In this thesis, we have done experimental studies on Radio Frequency Transport in mesoscopic size (30 micrometer in length and 10 micrometer wide) Hall Bar under High Magnetic field. The Hall Bar is made of Two-dimensional Electron Gas formed in semiconductor heterostructure of GaAs/GaAlAs.  Under High Magnetic fields, it exhibits the physics of Quantum Hall Effect where Hall resistance is quantized and electron transport happens along the edges of the device. These edge states act as ballistic electron channels. The sample also consists of mesoscopic conductor: Quantum Point Contact, which acts as a scattering centre for the incoming electrons in the edge states. This scattering leads to a fluctuating current (Shot noise) through the device. We want to understand the nature of the emitted photons generated due to this shot noise in the microwave regime. In particular, we want to see whether scattered electrons at Quantum Point Contact can generate photons that have anti-bunching statistics or not. To do so efficiently, we have lithographically patterned resonators made of gold which acts as impedance transformer, thereby , increasing detection efficiency of the setup. These resonators have resonance frequency of 4.6 GHz and are directly connected to electron gas. With this setup, we can also explore the RF properties of electron gas in Quantum Hall regime and know about the nature of excitations that travel along the edges, thus revealing to us the physics of this system. This setup is thus a new way to explore the matter (electrons in quantum hall regime) and light( photons in the resonators) coupling. We have done three main experiments. In the first set of experiments, we have measured Impedance of our Two-dimensional electron gas in Quantum Hall Regime via RF transmission measurements through Vector Network Analyzer. The results show that excitations that travel along edges acquire a propagative phase, thus making the behaviour of edge states as chiral transmission lines.  The Hall Bar acts as an Impedance Transformer and transformes the load impedance depending upon the length of the device , Hall conductance and load impedance.

In the second set of experiments, we have measured high-frequency shot noise through the device and determined the Impedance composition rules for it under various circuit setups. This was possible thanks to the impedance matching provided by the resonators. These results will be used to study nature of emitted photons generated by scattered electrons.

Lastly, we have attempted experiments to measure the quantum back-action of these resonators on the Quantum point contact in Quantum Hall regime at filling fraction of 2. We have observed that these effects are not canonical like in tunnel junctions, but are affected by impedance transformation nature of the Electron Gas. 

These set of experiments certainly shed new light on high-frequency behavior of electron gas under Quantum Hall regime and will pave the way for future fundamental work in understanding correlated behavior of these systems.