Phase variables and squeezed states

Donita Cohen, Y. Ben-Aryeh, A. Mann

Yanqiang Guo, Haojie Zhang, Xiaomin Guo +2 more

We study continuous variable coherence of phase-dependent squeezed state based on an extended Hanbury Brown-Twiss scheme. High-order coherence is continuously varied by adjusting squeezing parameter r, displacement α, and squeezing phase θ. We also analyze effects of background noise γ and detection efficiency η on the measurements. As the squeezing phase shifts from 0 to π, the photon statistics of the squeezed state continuously change from the anti-bunching (g(n) < 1) to super-bunching (g(n) > n!) which shows a transition from particle nature to wave nature. The experiment feasibility is also examined. It provides a practical method to generate phase-dependent squeezed states with high-order continuous-variable coherence by tuning squeezing phase θ. The controllable coherence source can be applied to sensitivity improvement in gravitational wave detection and quantum imaging.

Mark S. Hillery

Phase-space pictures have proven to be useful in analyzing standard squeezing. Here such pictures are developed for amplitude-squared squeezing, a form of higher-order squeezing. They are used to examine amplitude-squared squeezing of the squeezed vacuum state and to suggest a method of producing amplitude-squared squeezed states using a nonlinear interferometer. The phase-space representation of a variable which is a mixture of the usual amplitude-squared squeezing variables is also discussed.

Jeffrey H. Shapiro, Scott Roger Shepard, N. C. Wong

L. Mandeļ, E. Wolf

In Section 11.5 we showed that, although the complex amplitude of the electromagnetic field has a well-defined value in any coherent state, yet the real and imaginary (Hermitian and anti-Hermitian) parts of the field fluctuate with equal dispersions. The phenomenon of vacuum fluctuations is a manifestation of this effect, because the vacuum state is an example of a particular coherent state. This behavior is quite different from that of an ordinary, classical field. In a squeezed state, which is even more non-classical, as we shall see, one part of the field fluctuates less and another part fluctuates more than in the vacuum state. In general, a squeezed state is one in which the distribution of canonical variables over the phase space has been distorted or ‘squeezed’ in such a way that the dispersion of one variable is reduced at the cost of an increase in the dispersion of the other variable. In the following we shall examine the properties of squeezed states when the two canonical variables are two quadratures of the electromagnetic field. Although the squeezing terminology is sometimes applied to variables other than the two field quadratures, it is less meaningful in those cases. A number of review articles on squeezing have been published and can be consulted for more details (Walls, 1983; Schumaker, 1986; Loudon and Knight, 1987; Teich and Saleh, 1989, 1990; Kimble, 1992).

P. L. Knight, Vladimír Bužek