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Optics Letters

Continuous-variable entanglement measurement using an unbalanced Mach–Zehnder interferometer

Chuanqing Xia, Dong Wang, Yang Wu, Jiale Guo, Fang Liu, Yong Zhang, Min Xiao

Published Mar 12, 2015• 2 citations
Publisher

Abstract

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.

DOI
10.1364/ol.40.001121

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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.
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 demonstrate the experimental generation of quadrature amplitude entanglement in the 1550 nm band by using a fiber optical parametric amplifier. The measured noise variances of the difference and sum of the quadrature amplitudes of the pulsed signal and idler twin beams fall below the shot noise limit by about 1 and 0.8 dB (4.2 and 3.6 dB after the correction for efficiency), respectively, showing that the inseparability criterion of Einstein-Podolsky-Rosen entanglement I<2 is satisfied. Our investigation reveals that the quality of the measured entanglement can be further improved by increasing the transmission efficiency of the twin beams and by optimizing the temporal mode matching of the two sets of homodyne detection systems.
The dependence of the quantum correlation of twin beams generated from a non-degenerate optical parametric oscillator on the analysis frequency was theoretically studied with semi-classical method. It was pointed out that the quantum entanglement is higher at lower analysis frequency. By means of a pair of unbalanced fiber Mach-Zehnder interferometers，the correlation noise spectrum of the intensity-difference and the phase-sum of twin beams with non-degenerate frequencies and total power of 20mW were experimentally measured，which were 3.1 and 1.3dB below the corresponding shot noise limit at 2MHz，respectively. The experimental results are in agreement with the theoretical predictions.
The unconditional entanglement swapping for continuous variables is experimentally demonstrated. Two initial entangled states are produced from two nondegenerate optical parametric amplifiers operating at de-amplification. Through implementing the direct measurement of the Bell-state between two optical beams from each amplifier the remaining two optical beams, which have never directly interacted with each other, are entangled. The quantum correlation degrees of 1.23 and 1.12 dB below the shot noise limit for the amplitude and phase quadratures resulting from the entanglement swapping are measured straightly.
Balanced homodyne detection relies on a beam splitter to superpose the weak signal input and strong local oscillator. However, recent investigation shows that a high gain phase sensitive amplifier (PSA) can be viewed as homodyne detector, in which the strong pump of PSA serves as the local oscillator [1]. Here, we analyze a new method of measuring the continuous variable entanglement by assisting a balanced homodyne detector with the PSA and implement it experimentally. Before measuring quadrature amplitude with the balanced homodyne detectors, two entangled fields generated from a pulse pumped fiber optical parametric amplifier are simultaneously coupled into the PSA. We find that the normalized noise for both the difference and sum of the quadrature amplitudes of the two entangled fields fall below the shot noise limit by about 4.6 dB, which is the record degree of entanglement measured in optical fiber systems. The experimental results illustrate that the advantages of the new measurement method include but not limit to tolerance to detection loss and characterizing entanglement with only one homodyne detector. The influence of mode-mismatching due to multi-mode property of entanglement on the measured noise reduction can also be greatly mitigated, indicating the new method is advantageous over the traditional measurement in multi-mode case.
In this work, we propose a new simple entanglement measurement scheme, which can be utilized to take a measurement for the bright EPR beams generated by a nondegenerate optical parametric amplifier. Owing to the output signal and idler modes being frequency degenerate and in phase, one need not take a measurement for the signal and idler modes, respectively. By virtue of a quarter-wave plate and a half-wave plate, and then inserting a polarizing beam splitter, one can realize the measurements of the correlated phase quadratures and anti-correlated amplitude quadratures, simultaneously. Therefore, phase-locking and local oscillators are avoided.