Feedback-assisted measurement of the free-mass position under the StandardQuantum Limit

The Standard Quantum Limit (SQL) for the measurement of a free-mass positio n is illustrated, along with two necessary conditions for breaching it. A m easurement scheme that overcomes the SQL is engineered. It can be achieved in three steps: i) a pre-squeezing stage; ii) a standard von Neumann measur ement with momentum-position object-probe interaction and iii) a feedback. Advantages and limitations of this scheme are discussed. It is shown that a ll of the three steps are needed in order to overcome the SQL. In particula r, the von Neumann interaction is crucial in getting the right state reduct ion, whereas other experimentally achievable Hamiltonians, as, for example, the radiation-pressure interaction, lead to state reductions that on the a verage cannot overcome the SQL.