Abstract

Under continuous coordinate measurement back action noise of the meter is responsible for the limit of sensitivity known as standard quantum limit (SQL). In the simple optical displacement meter (Fig. 1) back action is produced by the fluctuations of light pressure force $\sim \sqrt{W}$ (W is the power of incident light wave in coherent state) and the error of coordinate measurement $\sim 1/\sqrt{W}$ defines by phase fluctuations of incident wave. Therefore there is an optimal value w_sql at which the SQL sensitivity is achieved. One can also understand it in other way: reflected wave is squeezed, because movable mirror transforms the amplitude fluctuations into phase ones (Fig. 2). Movable mirror can be considered as ponderomotive kind of χ⁽³⁾ nonlinear susceptibility. Coherent incident wave with fluctuations depicted as circle on phase diagram are transformed into a squeezed state depicted as ellipse. For traditional scheme of registration of phase of reflected wave, the big axis of ellipse should be about the diameter of the circle, so that uncertainties of phase in reflected and in incident waves are approximately the same — these speculations give the optimal number w_sql of used photons. In case of W ≫ w_sql the ellipse is considerably squeezed. In particular, this means that uncertainty of phase in reflected wave is much larger than that for coherent incident wave. This can be also explained as consequence of large fluctuations of back action force deteriorating the sensitivity due to enhancement in phase fluctuations.

© 1998 IEEE