Over the past decades, trapped atomic ions have developed into one of the most promising platforms for realizing quantum simulation and quantum computation. The highly controllable atomic qubits can also be used to probe and control co-trapped single molecular ion. Recently impressive progress has been achieved in diatomic molecular ions like CaH+ and N2+, realizing non-demolition state detection of molecular ions by coupling them to an atomic logic ion via a common motional mode. We aim to introduce entanglement enhanced single photon absorption spectroscopy to study ultrafast molecular dynamics on the platform. By preparing the auxiliary atomic ion in a non-classical cat state, the recoil signal produced by single photon absorption events on the target molecular ion can be amplified and read out. In this way, we plan to investigate intramolecular behaviours in time domain using ultrafast laser pulses. This may pave the way to the study of polyatomic molecules with complex vibrational structure at the single molecule level. The experimental system we are building consists of a linear Paul trap from AQT at room temperature, compact rack-based laser systems for manipulating Ca+ qubits and a high-power pulsed laser for performing spectroscopy. The laser can generate ultrafast pulses at the femtosecond scale for studying molecule vibration and has a wide tuning range from 210 to 16000 nm that allow us to explore most vibrational modes in molecules. Currently we are at the stage of setting up the system for trapping our first Ca+ ion and we will start with proof of concept experiments on simple diatomic ions like CaH+.