 55 comparison giants ( 4 halo , 29 thin disk and 22 thick disk giants ) in the solar neighborhood .
All stars have similar stellar parameters but cover a broad range in metallicity ( -1.5 < [ Fe/H ] < +0.5 ) .
A standard 1D local thermodynamic equilibrium analysis using both Kurucz and MARCS models yielded the abundances of O , Na , Mg , Al , Si , Ca , Ti and Fe .
Our homogeneous and differential analysis of the Galactic stellar populations ensured that systematic errors were minimized .

Results : We confirm the well-established differences for [ \alpha /Fe ] at a given metallicity between the local thin and thick disks .
For all the elements investigated , we find no chemical distinction between the bulge and the local thick disk , in agreement with our previous study of C , N and O but in contrast to other groups relying on literature values for nearby disk dwarf stars .
For -1.5 < [ Fe/H ] < -0.3 exactly the same trend is followed by both the bulge and thick disk stars , with a star-to-star scatter of only 0.03 dex .
Furthermore , both populations share the location of the knee in the [ \alpha /Fe ] vs [ Fe/H ] diagram .
It still remains to be confirmed that the local thick disk extends to super-solar metallicities as is the case for the bulge .
These are the most stringent constraints to date on the chemical similarity of these stellar populations .

Conclusions : Our findings suggest that the bulge and local thick disk stars experienced similar formation timescales , star formation rates and initial mass functions , confirming thus the main outcomes of our previous homogeneous analysis of [ O/Fe ] from infrared spectra for nearly the same sample .
The identical \alpha -enhancements of thick disk and bulge stars may reflect a rapid chemical evolution taking place before the bulge and thick disk structures we see today were formed , or it may reflect Galactic orbital migration of inner disk/bulge stars resulting in stars in the solar neighborhood with thick-disk kinematics .