Abstract

Standard quantum limit appears as a result of back action. It can be illustrated by simplified example: the constant signal force acts on free probe mass during time T and one quickly measures the coordinate of mass twice: in moments t = 0 (the result is x₁) and in moment t = T (the result is x₂). ”Quickness” means that the time τ of each measurement is small enough — τ ≫T. To register signal force one should measure the difference x_– = x₁ – x₂= x₁ – p₁T/m – x₂. where p₁ is back action momentum transfered to probe mass during the first measurement. The second measurement of coordinate x₂ can be made with very small error. However conversely the errors of x₁ and p₁ are dependent in accordance to uncertainty principle: Δx₁Δp₁ ≥ ħ/2. Therefore the error of measurement of x_– is restricted by the standard quantum limit: Δx_– ≃ ħT/m.

© 1998 IEEE