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Journal of Optical Technology

Estimating the phase modulator location in Sagnac interferometers for quantum key distribution systems

Konstantin V. Stepanov, A.V. Borisova, A. G. Vtyurina

Published Sep 1, 2025• 0 citations
Publisher

Abstract

Subject of study . A phase modulation device for encoding quantum states based on an electro-optical phase modulator asymmetrically located in a Sagnac interferometer is studied. Aim of study. An easily implemented and repeatable method for measuring the path difference to a phase modulator inside a Sagnac interferometer in quantum key distribution systems is developed. Method. A phase difference between the clockwise and counterclockwise continuous propagating light is introduced in the beamsplitter of a Sagnac interferometer when an electrical pulse is transmitted to a phase modulator. Moreover, the asymmetric location of the phase modulator means that this single electrical pulse introduces twice the optical phase difference. Main results. A technique for measuring the difference in propagation time for light traveling in opposite directions to reach the phase modulator in a Sagnac interferometer was proposed and experimentally tested; this technique can be used for simultaneous modulation of phase and intensity in quantum key distribution systems. Practical significance. Our results regarding this highly accurate and easily implementable technique for measuring the difference in propagation time for light traveling in opposite directions to reach the asymmetrically positioned phase modulator in a Sagnac interferometer are relevant for the production of optoelectronic modules used in quantum key distribution systems, where this time difference directly affects the system quality and overall performance.

DOI
10.1364/jot.92.000587

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Subject of study . A phase modulation device for encoding quantum states based on an electro-optical phase modulator asymmetrically located in a Sagnac interferometer is studied. Aim of study. An easily implemented and repeatable method for measuring the path difference to a phase modulator inside a Sagnac interferometer in quantum key distribution systems is developed. Method. A phase difference between the clockwise and counterclockwise continuous propagating light is introduced in the beamsplitter of a Sagnac interferometer when an electrical pulse is transmitted to a phase modulator. Moreover, the asymmetric location of the phase modulator means that this single electrical pulse introduces twice the optical phase difference. Main results. A technique for measuring the difference in propagation time for light traveling in opposite directions to reach the phase modulator in a Sagnac interferometer was proposed and experimentally tested; this technique can be used for simultaneous modulation of phase and intensity in quantum key distribution systems. Practical significance. Our results regarding this highly accurate and easily implementable technique for measuring the difference in propagation time for light traveling in opposite directions to reach the asymmetrically positioned phase modulator in a Sagnac interferometer are relevant for the production of optoelectronic modules used in quantum key distribution systems, where this time difference directly affects the system quality and overall performance.
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We present a design for a quantum key distribution (QKD) system in a Sagnac loop configuration, employing a novel phase modulation scheme based on frequency shift, and demonstrate stable BB84 QKD operation with high interference visibility and low quantum bit error rate (QBER). The phase modulation is achieved by sending two light pulses with a fixed time delay (or a fixed optical path delay) through a frequency shift element and by modulating the amount of frequency shift. The relative phase between two light pulses upon leaving the frequency-shift element is determined by both the time delay (or the optical path delay) and the frequency shift, and can therefore be controlled by varying the amount of frequency shift. To demonstrate its operation, we used an acousto-optic modulator (AOM) as the frequency-shift element, and vary the driving frequency of the AOM to encode phase information. The interference visibility for a 40 km and a 10 km fiber loop is 96% and 99%, respectively, at single photon level. We ran BB84 protocol in a 40-km Sagnac loop setup continuously for one hour and the measured QBER remained within the 2%-5% range. A further advantage of our scheme is that both phase and amplitude modulation can be achieved simultaneously by frequency and amplitude modulation of the AOM's driving signal, allowing our QKD system the capability of implementing other protocols, such as the decoy-state QKD and the continuous-variable QKD. We also briefly discuss a new type of Eavesdropping strategy ("phase-remapping" attack) in bidirectional QKD system
In this letter, we report the experimental demonstration of a single-photon router based on a time-division Sagnac interferometer, wherein differential phase shifts are applied on either the clockwise or counterclockwise quasi-single-photon pulses to determine the single photon interference and consequently output photon routing. High fidelity (>85%) of single-photon routing was demonstrated over a long-distance Sagnac loop. Stable performance was guaranteed by passive compensation of stress and temperature dependent drifts of the fiber-optic path. Experimental data show that time-division single-photon routing can be realized by controlling the applied electric pulses on the integrated phase modulators in the Sagnac loop, which makes this setup suitable for a practical quantum cryptography system.
We study the modulation of Pancharatnam-Berry phase by lonexugitudinal electro-optical modulator which is an uniaxial crystal inserted into Sagnac interferometer.Because the difference of optical paths between clockwise and anticlockwise loop is zero,under the condition of zero-phase-difference related to the optical paths,the Pancharatnam-Berry phase between clockwise and anticlockwise loop can be distinguished more favorably.The results show that when the applied voltage vary continuously,the Pancharatnam-Berry phase jumps twice due to the characteristics of uniaxial crystal,while the coherent superposition intensity vary continuously.
In this work, we present a new time-bin phase-encoding quantum key distribution (QKD), where the transmitter utilizes an inherently stable Sagnac-type interferometer, and has comparable electrical requirements to existing polarization or phase encoding schemes. This approach does not require intensity calibration and is insensitive to environmental disturbances, making it both flexible and high-performing. We conducted experiments with a compact QKD system to demonstrate the stability and secure key rate performance of the presented scheme. The results show a typical secure key rate of 6.2 kbps@20 dB and 0.4 kbps@30 dB with channel loss emulated by variable optical attenuators. A continuous test of 120-km fiber spool shows a stable quantum bit error rate of the time-bin basis within 0.4%∼0.6% over a consecutive 9-day period without any adjustment. This intrinsically stable and compatible scheme of time-bin phase encoding is extensively applicable in various QKD experiments, including BB84 and measurement-device-independent QKD.