Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics

Physical Review D

Volumn 65, Issue 2, 2002, Pages

  Kimble, H J ^a   Levin, Yuri ^a,d   Matsko, Andrey B ^b   Thorne, Kip S ^a   Vyatchanin, Sergey P ^c  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

^c MOSCOW STATE UNIVERSITY   (Russian Federation)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; FREQUENCY MODULATION; GRAVITY; INTERFEROMETER; MATHEMATICAL ANALYSIS; MOTION; OPTICS; QUANTUM MECHANICS; VACUUM;

EID: 0037080790     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.65.022002     Document Type: Article

References (67)

1. http://www.ligo.caltech.edu/.
2. V. B. Braginsky and F. Ya. Khalili, Rev. Mod. Phys. 68, 1 (1996).
3. V. B. Braginsky and F. Ya. Khalili, Quantum Measurement (Cambridge University Press, Cambridge, England, 1992). Note: In this reference the spectral densities are double sided and thus are 1/2 the single-sided spectral densities used in the present paper.
4. V. B. Braginsky, M. L. Gorodetsky, F. Ya. Khalili, A. B. Matsko, K. S. Thorne, and S. P. Vyatchanin, gr-qc/0109003.
5. V. B. Braginsky, Sov. Phys. JETP 26, 831 (1968);
6. V. B. Braginsky, in Physical Experiments with Test Bodies, NASA Technical Translation TT F-672 (U.S. Technical Information Service, Springfied, VA, 1972).
7. V. B. Braginsky and Yu. I. Vorontsov, Sov. Phys. Usp. 17, 644 (1975).
8. E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, "LSC White Paper on Detector Research and Development," LIGO Document Number T990080-00-D (Caltech/MIT, 1999).
9. See, e.g., S. Rowan et al., Phys. Lett. A 233, 303 (1997);
10. V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, Phys. Lett. A ibid. 264, 1 (1999), and references therein.
11. For a very general demonstration that ∼ 1 MW is the minimum circulating power that is required to beat the standard quantum limit in a wide variety of QND interferometer designs, see V. B. Braginsky, M. L. Gorodetsky, F. Ya. Khalili, and K. S. Thorne, in Proceedings of the Third Edoardo Amaldi Meeting on Gravitational Waves, edited by S. Meshkov (AIP Press, Melville, NY, 2000), p. 180.
12. V. B. Braginsky, M. L. Gorodetsky, F. Ya. Khalili, and K. S. Thorne, Phys. Rev. D 61, 044002 (2000).
13. P. Purdue, Phys. Rev. D (to be published), gr-qc/0111042.
14. C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann, Rev. Mod. Phys. 52, 341 (1980);
15. V. B. Braginsky, Yu. I. Vorontsov, and K. S. Thorne, Science 209, 547 (1980);
16. C. M. Caves, in Quantum Optics, Experimental Gravity, and Measurement Theory, edited by P. Meystre and M. O. Scully (Plenum, New York, 1982), p. 567.
17. See also W. G. Unruh, Phys. Rev. D 19, 2888 (1979).
18. V. B. Braginsky, M. L. Gorodetsky, and F. Ya. Khalili, Phys. Lett. A 232, 340 (1997);
19. V. B. Braginsky, M. L. Gorodetsky, and F. Ya. Khalili, Phys. Lett. A 246, 485 (1998);
20. V. B. Braginsky and F. Ya. Khalili, Phys. Lett. A ibid. 257, 241 (1999).
21. W. G. Unruh, in Quantum Optics, Experimental Gravitation, and Measurement Theory, edited by P. Meystre and M. O. Scully (Plenum, New York, 1982), p. 647.
22. V. B. Braginsky and A. B. Manukin, Zh. Éksp. Teor. Fiz. 52, 987 (1967)
23. [Sov. Phys. JETP 25, 653 (1967)].
24. A similar effect has been considered by A. V. Gusev and V. N. Rudenko, Zh. Eksp. Teor. Fiz. 76, 1488 (1979).
25. C. M. Caves, Phys. Rev. D 23, 1693 (1981).
26. M. T. Jaekel and S. Reynaud, Europhys. Lett. 13, 301 (1990).
27. A. F. Pace, M. J. Collett, and D. F. Walls, Phys. Rev. A 47, 3173 (1993).
28. M. Xiao, L.-A. Wu, and H. J. Kimble, Phys. Rev. Lett. 59, 278 (1987).
29. P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, Phys. Rev. Lett. 59, 2153 (1987).
30. See, e.g., the following special issues of journals dealing with squeezing via nonlinear optics: J. Opt. Soc. Am. B 4, 1453 (1987);
31. and Quantum Noise Reduction in Optical Systems, edited by C. Fabre and E. Giacobino [Appl. Phys. B 55, 189ff (1992)].
32. S. P. Vyatchanin and A. B. Matsko, JETP 77, 218 (1993);
33. S. P. Vyatchanin and E. A. Zubova, Phys. Lett. A 203, 269 (1995);
34. S. P. Vyatchanin, Phys. Lett. A ibid. 239, 201 (1998).
35. S. P. Vyatchanin and A. B. Matsko, JETP 82, 1007 (1996).
