The conversion of phase to amplitude fluctuations of a light beam by an optical cavity

American Journal of Physics

Volumn 76, Issue 10, 2008, Pages 922-929

  Villar, Alessandro S ^a,b,c  

^a UNIVERSITY OF INNSBRUCK   (Austria)

^b ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^c UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 56749104053     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.2937903     Document Type: Article

References (27)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U.P., Cambridge, 2000).
2. S. L. Braunstein and P. van Loock, " Quantum information with continuous variables.," Rev. Mod. Phys. 77, 513-577 (2005).
3. G. Grynberg, A. Aspect, and C. Fabre, An Introduction to Lasers and Quantum Optics (Cambridge U.P., Cambridge, 2001).
4. A. Einstein, B. Podolsky, and N. Rosen, " Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777-780 (1935).
5. R. Jozsa and N. Linden, " On the role of entanglement in quantum-computational speed-up.," Proc. R. Soc. London, Ser. A 459, 2011-2032 (2003).
6. T. M. Forcer, A. J. G. Hey, D. A. Ross, and P. G. R. Smith, " Superposition, entanglement and quantum computation.," Quantum Inf. Comput. 2, 97-116 (2002).
7. P. Nachman, " Mach-Zehnder interferometer as an instructional tool.," Am. J. Phys. 63, 39-43 (1995).
8. H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, 2004).
9. A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, " Generation of bright two-color continuous variable entanglement.," Phys. Rev. Lett. 95, 243603-1-4 (2005).
10. E. D. Black, " An introduction to Pound-Drever-Hall laser frequency stabilization.," Am. J. Phys. 69, 79-87 (2001).
11. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, and G. M. Ford, " Laser phase and frequency stabilization using an optical resonator.," Appl. Phys. B 31, 97-105 (1983).
12. M. D. Levenson, R. M. Shelby, A. Aspect, M. Reid, and D. F. Walls, " Generation and detection of squeezed states of light by nondegenerate four-wave mixing in an optical fiber.," Phys. Rev. A 32, 1550-1562 (1985).
13. P. Galatola, L. A. Lugiato, M. G. Porreca, P. Tombesi, and G. Leuchs, " System control by variation of the squeezing phase.," Opt. Commun. 85, 95-103 (1991).
14. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 2007).
15. R. W. Henry and S. C. Glotzer, " A squeezed-state primer.," Am. J. Phys. 56, 318-328 (1988).
16. A. K. Ekert and P. L. Knight, " Correlations and squeezing of two-mode oscillations.," Am. J. Phys. 57, 692-697 (1989).
17. P. G. Kwiat and L. Hardy, " The mystery of the quantum cakes.," Am. J. Phys. 68, 33-36 (2001).
18. C. Fabre and S. Reynaud, " Quantum noise in optical systems: A semiclassical approach.," in Les Houches Session LIII, edited by, J. Dalibard, J. M. Raimond, and, J. Zinn-Justin, (Elsevier, New York, 1992), pp. 675-711.
19. This concept fails for very weak fields, because a phase operator is a difficult object to define rigorously (see Ref.).
20. W. Schleich and J. A. Wheeler, " Oscillations in photon distribution of squeezed states and interference in phase space.," Nature (London) 326, 574-577 (1987).
21. Note that L corresponds to twice the distance between the mirrors in the specific case of a linear cavity (Fig.). This notation is employed to easily allow for any cavity geometry.
22. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U.P., Cambridge, 1995).
23. C. W. Gardiner, Quantum Noise (Springer-Verlag, Berlin, 1991).
24. G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, " Frequency modulation (FM) spectroscopy.," Appl. Phys. B 32, 145-152 (1983).
25. The definition of the noise power involves the variance of the fluctuations (the ellipse). It has been tacitly assumed that the field state possesses a Gaussian Wigner function (the fluctuations satisfy Gaussian statistics), because it is the common situation found in the laboratory. Higher order moments necessary to reconstruct the state in the more general case are in principle accessible from the direct measurement of the fluctuations, as shown by Eq., given that the linearization procedure of Eq. applies. The statistics of any quadrature direction in phase space can be completely transferred (disregarding losses) to the reflected amplitude statistics.
26. J. Zhang, T. Zhang, K. Zhang, C. Xie, and K. Peng, " Quantum self-homodyne tomography with an empty cavity.," J. Opt. Soc. Am. B 17, 1920-1925 (2000).
27. A. Zavatta, F. Marin, and G. Giacomelli, " Quantum-state reconstruction of a squeezed laser field by self-homodyne tomography.," Phys. Rev. A 66, 043805-1-8 (2002).