Luis Aina, Alfredo2023-06-202023-06-202004-04-01[1] Z. Y. Ou, Phys. Rev. A 55, 2598 (1997). [2] A. Luis and L. L. Sánchez-Soto, Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 2000), Vol. 41, p. 421. [3] A. Luis, Phys. Rev. A 65, 025802 (2002). [4] G. M. D’Ariano and M. F. Sacchi, Phys. Rev. A 52, R4309 (1995). [5] W. J. Munro, K. Nemoto, G. J. Milburn, and S. L. Braunstein, Phys. Rev. A 66, 023819 (2002). [6] C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann, Rev. Mod. Phys. 52, 341 (1980); H. P. Yuen, Phys. Rev. Lett. 51, 719 (1983); M. H. Partovi and R. Blankenbecler, ibid. 57, 2891 (1986); M. Ozawa, ibid. 60, 385 (1988). [7] M. Brune, S. Haroche, V. Lefevre, J. M. Raimond, and N. Zagury, Phys. Rev. Lett. 65, 976 (1990); H. Paul, Quantum Opt. 3, 169 (1991). [8] M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997). [9] H. P. Yuen and J. H. Saphiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); B. Yurke, Phys. Rev. A 32, 311 (1985); T. Kim, Y. Ha, J. Shin, H. Kim, G. Park, K. Kim, T.-G. Noh, and Ch. K. Hong, ibid. 60, 708 (1999). [10] C. Monroe, D. M. Meekhof, B. E. King, and D. J. Wineland, Science 272, 1131 (1996).1050-294710.1103/PhysRevA.69.044101https://hdl.handle.net/20.500.14352/51517©2004 The American Physical Society. This work was supported by Project No. PR1/03-11630 of the University Complutense.We analyze the quantum limit to the sensitivity of the detection of small displacements. We focus on the case of free particles and harmonic oscillators as the systems experiencing the displacement. We show that the minimum displacement detectable is proportional to the inverse of the square root of the mean value of the energy in the state experiencing the displacement (Heisenberg limit). We present a measuring scheme that reaches this limit using semiclassical states. We examine the performance of this strategy under realistic practical conditions by computing the effect of imperfections such as losses and nonunit detection efficiencies. This analysis confirms the robustness of this measuring strategy by showing that the experimental imperfections can be suitably compensated by increasing the mean energy of the input state.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.69.044101http://journals.aps.org/open access535Quantum nondemolition measurementPositionAtomÓptica (Física)2209.19 Óptica Física