Generation of Continuous Variable Einstein-Podolsky-Rosen Entanglement via the Kerr Nonlinearity in an Optical Fiber

Abstract

We report on the generation of a continuous variable Einstein-Podolsky-Rosen (EPR) entanglement using an optical fibre interferometer. The Kerr nonlinearity in the fibre is exploited for the generation of two independent squeezed beams. These interfere at a beam splitter and EPR entanglement is obtained between the output beams. The correlation of the amplitude (phase) quadratures are measured to be 4.0 ± 0.2 (4.0 ± 0.4) dB below the quantum noise limit. The sum criterion for these squeezing variances 0.80 ± 0.03 < 2 verifies the nonseparability of the state. The product of the inferred uncertainties for one beam (0.64 ± 0.08) is well below the EPR limit of unity.Since the original proposal of a Gedankenexperiment intending to show the incompleteness of quantum mechanics in 1935 [1], a number of schemes for generating the Einstein-Podolsky-Rosen (EPR) entanglement have been realized. The schemes range from the production of gamma-ray pairs from positron-electron annihilations [2], to proton pairs [3], to pairs of low-energy photons from atomic radiative cascade [4] and more recently to schemes involving optical parametric processes [5]. Most of these initial experiments utilized the entanglement as originally intended: to test the validity of quantum mechanics via either the violation of Bell inequality [4] or the demonstration of the EPR paradox [6]. Following the proposals of a myriad of quantum information schemes in recent years where entanglement is regarded as a basic requisite, the subject matter has experienced a resurgence of interest. The purposes of entanglement generation are now shifting to that of quantum information applications. Amongst these applications are the realization of quantum teleportation, the implementation of dense coding, quantum cryptography and other quantum communication schemes [7]. In view of these changing needs, it is desirable to explore simpler and more reliable alternatives for the generation of EPR entanglement.In this letter, we report on what is to our knowledge the first generation of EPR entanglement of photons that does not rely on any pair production process, such as those in the above-mentioned examples. Instead, the Kerr (χ (3) ) nonlinearity of an optical fibre is utilized to produce two amplitude squeezed beams, with the nonlinear interaction on each beam uncoupled to the other. To create the EPR entanglement, no additional nonlinear interaction is required. Instead, the amplitude squeezed beams are made to interfere at a 50/50 beam splitter [8]. In this vein sum squeezing is obtained for the amplitude quadratures and difference squeezing for the phase quadratures. The signs of these correlations are interchanged compared to those achieved in other systems. This fact may be of importance in applications involving the opto-mechanical coupling of radiation pressure [9]. Apart from the simplicity of our scheme, it also has the potential advantage of being integrable into existing fibre-optics communication networks.

Quantifying non-Gaussianity for quantum information

“…Kerr interaction has been suggested to realize quantum nondemolition measurements, to enhance quantum estimation performances in quantum optics and to generate quantum superpositions [111,112] as well as squeezing [113] and entanglement [58,59]. A known example of Kerr medium is provided by optical fibers where, however, nonlinearities are small and accompanied by other unwanted effects.…”

“…For γ ≈ 10 −2 the maximum nG achievable at fixed energy is quite rapidly achieved, while for more realistic values of the Kerr coupling nG is obtained only for large values of the average number of photons. In the experiments proposed to obtain entanglement via Kerr interaction [58,59], pulses with an average number up to 10 8 photons are needed to compensate the small nonlinearities of standard glass fibers. Therefore, in these regimes, the generation of entanglement is always accompanied by a large degree of nG.…”

“…Basically, they may be divided into two main categories: those based on non-linear interaction of order higher than two [56,57], as for example the Kerr effect [58][59][60]), and those based on conditional measurements. Indeed, the nonlinear dynamics induced by conditional measurements has been analyzed for a large variety of schemes [61][62][63][64][65][66][67][68][69][70][71][72][73][74][75], also including, besides photon addition and subtraction schemes, optical state truncation of coherent states [64], state filtering by active cavities [65,66], synthesis of arbitrary unitary operators [67] and generation of optical qubit by conditional interferometry [68].…”

Polarization squeezing of light by single passage through an atomic vapor

“…However, RIS can also occur between orthogonal polarization components of a single light beam. In such case, the field is said to be polarization squeezed [8,9] and the noise reduction is described in terms of squeezing of the fluctuations of one of the Stokes operators:Here a x , a y are the field destruction operators for the orthogonal linear polarizations x and y. Polarization squeezing has been produced via propagation in optical fibers [10,11], through the combination on a polarizing beam splitter of two quadrature squeezed light beams [12] and through the interaction of linearly polarized light with cold atoms inside an optical cavity [9,13].It has been recently demonstrated that the single passage of a linearly polarized pump beam through a few-cmlong atomic vapor cell results in squeezing of the polarization orthogonal to that of the pump (vacuum squeezing) [14][15][16][17] as a consequence of the nonlinear optics mechanism known as polarization self-rotation (PSR) [18][19][20]. Vacuum squeezing via PSR has been observed for the D1 [15][16][17] and D2 [14] transitions using 87 Rb vapor.…”

Quantum downconversion and multipartite entanglement via a mesoscopic superconducting quantum interference device ring

“…In fact, there are strong similarities between a quantum regime SQUID ring and a device frequently employed in quantum optics-the nonlinear optical coupler-this being formed from two or more linearly coupled waveguides where at least one is composed of an optically nonlinear medium. [41][42][43][44][45] However, there are two important differences between optical couplers and the SQUID ring: ͑i͒ optical nonlinear interactions usually have a nonresonant character and ͑ii͒ optical nonlinear couplers are difficult to make because of the strict phase and frequency matching conditions that must be obeyed by all involved processes simultaneously. Hence, it may well be that SQUID ring coupled devices, such as those presented here, could lead to a feasible way of realizing ͑or at least simulating͒ nonlinears optical couplers.…”