Amplitude Noise Reduction in a Nano-mechanical Oscillator

We study the quantum properties of a nano-mechanical oscillator via the squeezing of the oscillator amplitude. The static longitudinal compressive force 0 F close to a critical value at the Euler buckling instability leads to an anharmonic term in the Hamiltonian and thus the squeezing properties of the nano-mechanical oscillator are to be obtained from the Hamiltonian of the form 4 / ) ( a a a a H       . This Hamiltonian has no exact solution unlike the other known models of nonlinear interactions of the forms 2 a a  , 2 ) ( a a  and ) ( 2 2 2 2 4 4       a a a a a a previously employed in quantum optics to study squeezing. Here we solve the Schrodinger equation numerically and show that in-phase quadrature gets squeezed for both vacuum and coherent states. The squeezing can be controlled by bringing 0 F close to or far from the critical value c F . We further study the effect of the transverse driving force on the squeezing in nano-mechanical oscillator. Key WordsSqueezing, Nano-mechanical Systems, Quantum Noise