FOUR-WAVE MIXING AND BOSE-EINSTEIN CONDENSATION IN NANO-ELECTRO-OPTOMECHANICS

Abstract

In this dissertation we theoretically study the dynamics of a Nano Electro Optomechanical system (NEOMS) in the presence of a strong pump eld and a weak probe eld.The system consists of a Fabry-Perot cavity which is composed of a xed and partially transparent mirror at one end and a fully re ecting movable mirror MR1 at the other end. MR1 is coupled to the intra-cavity eld through optomechanical coupling. An additional movable micro-resonator MR2 is provided to the cavity which is electrostatically coupled to MR1 via Coulomb interaction. Mechanical driving elds "1 and "2 are applied to selectively pump the mechanical resonators (MRs). A non-linear e ect, in the probe transmission eld, known as Four-wave mixing, is investigated in the Nano-electro-optomechanical system (NEOMS). The nonlinearity which is caused by the radiation pressure force of the intra-cavity eld, gives rise to Four-wave mixing (FWM) phenomenon, which is equivalent to the nonlinear Kerr e ect in optical bers that causes a nonlinear susceptibility in the medium. Here this nonlinear e ect is called e ective Kerr e ect, which is caused by the radiation pressure force and is responsible for Four-wave mixing (FWM). In the probe transmission eld, Four-wave mixing (FWM) is reported by selectively driving the mechanical resonators MR1 and MR2, which provides extra control of FWM. The FWM is observed to show consistent modi cations by changing the amplitudes and phases of the external driving elds. We show in our results that signi cant suppression and ampli cation can be achieved in the FWM peaks by controlling the phases of external driving elds. We also report enhancement in the FWM phenomenon, in the presence of Bose- Einstein Condensate (BEC) trapped inside the cavity. We show that the FWM intensity is greatly suppressed and ampli ed in the presence of atomic medium vi (BEC) in the optical cavity. The intensities of FWM peaks change coherently by varying the value of atom- eld coupling. Moreover, we show that the medium mediated FWM signal is e ciently controlled by selective mechanical drivings of