Broadband Coherent Multidimensional Variational Measurement

Standard Quantum Limit (SQL) of a classical mechanical force detection results from quantum back action perturbing evolution of a mechanical system. In this paper we show that usage of a multidimensional optical transducer may enable a broadband quantum back action evading measurement. We study a corresponding technique for measurement of a resonant signal force acting on a linear mechanical oscillator coupled to an optical system with three optical modes with separation nearly equal to the mechanical frequency. The measurement is performed by optical pumping of the central optical mode and measuring the light escaping the two other modes. By detecting optimal quadrature components of the optical modes and post-processing the measurement results we are able to exclude the back action in a broad frequency band and characterize the force with sensitivity better than SQL. We discuss how proposed scheme relates to multidimensional system containing quantum-mechanics-free subsystems (QMFS) which can evade the SQL using idea of so called "negative mass".