Hybrid Cavity-Optomechanics With Dressed Bose-Einstein Condensate

The optomechanics,a dramatic manipulation of mechanical effects of light to produce motion in mechanical optics,has emerged as a fantastic field that has contributed a lot in revealing the hidden picture of nature.It helped us to feel the ripples in space and time originated at thousands of lights years distance,and it also helped to see the shape of nano-size objects.The major obstacle that limits the applications of optomechanical phenomena,especially in cavity environment,is the uncontrolled interaction of multiple subsystems that generates high order nonlinearities,for both optical and mechanical(or atomic)degrees of freedoms.The second thing that appears as a more crucial hurdle is the thermo-mechanical heating of the mechanical objects because of the associated quantum noises.We start by discussing the first problem,where we proposed a scheme to control the nonlinear dynamics of the cavity-optomechanics with Cigar-shaped Bose-Einstein condensate(BEC)– a cavity with moving-end mirror and containing BEC,driven by a single mode laser – by using transverse laser which perpendicularly interacts with intra-cavity BEC.The transverse laser scatters photons inside the cavity,depending upon the orientation of BEC,and modifies intracavity optical mode,which eventually yields in the enhanced radiation pressure.We illustrate that the transversely scattered photons gather in the upper branch of bistable photons which,at higher strengths of transverse laser,leads to the suppression of optical bistability.Further,the transverse field not only controls the bistable dynamics of moving-end mirror and BEC but also acts as a switch for temporal chaos for both atoms as well as mirror.By adopting same mechanism and driving cavity with another weak probe laser,we demonstrate that the transverse field also completely alters the optical nonlinearities occurring in the form of electromagnetically induced transparency(EIT).We show that the combination of cavity-optomechanics with BEC results in another transparency in probe transmission because of atom-field coupling inside cavity.The transverse field also significantly enhances the EIT interval as well as the Fano line shapes in the cavity transmission.In order to deal with second obstacle,i.e.the heating of mechanical degree of freedom under radiation pressure,we integrate synthetically engineered spin-orbit(SO)-coupled dressed states of BEC with optomechanical cavity,by accumulating standard Raman process.The Raman process splits BEC into two dressed states which inside the cavity – acting as two atomic mirrors driven by the radiation pressure – generate strong photonic back-action.We illustrate that the SO-coupling mediated back-action not only revamps low-temperature dynamics of atomic mirrors but also provides a way to cool the moving-end mirror of the cavity to its quantum mechanical ground state.Further,the strength of SO-coupling also enhances the dynamic structure factor,revealing the overall density excitation of the system,by squeezing associated quantum noises,like thermo-mechanical and photon short-noise.Furthermore,we demonstrate SO-coupled BEC induced topological nonlinear optics in an optical cavity.As the Raman process splits the BEC into hyperfine states,so the quantum interference at these states opens another opportunity for the dark-state.We show that the photon interactions during the probe transition through the dressed states and the Zeeman shift generate new type of EIT-like transparencies,which in gain regime – where the atomic damping greater than a particular value acts as a gain to the cavity field – get completely inverted.We illustrate that these nonlinear interaction of pseudo spin states also implants different spin phases to the probe field,causing optical transparencies to form gapless band structures(or Dirac-like modes)in probe transmission,which become gaped with Raman detuning.However,in amplification case,a gapless edgelike topological transparency mode,even with non-zero Raman detuning,appears between upper and lower band.These findings reveal that the SO-coupled states imprint the synthetic spin-texture to the probe field and cause non-trivial optical quantum phase transition.