Context. Spitzer's wide-field surveys and followup capabilities have allowed a new breakthrough in mid-IR spectroscopy up to redshifts ≥2, especially for 24 μm detected sources. Aims. We want to study the mid-infrared properties and the starburst and AGN contributions, of 24 μm sources at z ∼ 2, through analysis of mid-infrared spectra combined with millimeter, radio, and infrared photometry. Mid-infrared spectroscopy allows us to recover accurate redshifts. Methods. A complete sample of 16 Spitzer-selected sources (ULIRGs) believed to be starbursts at z ∼ 2 ("5.8 μm-peakers") was selected in the (0.5 deg 2 ) J1064+56 SWIRE Lockman Hole field ("Lockman-North"). These sources have S 24 μm > 0.5 mJy, a stellar emission peak redshifted to 5.8 μm, and r Vega > 23. The entire sample was observed with the low resolution units of the Spitzer/IRS infrared spectrograph. These sources have 1.2 mm observations with IRAM 30 m/MAMBO and very deep 20 cm observations from the VLA. Nine of our sources also benefit from 350 μm observation and detection from CSO/SHARC-II. All these data were jointly analyzed.Results. The entire sample shows good quality IRS spectra dominated by strong PAH features. The main PAH features at 6.2, 7.7, 8.6, and 11.3 μm have high S /N average luminosities of 2.90 ± 0.31, 10.38 ± 1.09, 3.62 ± 0.27, and 2.29 ± 0.26 × 10 10 L , respectively. Thanks to their PAH spectra, we derived accurate redshifts spanning from 1.750 to 2.284. The average of these redshifts is 2.017 ± 0.038. This result confirms that the selection criteria of "5.8 μm-peakers" associated with a strong detection at 24 μm are reliable to select sources at z ∼ 2. We have analyzed the different correlations between PAH emission and infrared, millimeter, and radio emissions. Practically all our sources are strongly dominated by starburst emission, with only one source showing an important AGN contribution. We have also defined two subsamples based on the equivalent width at 7.7 μm to investigate AGN contributions. Conclusions. Our sample contains strong starbursts and represents a particularly 24 μm-bright class of SMGs. The very good correlation between PAH and far-IR luminosities is now confirmed in high-z starburst ULIRGs. These sources show a small AGN contribution to the mid-IR, around ∼20% or less in most cases.