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arXiv:0803.3784 · Physical Review Letters

Observation of Entanglement between Two Light Beams Spanning an Octave in Optical Frequency

Nicolai B. Grosse, Syed M. Assad, Moritz Mehmet, Roman Schnabel, Thomas Symul, Ping Koy Lam

Published Jun 18, 2008• 44 citations
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Abstract

We have experimentally demonstrated how two beams of light separated by an octave in frequency can become entangled after their interaction in a chi;{(2)} nonlinear medium. The entangler was a nonlinear optical resonator that was strongly driven by coherent light at the fundamental and second-harmonic wavelengths. An interconversion between the fields created quantum correlations in the amplitude and phase quadratures, which were measured by two independent homodyne detectors. Analysis of the resulting correlation matrix revealed a wave function inseparability of 0.74(1)<1, thereby satisfying the criterion of entanglement.

DOI
10.1103/physrevlett.100.243601

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We have experimentally demonstrated how two beams of light separated by an octave in frequency can become entangled after their interaction in a chi;{(2)} nonlinear medium. The entangler was a nonlinear optical resonator that was strongly driven by coherent light at the fundamental and second-harmonic wavelengths. An interconversion between the fields created quantum correlations in the amplitude and phase quadratures, which were measured by two independent homodyne detectors. Analysis of the resulting correlation matrix revealed a wave function inseparability of 0.74(1)<1, thereby satisfying the criterion of entanglement.
We demonstrate production of short wavelength beams with nonclassical intensity correlations and quadrature entanglement using second harmonic generation in a nonlinear resonator with two output ports. The two output beams at the harmonic frequency have no direct interaction but are both nonlinearly coupled to a common pump beam. The nonlinear coupling produces amplitude and phase correlations between the beams which results in quadrature entanglement. The output beams at λ = 428.5 nm are shown to exhibit 0.6 dB of amplitude quadrature squeezing, 0.9 dB of nonclassical intensity correlations, and 0.3 dB of entanglement using about 30 mW of pump power.
Quantum entanglement is a crucial resource for performing quantum computing and constructing quantum communication networks. The preparation and manipulation of entangled light field are the basic elements of quantum communication. With the development of science and technology, multicolor multipartite entanglement is becoming a kind of special resource for quantum information, quantum networks, and quantum memory. In this paper, we propose a scheme of generating quadripartite entanglement among four output beams from a two-port frequency doubling resonator, in which a type-II phase matching nonlinear crystal is placed. We make two fundamental-frequency pump beams with the same frequency and vertical polarization pass through the nonlinear crystal to produce two frequency-doubling beams. There is a quadripartite entanglement between the frequency-doubling beams, which are output at two ports of the optical resonator, and the incident fundamental beams. Based on the transmission matrix from the coupled wave equation, the self-consistent equations of the intracavity modes and the corresponding noise properties of the output modes can be obtained. Then, the quadripartite entanglement produced from two second harmonic beams and two reflected fundamental-frequency pump beams, is verified by using the positive partial transposition criterion, in a wide range of pumping power and analysis frequency. The setup proposed in this work is compact and experimentally feasible. It is also convenient to separate the four entangled beams spatially, with different wavelengths and polarizations. When the beam wavelengths are matched with 1560 nm (low loss window of fiber) and 780 nm (atomic absorption line of Rb), this scheme can be more useful in both quantum communication and quantum memory.
We report on the generation of non-separable beams produced via the interaction of a linearly polarized beam with a cloud of cold caesium atoms placed in an optical cavity. We convert the squeezing of the two linear polarization modes into quadrature entanglement and show how to find the best entanglement generated in a two-mode system using the inseparability criterion for continuous variables (Duan et al 2000 Phys. Rev. Lett. 84 2722). We verify this method experimentally with a direct measurement of the inseparability using two homodyne detectors. We then map this entanglement into a polarization basis and achieve polarization entanglement .
We propose and demonstrate a scheme to stably generate quadrature-entangled optical pulses using a ring interferometer composed of an optical parametric amplifier and a dispersive media. The entangled light pulses at telecommunication wavelength are generated by combining two squeezed beams. In our scheme, the relative phase between the two beams is kept stable by the ring interferometer and is controllable using dispersive media. The amplitude and phase quadratures of the entangled beams are measured using two time-domain pulsed homodyne detectors. When the relative phase is fixed at $\ensuremath{\pi}/2$, we verify the inseparability of the states by a sufficient criterion $⟨{\ensuremath{\Delta}}^{2}[{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}}_{a}({\ensuremath{\phi}}_{0})+{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}}_{b}(\ensuremath{\pi}\ensuremath{-}{\ensuremath{\phi}}_{0})]⟩+⟨{\ensuremath{\Delta}}^{2}[{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}}_{a}({\ensuremath{\phi}}_{0}^{\ensuremath{'}})\ensuremath{-}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}}_{b}(\ensuremath{-}{\ensuremath{\phi}}_{0}^{\ensuremath{'}})]⟩=0.64<1$ where ${\ensuremath{\phi}}_{0}^{\ensuremath{'}}\ensuremath{-}{\ensuremath{\phi}}_{0}=\ensuremath{\pi}/2$.
We propose and analyze a cascaded optical parametric system which involves three interacting modes across two octaves of frequency difference. Our system, combining degenerate optical parametric oscillation (OPO) with second harmonic generation (SHG), promises to be a useful source of squeezed and entangled light at three differing frequencies. We show how changes in damping rates and the ratio of the two concurrent nonlinearities affect the quantum correlations in the output fields. We analyze the threshold behavior, showing how the normal OPO threshold is changed by the addition of the SHG interactions. We also find that the inclusion of the OPO interaction removes the self-pulsing behavior found in normal SHG. Finally, we show how the Einstein-Podolsky-Rosen correlations can be controlled by the injection of a coherent seed field at the lower frequency.