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Quantum Electronics

Influence of birefringent fibre joints on the visibility drift in a Mach – Zehnder interferometer

G.M. Krylov, Oleg V. Fat’yanov, А.В. Дуплинский

Published May 1, 2020• 1 citation
Publisher

Abstract

Abstract It is shown that imperfect joints of linear birefringent fibres in a fibre interferometer may result in an uncontrolled visibility drift under varying environmental conditions even with a standard phase matching device. As an example, a double Mach – Zehnder interferometer is considered, which is employed in schemes of quantum key distribution. Results of numerical simulation demonstrate the standard deviation of the quantum bit error rate (QBER), which is comparable to an average QBER value.

DOI
10.1070/qel17284

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Abstract It is shown that imperfect joints of linear birefringent fibres in a fibre interferometer may result in an uncontrolled visibility drift under varying environmental conditions even with a standard phase matching device. As an example, a double Mach – Zehnder interferometer is considered, which is employed in schemes of quantum key distribution. Results of numerical simulation demonstrate the standard deviation of the quantum bit error rate (QBER), which is comparable to an average QBER value.
Quantum bit error rate (QBER) of the quantum key distribution system based on the unbalanced Mach-Zehnder interferometer is theoretically analyzed. The influence of the unsymmetry of the two Mach-Zehnder interferometers, the birefringence in the fiber and the fluctuation of the temperature, on the QBER have been discussed in detail. The analytical expression of the QBER is deduced. It shows that the QBER caused by the unsymmetry of the two Mach-Zehnder interferometers defers to the Gauss distribution, QBER caused by the birefringence in the fiber which results in the disaccord of the polarization of the two pulses defers to the cosine distribution, and the fluctuation of the temperature exert great influence on the QBER.
It is experimentally demonstrated that a long distance actively stabilised Mach-Zehnder fibre optical interferometer can be used to reliably implement the GV95 quantum cryptography protocol employing orthogonal states. A proof-of-principle experiment using an interferometer composed of 1 km of spooled optical fibres connecting Alice and Bob is performed. The active stabilisation against phase drifts is done with a classical channel wavelength-multiplexed with the quantum channel and a highly stable visibility implying a quantum bit error rate of 2.2 % is shown.
Quantum Key Distribution (QKD) system based on the two asymmetric Mach-Zehnder optical fiber interferometers is easily influenced by the external environmental interference, which causes phase excursion. And the high interference visibility of QKD system can’t keep for long and the instability of interference could cause the bit error of QKD. By tracking the stochastic phase excursion in statistical manner, the experiment of quantum key distribution over 75km was done successfully during the time of high interference visibility. The method of QKD in this paper is possessed of high security, less component, and easy operation.
Our system is based upon a Mach-Zender interferometer using phase modulation. Photons are generated by a 1.55 pm DFB pulsed laser diode operating with a repetition rate of 2 MHz. The pulses are strongly attenuated so that on average 0. I photons/clock cycle leaves the senders apparatus. Phase modulators. controlled by custom electronics, in the two interfering arms were used to encode the bit information. The signal is multiplexed with pulses from a 1.3 pm clock laser which serves as a timing reference. Cooled InGaAs avalanche photodiodes operating in Geiger mode are used to detect the single photons. It is imperative for operation over long fibres that the dark count rate in the single photon detector is as low as possible. Our detectors typically have a dark count probability of 3.2~10.~ er gate, along with a detection efficiency of 12% at 1.55 pm. This yields a Noise Equivalent Power of I .OXIO-'~ WHz- , whcch IS one of the lowest reported to date. R ' . The interferometer displayed a single photon interference fringe visibility between 99.1% and 99.7% for fibre lengths up to 65km. For longer fibre lengths the visibility falls, but remains around 96% at IOlkm, see Figure 1. The QBER, shown in Figure 2, remains virtually constant at around 3.6% for fibre length up to 50km, suggesting that the dominant contribution derives from inaccuracy in the phase modulation. Beyond 50km the QBER increases with fibre length, due to dark count noise. At 101 km, the QBER averaged over a 2-minute key transfer is typically 7. I %. This error rate is below the 1 I .5% limit, thus allowing us to perform error correction and privacy amplification to form a secure key. The sifted bit rate (shown in Figure 2) decreases with increasing fibre length at a rate of -0.20 dB/km, close to the specified value. At IOOkm the average bit rate was typically 15 Hz, sufficient to allow a cryptographic key to be transferred in several tens of seconds. 100
The polarisation drift between the arms of an 8 km-long fibre-optical Mach-Zehnder interferometer is experimentally stabilised, while simultaneously compensating the phase fluctuations. The single photons are wavelength-multiplexed with three classical channels, which are used as feedback for the control systems. Two of these channels are used for the active polarisation control systems, while the other is used to phase-lock the interferometer. Long-term stabilisation of the single-photon visibility when polarisation control is used is demonstrated.
We experimentally stabilise the polarisation drift between the arms of an 8 km-long fibre-optical Mach-Zehnder interferometer, while simultaneously compensating the phase fluctuations. The single photons are wavelength-multiplexed with three classical channels, which are used as feedback for the control systems. Two of these channels are used for the active polarisation control systems, while the other is used to phase-lock the interferometer. We demonstrate long-term stabilisation of the single-photon visibility when polarisation control is used.