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arXiv:quant-ph/0504164 · Physical Review A

Effects of mismatched transmissions on two-mode squeezing and EPR correlations with a slow light medium

Sulakshana Thanvanthri, Jianming Wen, Morton H. Rubin

Published Aug 25, 2005• 7 citations
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Abstract

We theoretically discuss the preservation of squeezing and continuous-variable entanglement of two-mode squeezed light when the two modes are subjected to unequal transmission. One of the modes is transmitted through a slow light medium while the other is sent through an optical fiber of unit transmission. Balanced homodyne detection is used to check the presence of squeezing. It is found that loss of squeezing occurs when the mismatch in the transmission of the two modes is greater than 40% while near-ideal squeezing is preserved when the transmissions are equal. We also discuss the effect of this loss on continuous-variable entanglement using strong and weak Einstein-Podolsky-Rosen criteria and possible applications for this experimental scheme.

DOI
10.1103/physreva.72.023822

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We theoretically discuss the preservation of squeezing and continuous-variable entanglement of two-mode squeezed light when the two modes are subjected to unequal transmission. One of the modes is transmitted through a slow light medium while the other is sent through an optical fiber of unit transmission. Balanced homodyne detection is used to check the presence of squeezing. It is found that loss of squeezing occurs when the mismatch in the transmission of the two modes is greater than 40% while near-ideal squeezing is preserved when the transmissions are equal. We also discuss the effect of this loss on continuous-variable entanglement using strong and weak Einstein-Podolsky-Rosen criteria and possible applications for this experimental scheme.
We study the effects of losses on the entanglement created between two separate atomic gases by optical probing and homodyne detection of the transmitted light. The system is well-described in the Gaussian state formulation. Analytical results quantifying the degree of entanglement between the two gases are derived and compared with the entanglement in a pair of light pulses generated by an Einstein-Podolsky-Rosen (EPR) source. For low (high) transmission losses, the highest degree of entanglement is obtained by probing with squeezed (antisqueezed) light. In an asymmetric setup where light is only sent one way through the atomic samples, we find that the logarithmic negativity of entanglement attains a constant value $\ensuremath{-}{\mathrm{log}}_{2}(N)$ with N=1∕3N=1∕3N=1∕3, irrespective of the loss along the transmission line.
Einstein-Podolsky-Rosen (EPR) entanglement is a criterion that is more demanding than just certifying entanglement. We theoretically and experimentally analyze the low-resource generation of bipartite continuous-variable entanglement, as realized by mixing a squeezed mode with a vacuum mode at a balanced beam splitter, i.e., the generation of so-called vacuum-class entanglement. We find that in order to observe EPR entanglement the total optical loss must be smaller than 33.333.333.3 %. However, arbitrarily strong EPR entanglement is generally possible with this scheme. We realize continuous-wave squeezed light at 155015501550 nm with up to 9.99.99.9 dB of nonclassical noise reduction, which is the highest value at a telecom wavelength so far. Using two phase-controlled balanced homodyne detectors we observe an EPR covariance product of $0.502\ifmmode\pm\else\textpm\fi{}0.006<1$, where 111 is the critical value. We discuss the feasibility of strong Gaussian entanglement and its application for quantum key distribution in a short-distance fiber network.
Two amplification schemes are considered for entangled squeezed states of light, including an Einstein-Podolsky-Rosen entangled state of continuous variables (EPR pair): propagation in a nonlinear medium and reflection from a cavity. Both schemes make use of a parametric process that can be implemented in a periodic nonlinear medium. The existence of an integral of motion makes it possible to amplify an entangled state of light while preserving the initial entanglement. To analyze the cavity-based scheme, a master equation is derived for the density matrix of the field inside the cavity. The feasibility of amplification that preserves entanglement of an EPR pair is demonstrated for this scheme.
We present the experimental realization of a theoretical effect discovered by Olivares and Paris (2009 Phys. Rev. A 80 032329), in which a pair of entangled optical beams undergoing independent losses can see nonlocal correlations restored by the use of a nonlocal resource correlating the losses. Twin optical beams created in an entangled, Einstein–Podolsky–Rosen (EPR) state by an optical parametric oscillator above threshold were subjected to 50% loss from beamsplitters in their paths. The resulting severe degradation of the amplitude-quadrature correlations between the two beams was then suppressed when another, independent EPR state impinged upon the other input ports of the beamsplitters, effectively entangling the losses inflicted to the initial EPR state. The additional EPR beam pair was classically coherent with the primary one but had no quantum correlations with it. This result may find applications as a 'quantum tap' for entanglement.
Einstein-Podolsky-Rosen (EPR)-entangled state light field at a telecommunication wavelength of 1.5 μm is an important quantum source for realizing the continuous variable quantum information processing and some quantum protocols over optical fiber channel. When the EPR-entangled state light field is distributed over the optical fiber channel, the disentanglement is always present because the the EPR entangled state interacts with the fiber channel. It affects the performance of quantum information processing. In this paper, we theoretically calculate the positive partial transposition (PPT) of the entangled state distributed over the optical fiber channel in the single-channel and dual-channel distribution scheme, respectively. Three types of initial entangled light field are considered and analyzed, they being an initial EPR entangled state, an EPR entangled state with asymmetric quadratures, and an EPR entangled state with asymmetric modes. Furthermore, the influence of the extra noise in the optical fiber on the transmission distance of EPR entangled state over the optical fiber channel is investigated. In the single-channel scheme or dual-channel scheme, the extra noise in the optical fiber channel leads the entangled state light field to be disentangled, and the transmission distance of EPR entangled state over the optical fiber channel to decrease rapidly with the increase of the extra noise. For maintaining the robustness of EPR entangled states in lossy optical fiber channels, the dual-channel scheme has more stringent requirements for the correlation quadrature symmetry and purity of the initial entangled state than the single-channel scheme. In the single fiber noise channel scheme, the maximum transmission distance and the robustness of the EPR entangled states with asymmetric modes are not sensitive to the asymmetry between modes. The change of asymmetry between modes does not lead to being disentangled. The maximum transmission distance does not change either. However, the decrease of asymmetry between modes results in the disentanglement in the double fiber noise channels’ scheme. The maximum transmission distance is reduced and the sudden death occurs to the entanglement. The present results will lay a foundation for continuous variables quantum information processing based on optical fiber, such as realizing continuous variables quantum communication over optical fiber and constructing metropolitan quantum network over optical fiber.