Mixing and $CP$ violation in the decay of $B_s \rightarrow J/\psi \phi$ in ATLAS

The $B_s \rightarrow J/\psi \phi$ decay is characterized by the average decay width $\Gamma_s$ of the heavy and the light mass eigenstates, the decay width difference $\Delta\Gamma_s$ and by the CP violating phase $\phi_s$. The final state is a mixture of CP even and CP odd components that are disentangled via an angular analysis. The measurement of the decay channel provides the possibility to test the predictions of the Standard Model. In particular the measurement of the CP violating phase $\phi_s$ has the capability to unveil New Physics induced enhancement of the small Standard Model value. In this document the analyses of the $B_s \rightarrow J/\psi \phi$ decay with the ATLAS detector at the LHC is presented.