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Fortschritte der Physik

Continuous variable entanglement between frequency modes

O. Glöckl, Ulrik L. Andersen, Gerd Leuchs

Published Aug 1, 2006• 3 citations
Publisher

Abstract

Abstract The pairwise production of photons in nonlinear optical processes ensures entanglement to occur between two photons. E.g. when the Kerr effect is exploited, the photons are produced in different frequency modes, which are symmetric with respect to the pump frequency. Since these photons are produced into the same spatial mode, the quadrature entanglement can be witnessed only by the use of a frequency selective device which transforms the adjacent frequency modes into two different spatial modes. We use a Mach‐Zehnder interferometer with a large path length difference to separate symmetric frequency modes located 10.25 MHz from the carrier. We measure correlations of the quadrature components of 1.6 ± 0.1dB below the shot noise in the amplitude and 1.4 ± 0.1dB in the phase.

DOI
10.1002/prop.200610309

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Abstract The pairwise production of photons in nonlinear optical processes ensures entanglement to occur between two photons. E.g. when the Kerr effect is exploited, the photons are produced in different frequency modes, which are symmetric with respect to the pump frequency. Since these photons are produced into the same spatial mode, the quadrature entanglement can be witnessed only by the use of a frequency selective device which transforms the adjacent frequency modes into two different spatial modes. We use a Mach‐Zehnder interferometer with a large path length difference to separate symmetric frequency modes located 10.25 MHz from the carrier. We measure correlations of the quadrature components of 1.6 ± 0.1dB below the shot noise in the amplitude and 1.4 ± 0.1dB in the phase.
The quantum entanglement of amplitude and phase quadratures between two intense optical beams with a total intensity of 22 mW and a frequency difference of 1 nm, which are produced from an optical parametric oscillator operating above threshold, is experimentally demonstrated with two sets of unbalanced Mach-Zehnder interferometers. The measured quantum correlations of intensity and phase are in reasonable agreement with the results calculated based on a semiclassical analysis of the noise characteristics given by Fabre et al. [J. Phys. (France) 50, 1209 (1989)].
We propose a simple scheme using an unbalanced Mach-Zehnder interferometer to directly measure the entangled beams with correlation of amplitude quadratures and anticorrelation of phase quadratures. In the experiment, we use two fibers with lengths of 2 and 50 m to construct the interferometer. The correlation variances of amplitude difference and phase sum of the entangled beams from a nondegenerate optical parametric amplifier are simultaneously measured to be 1.79 and 1.62 dB below the shot noise limit, respectively. Such a simple and convenient method has potential applications in quantum measurements.
Three different methods have been discussed to verify continuous variable entanglement of intense light beams. We demonstrate all three methods using the same setup to facilitate the comparison. The nonlinearity used to generate entanglement is the Kerr effect in optical fibers. Due to the brightness of the entangled pulses, standard homodyne detection is not an appropriate tool for the verification. However, we show that by using large asymmetric interferometers on each beam individually, two noncommuting variables can be accessed and the presence of entanglement verified via joint measurements on the two beams. Alternatively, we witness entanglement by combining the two beams on a beam splitter that yields certain linear combinations of quadrature amplitudes which suffice to prove the presence of entanglement.
Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. Here we demonstrate experiments that show the entanglement between microwave photons of different energy in a broadband squeezed beam. We use a Josephson parametric amplifier to generate the two-mode correlated state and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quadratures allows us to determine the full covariance matrix, which is in good agreement with the one expected for a two-mode squeezed state.
We report on the generation of a continuous variable Einstein-Podolsky-Rosen (EPR) entanglement using an optical fiber interferometer. The Kerr nonlinearity in the fiber 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 is 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.
Multipartite entanglement is a resource for quantum communication and computation. Vector four-wave mixing (FWM) in a fiber, driven by two strong optical pumps, couples the evolution of four weak optical sidebands (modes). Depending on the fiber dispersion and pump frequencies, the mode frequencies can be similar (separated by less than 1 THz) or dissimilar (separated by more than 10 THz). In this report, the discrete- and continuous-variable entanglement produced by vector FWM is studied in detail. Formulas are derived for the variances of, and correlations between, the mode quadratures and photon numbers. These formulas and related results show that the modes are four-partite entangled.