36. S. P. Vyatchanin and A. B. Matsko, JETP 83, 690 (1996).
37. C. M. Caves and B. L. Schumaker, Phys. Rev. A 31, 3068 (1985).
38. B. S. Schumaker and C. M. Caves, Phys. Rev. A 31, 3093 (1985).
39. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994);
40. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, England, 1995).
41. Some readers may also find useful background in C. W. Gardiner, Quantum Noise (Springer-Verlag, Berlin, 1991).
42. R. W. P. Drever et al., in Quantum Optics, Experimental Gravity and Measurement Theory, edited by P. Meystre and M. O. -Scully (Plenum, New York, 1981), p. 503.
43. C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, Phys. Rev. A 49, 1337 (1994);
44. S. Mancini and P. Tombesi, Phys. Rev. A ibid. 49, 4055 (1994);
45. A. Heidmann and S. Reynaud, Phys. Rev. A ibid. 50, 4237 (1994);
46. M. Pinard, C. Fabre, and A. Heidmann, Phys. Rev. A ibid. 51, 2443 (1995).
47. H. J. Kimble, in Fundamental Systems in Quantum Optics, Les Houches Session LIII, 1990, edited by J. Dalibard, J. M. Raimond, and J. Zinn-Justin (Elsevier, Amsterdam, 1992), pp. 549-674.
48. Y. Chen (private communication).
49. -2R in L.-A. Wu, M. Xiao, and H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987)
50. was only -4.3 dB, the inferred degree of squeezing was much larger: after making an absolute accounting for passive linear losses, these authors inferred a degree of squeezing corresponding to approximately -12 dB, which provides a benchmark for how well the basis nonlinear optical process of parametric down conversion conforms to simple theoretical models [31]. Somewhat more recently, E. S. Polzik, J. Carri, and J. H. Kimble, Appl. Phys. B: Photophys. Laser Chem. B55, 279 (1992),
51. have recorded quantum noise reductions of -6 dB directly in the observed homodyne current. In this case the degree of squeezing was limited not by passive linear losses, but instead by nonlinear light induced absorption in the potassium niobate crystal used for parametric down conversion. Quite recently, K. Schneider, M. Lang, J. Mlynek, and S. Schiller, Opt. Express 2, 59 (1998),
52. have reported 6.5 dB of vacuum squeezing from a below-threshold optical parametric oscillator, with comparable levels reported by P. K. Lam et al., J. Opt. B: Quantum Semiclassical Opt. 1, 469 (1999).
53. Equation (44) of K. S. Thorne, in 300 Years of Gravitation, edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, England, 1987).
54. P. R. Saulson, Phys. Rev. D 42, 2437 (1990).
55. V. B. Braginsky, V. P. Mitrofanov, and K. V. Tokmakov, Phys. Lett. A 218, 164 (1996);
56. K. Tokmakov, V. Mitrofanov, V. Braginsky, S. Rowan, and J. Hough, in Proceedings of the Third Edoardo Amaldi Conference on Gravitational Waves, edited by S. Meshkov (AIP Press, Melville, NY, 2000), p. 445.
57. For analyses of the compatibility of input squeezing, modulations, and signal recycling, see S. Song, Ph.D. thesis, University of Southern California, 1994;
58. and J. Geabanacloche and G. Leuchs, J. Mod. Opt. 34, 793 (1987).
59. J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rudiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993).
60. Equation (133) can be derived by the techniques used in Ref. [25]; see especially Eqs. (13)-(15) of [25].
61. The experimental challenge simply to reach the SQL for mirror position is daunting. Two recent experiments that addressed this challenge with small masses but were impeded by thermal noise are reported in Refs. [42] and [43].
62. A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, Phys. Rev. Lett. 51, 1550 (1983).
63. Y. Hadjar, P. F. Cohadon, C. J. Aminoff, M. Pinard, and A. Heidmann, Europhys. Lett. 47, 545 (1999).
64. I. Tittonen et al., Phys. Rev. A 59, 1038 (1999).
65. K. Jacobs, I. Tittonen, H. M. Wiseman, and S. Schiller, Phys. Rev. A 60, 538 (1999).
66. For a detailed discussion of losses and various efficiency factors associated with the spatial overlap of fields in interferometry with squeezed light, see Min Xiao, Ph.D. thesis, University of Texas at Austin, 1988, Chap. 4, Sec. II A.
67. A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Appendix C, Eq. (14).