Squeezed State Effects on Continuous Variable Quantum Erasing

Experimental verification of complementarity using quantum erasing for the continuous variable (CV) infinite dimensional Hilbert space has been considered. [1] The complemetary pair is that of the canonically conjugate amplitude and phase quadratures of light. The amplitude quadrature is labeled to a squeezed meter signal by quantum nondemolition (QND) [2] entanglement coupling. [3] Knowledge of \textit{which eigenstate} (WE) can be obtained by measuring this amplitude in the meter state, and can thereafter be `lost' by measuring the quadrature phase of the meter, thus restoring the quadrature phase of the signal beam in a process known as \textit{quantum erasure.} [4] The coupling, i.e. the labeling of the signal state to the meter state, is implemented with a beam splitter coupled to the squeezed light meter beam. [4] We investigate the effects of using the unitary squeeze operator S(z)=exp$\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $(z*a$^{2}$ - za$^{+2}$) where z = re$^{i(squeezing angle)}$ on selected coherent states under certain conditions. [5,6] [1] U. L. Anderson et al., Phys. Rev. Lett. 93, 100403 (2004). [2] V. B. Braginsky et al., Science 209, 547 (1980). [3] R. Bruckmeimer et al., Phys. Rev. Lett. 79, 43 (1997). [4] P. Grangier et al., Nature 396, 537 (1998). [5] C. M. Caves, Phys. Rev. D 23, 1693 (1981). [6] D. Stoler, Phys. Rev. D. 1, 3217 (1970), D. Stoler, Phys. Rev. D. 4, 1925 (1971). .