RT Journal Article T1 Characterization of quantum angular-momentum fluctuations via principal components A1 Rivas, Ángel A1 Luis Aina, Alfredo AB We elaborate an approach to quantum fluctuations of angular momentum based on the diagonalization of the covariance matrix in two versions: real symmetric and complex Hermitian. At difference with previous approaches this is SU(2) invariant and avoids any difficulty caused by nontrivial commutators. Meaningful uncertainty relations are derived which are nontrivial even for vanishing mean angular momentum. We apply this approach to some relevant states. PB American Physical Society SN 1050-2947 YR 2008 FD 2008-02-12 LK https://hdl.handle.net/20.500.14352/51488 UL https://hdl.handle.net/20.500.14352/51488 LA eng NO [1] B. Yurke, S. L. McCall, and J. R. Klauder, Phys. Rev. A 33, 4033 (1986); M. Hillery and L. Mlodinow, ibid. 48, 1548 (1993); C. Brif and A. Mann, ibid. 54, 4505 (1996).[2] Y. Castin and J. Dalibard, Phys. Rev. A 55, 4330 (1997); J.A. Dunningham and K. Burnett, ibid. 61, 065601 (2000); 70, 033601 (2004); V. Meyer, M. A. Rowe, D. Kielpinski, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Phys. Rev. Lett. 86, 5870 (2001).[3] D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. Heinzen, Phys. Rev. A 50, 67 (1994).[4] A. Sørensen, L.-M. Duan, J. I. Cirac, and P. Zoller, Nature (London) 409, 63 (2001); G. Tóth, Phys. Rev. A 69, 052327 (2004).[5] N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and Ch. Silberhorn, Phys. Rev. A 65, 052306 (2002); N. Korolkova and R. Loudon, ibid. 71, 032343 (2005).[6] A. Luis and L. L. Sánchez-Soto, in Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 2000), Vol. 41, p. 421, and references therein.[7] M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).[8] A. Luis and L. L. Sánchez-Soto, Quantum Semiclassic. Opt. 7, 153 (1995).[9] J. Schwinger, Quantum Theory of Angular Momentum (Academic Press, New York, 1965).[10] F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972).[11] M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 (1993).[12] A. Luis and N. Korolkova, Phys. Rev. A 74, 043817 (2006).[13] S. L. Braunstein and C. M. Caves, Phys. Rev. Lett. 72, 3439 (1994); S. L. Braunstein, C. M. Caves, and G. J. Milburn, Ann. Phys. 247, 135 (1996); A. Monras, Phys. Rev. A 73, 033821 (2006).[14] J.-M. Lévy-Leblond, Ann. Phys. 101, 319 (1976); V. V. Dodonov, E. V. Kurmyshev, and V. I. Man’ko, Phys. Lett. 79A, 150 (1980).[15] P. H. Moravek and D. W. Joseph, J. Math. Phys. 4, 1363 (1963); K. Nemoto, J. Phys. A 33, 3493 (2000); K. Nemoto and B. C. Sanders, ibid. 34, 2051 (2001).[16] U. Leonhardt and H. Paul, Prog. Quantum Electron. 19, 89 (1995); U. Leonhardt, Measuring the Quantum State of Light (Cambridge University Press, Cambridge, England, 1997); D.-G. Welsch, W. Vogel, and T. Opatrný, in Progress in Optics, edited by E. Wolf (Elsevier Science, Amsterdam, 1999), Vol. 39.[17] G. S. Agarwal, Phys. Rev. A 57, 671 (1998); J. P. Amiet and S. Weigert, J. Opt. B: Quantum Semiclassical Opt. 2, 118 (2000); S. Weigert, ibid. 6, 489 (2004).[18] K. Wodkiewicz and J. H. Eberly, J. Opt. Soc. Am. B 2, 458 (1985).[19] R. Delbourgo, J. Phys. A 10, 1837 (1977).[20] M. J. Holland and K. Burnett, Phys. Rev. Lett. 71, 1355 (1993).[21] N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990); J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996); S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Phys. Rev. Lett. 79, 3865 (1997); A. Luis, Phys. Rev. A 64, 054102 (2001); 65, 034102 (2002); Ph. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature (London) 429, 158 (2004); M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, ibid. 429, 161 (2004).[22] E. Schrödinger, Bulg. J. Phys. 26, 193 (1999).[23] R. N. Deb, N. Nayak, and B. Dutta-Roy, Eur. Phys. J. D 33, 149 (2005). NO ©2008 The American Physical Society. A.L. acknowledges the support from project No. PR1-A/07-15378 of the Universidad Complutense. NO Universidad Complutense de Madrid (UCM) DS Docta Complutense RD 1 may 2024