Feedback-assisted measurement of the free mass position under the Standard Quantum Limit

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