Abstract
The marginal distribution of squeezed and rotated quadrature for two types of nonclassical states of a trapped ion — squeezed and correlated states and squeezed even and odd coherent states (squeezed Schrödinger cat states) — is studied. The marginal distribution obtained for the two types of states is shown to satisfy a classical dynamic equation equivalent to the standard quantum evolution equation for the density matrix (wave function) derived in a symplectic-tomography scheme.
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References
R. L. de Matos Filho and W. Vogel,Phys. Rev. Lett.,76, 608 (1996).
R. J. Glauber,Phys. Rev. Lett.,10, 84 (1963).
V. V. Dodonov, I. A. Malkin, and V. I. Man'ko,Physica,72, 597 (1974).
B. Yurke and D. Stoler,Phys. Rev. Lett.,57, 13 (1986).
E. Schrödinger,Naturwissenschaften,23, 844 (1935).
R. J. Glauber, in: R. Inguva (ed.),Recent Developments in Quantum Optics, Proceedings of the International Conference on Quantum Optics (Hyderabad, India, January 1991), Plenum Press, New York (1993), p. 1;
P. Tombesi and D. F. Walls (eds.),Quantum Measurements in Quantum Optics, Proceedings of the NATO Advanced Research Workshop (Cortina d'Ampezzo, Italy, January 1991), Plenum Press, New York (1991), p. 3;
T. D. Black et al. (eds.),Foundations of Quantum Mechanics, Proceedings of the Conference (Santa Fe, NM, USA, May 1991), World Scientific, Singapore (1992), p. 23;
E. Arimondo et al. (eds.),Laser Manipulation of Atoms and Ions, Proceedings of the International School of Physics “Enrico Fermi” Course 118 (Varenna, Italy, July 1992), North Holland, Amsterdam (1992), p. 643.
G. Schrade, V. I. Man'ko, W. Schleich, and R. J. Glauber,Quantum Semiclass. Opt.,7, 307 (1995).
K. Husimi,Prog. Theor. Phys.,9, 238 (1953).
I. A. Malkin and V. I. Man'ko,Phys. Lett. A,32, 243 (1970);
I. A. Malkin, V. I. Man'ko, and D. A. Trifonov,Phys. Rev. D,2, 1371 (1970).
K. Vogel and H. Risken,Phys. Rev. A,40, 2847 (1989).
K. E. Cahill and R. J. Glauber,Phys. Rev.,177, 1882 (1969).
D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani,Phys. Rev. Lett.,70, 1244 (1993).
S. Mancini, V. I. Man'ko, and P. Tombesi,Quantum Semiclass. Opt.,7, 615 (1995).
S. Mancini, V. I. Man'ko, and P. Tombesi, “Symplectic tomography as a classical approach to quantum systems,”Los Alamos Report No. quant-ph/9603002; Phys. Lett. A,213, 1 (1996).
G. Schrade, P. J. Bardroff, C. Leichte, and W. Schleich, “Endoscopy in the Paul trap” (in preparation).
V. V. Dodonov, E. V. Kurmyshev, and V. I. Man'ko,Phys. Lett. A,79, 150 (1980).
V. V. Dodonov, O. V. Man'ko, and V. I. Man'ko,Phys. Rev. A,49, 2993; 50, 813 (1994).
V. V. Dodonov and V. I. Man'ko,Invariants and Evolution of Nonstationary Quantum Systems, Proceedings of the Lebedev Physical Institute,183, Nova Science, Commack, New York (1989).
E. Schrödinger,Sitzungsber. Preuss. Acad. Wiss.,24, 296 (1930).
V. V. Dodonov, V. I. Man'ko, and D. E. Nikonov,Phys. Rev. A,51, 3328 (1995).
V. I. Man'ko, “Introduction to quantum optics,”,Latin-American School of Physics, XXXELAF, Group Theory and its Applications, Mexico, July–August, 1995, AIP Conference Proceedings,365, AIP, New York (1996), p. 337.
N. A. Ansari and V. I. Man'ko,Phys. Rev. A,50, 1942 (1994).
G. M. D'Ariano, S. Mancini, V. I. Man'ko, and P. Tombesi, “Reconstructing the density operator by using generalized field quadratures” (to be published inQuantum Semiclass. Opt.).
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On leave from the P. N. Lebedev Physical Institete, Moscow, Russia.
Contribution to the Adriatico Research Conference “Interferometry 2” (ICTP, Trieste, March 1–11, 1996), submitted March 13, 1996.
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Manko, O.V. Symplectic tomography of nonclassical states of a trapped ion. J Russ Laser Res 17, 439–448 (1996). https://doi.org/10.1007/BF02090622
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DOI: https://doi.org/10.1007/BF02090622