Summary
An operator approach, allowing the evaluation of the output statistics of a balanced homodyne detector with an input beam in a squeezed state, is presented. The case of one squeezed input is connected to the one with a coherent input through a novelSU(1,1) symmetry transformation. This symmetry is peculiar of the 50-50 balanced scheme and corresponds to a symmetrical squeezing of the two inputs. The squeezing of the local oscillator and the associated effects on the statistics are analysed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. M. Caves:Phys. Rev. D,23, 1693 (1981).
R. S. Bondurant andH. J. Shapiro:Phys. Rev. D,30, 2548 (1984).
B. Yurke, S. L. McCall andJ. R. Klauder:Phys. Rev. A.,33, 4033 (1986).
For reviews on squeezed states seea) Squeezed States of the Electromagnetic Field, edited byH. J. Kimble andD. Walls:J. Opt. Soc. B,4, (1987) (special issue);b) Squeezed Light, edited byR. Loudon andP. L. Knight:J. Mod. Opt., 34 (1987) (special issue);c) Squeezed and Nonclassical Light, edited byP. Tombesi andE. R. Pike (Plenum, New York, N. Y., 1989).
P. Grangier, R. E. Slusher, B. Yurke andA. LaPorta:Phys. Rev. Lett.,59, 2153 (1987).
Min Xiao, Ling-An Wu andH. J. Kimble:Phys. Rev. Lett.,59, 278 (1987).
S. L. Braunstein:Phys. Rev. A,42, 474 (1990).
H. P. Yuen andV. W. S. Chan:Opt. Lett.,8, 177 (1983).
B. L. Schumaker:Opt. Lett.,9, 189 (1984).
B. Yurke:Phys. Rev.,32, 311 (1985).
R. A. Campos, B. E. Saleh andM. C. Teich:Phys. Rev. A,40, 1371 (1989).
P. D. Drummond andC. W. Gardiner:Phys. Rev. A,13, 2353 (1980).
H. P. Yuen:Phys. Rev. A,13, 2226 (1976) Ŝ a (μ, ν) is the evolution operator of a Hamitonian Ĥ which is a quadratic function ofa anda +. In the simplest case of μ real and Ĥ constant as a function of time Ŝ a (μ, ν) is the usual squeezing operator\(\hat S_a (\mu ,\nu ) = exp[(1/2)\zeta a^{\dag 2} - (1/2)\bar \zeta a^2 ]\) where μ=cosh |ζ|, ν=(ζ/|ζ|) sinh |ζ|).
G. M. D'Ariano: inQuantum Aspects of Optical Communications, edited byC. Bendjaballah, O. Hirota andS. Reynaud:Lecture Notes in Physics 378 (Springer, Berlin-New York, 1991), p. 325.
J. Schwinger:Quantum Theory of Angular Momentum, edited byL. C. Biedenharn andH. Van Dam (Academic Press, New York, N. Y., 1965), p. 229.
R. Gilmore:Lie Groups, Lie Algebras, and Some of Their Applications (Wiley, New York, N. Y., 1974), p. 149.
Y. Yamamoto andH. A. Haus:Rev. Mod. Phys.,58, 1001 (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
D'Ariano, G.M. SU(1,1) symmetry of the balanced homodyne and statistics of the output. Nuov Cim B 107, 643–651 (1992). https://doi.org/10.1007/BF02723172
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02723172