Abstract
It is well known that the complete information about all the quantum statistical properties of a quantum mechanical system are contained in the density operator ρ. Various representations of the density matrix operator were introduced in quantum optics as valuable mathematical tools. These are the Glauber-Sudarshan P-representation [1], [2], the Husimi Q-function [3] and the Wigner function [4]. All these representations are called quasi-probability distributions. The Wigner function is the first quasi-probability density introduced in Quantum Mechanics. It may be defined as the Fourier transform of the symmetrically ordered characteristic function χ(ŋ) of the density operator ρ.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. J. Glauber, Phys. Rev. Lett. 10, 84 (1963).
E. C. G. Sudarshan, Phys. Rev. Lett. 10, 177 (1963).
K. Husimi, Proc. Phys. Math. Soc. Japan 23, 264 (1940).
E. Wigner, Phys. Rev. 40, 749 (1932).
K. E. Cahill, and R. J. Glauber, Phys. Rev. 177, 1882 (1969).
K. Vogel, and H. Risken, Phys. Rev. A 40, 2847 (1989).
J.H. Shapiro and H.P. Yuen, IEEE Trans. Inf. Theory IT25, 179 (1979)
P.L. Kelley and W.H. Kleiner, Phys. Rev. 136, 316 (1964).
J.H. Shapiro, G. Saplakoglu, S.-T. Ho, P. Kumar. B.E.A. Saleh and M.C. Teich, J.Opt. Soc. Am. B 4, 1604 (1987).
H.M. Wiseman, and G.J. Milburn, Phys. Rev. A 47, 642 (1993).
S. Mancini, V. I. Man’ko and P. Tombesi, to appear on Quantum Semiclass. Opt.
see for example W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1973).
C. W. Gardiner, Quantum Noise (Springer, Heidelberg, 1991).
D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. ev. Lett. 70, 1244 (1993).
F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986).
G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, Phys. Rev. A 50, 4298 (1994).
H. Kühn, D. G. Welsch and W. Vogel, J. of Mod. Opt. 41, 1607 (1994).
G. M. D’Ariano, U. Leonhardt and H. Paul, Phys. Rev. A 52 (1995) (in press).
G.M. D’Ariano, S. Mancini, V.I. Man’ko and P. Tombesi, Quantum Semiclass. Opt. (submitted)
U. Leonhardt and H. Paul, Phys. Rev. A 48, 4598 (1993).
G. M. D’Ariano, Int. J. Mod. Phys. B 6, 1291 (1992).
B. Yurke and D. Stoler, Phys. Rev. Lett. 57, 13 (1986);
S. Song, C.M. Caves, B. Yurke, Phys. Rev. A 41, 5261 (1990);
B. Yurke, W. Schleich, D.F. Walls, Phys. Rev. A 42, 1703 (1990);
M. Brune, S. Haroche, J.M. Raimond, L. Davidovich and N. Zagury, Phys. Rev. A 45, 5193 (1992);
L. Krippner, W.J. Munro and M.D. Reid, Phys. Rev. A 50, 4330 (1994).
A.M. Fox, J.J. Baumberg, M. Dabbicco, B. Huttner, and J.F. Ryan, Phys. Rev. Lett. 74, 1728(1995).
S.T. Ho, C.E. Soccolich, M.N. Islam, W.S. Hobson, A.F.J. Levi, and R.E. Slusher, Appl. Phys. Lett. 59, 2558(1991)
G.M. D’Ariano, M. Fortunato,and P. Tombesi, Quantum Semicl. Opt. (to appear)
P. Tombesi and D. Vitali, Phys. Rev. A 50, 4253 (1994).
S. Mancini, and P. Tombesi, Phys. Rev. A (to appear)
T.A.B. Kennedy and D.F. Walls, Phys. Rev. A 37, 152 (1988).
A. Mecozzi and P. Tombesi, Phys. Lett. A 121, 101 (1987);
A. Mecozzi and P. Tombesi, J. Opt. Soc. Am. B 4, 1700 (1987).
P. Tombesi and D. Vitali, Phys. Rev. Lett. submitted
P. Alsing, G. J. Milburn and D. F. Walls, Phys. Rev. A 37, 2970 (1988).
P. Tombesi and D. Vitali, Appl. Phys. B 60, S69 (1995);
P. Tombesi and D. Vitali, Phys. Rev. A 51, 4913 (1995).
H.M. Wiseman, and G.J. Milburn, Phys. Rev. A 47, 642 (1993).
H. Risken, The Fokker Planck Equation 2nd ed. (Springer, Berlin 1989).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Tombesi, P. (1997). Optical Tomography and Macroscopic Coherence. In: Hakioğlu, T., Shumovsky, A.S. (eds) Quantum Optics and the Spectroscopy of Solids. Fundamental Theories of Physics, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8796-9_10
Download citation
DOI: https://doi.org/10.1007/978-94-015-8796-9_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4797-7
Online ISBN: 978-94-015-8796-9
eBook Packages: Springer Book Archive