Arbitrary bias control of LiNbO${}_3$ based Mach-Zehnder intensity modulators for QKD system

Quantum key distribution (QKD) can help distant agents to share unconditional secret keys, and the achievable secret key rate can be enhanced with the help of decoy-state protocol. To implement QKD experimentally, the agents are supposed to accurately transmit a number of different intensity pulses with the LiNbO${}_3$ based Mach-Zehnder (LNMZ) intensity modulator. However, the bias drift of LNMZ intensity modulator may affect the performance of a QKD system. In this letter, we reveal a simple RC circuit model to demonstrate the bias drift in the LNMZ intensity modulator. And based on the model, we propose a multi-step bias stable scheme to control the bias working point. Experimental result shows that our scheme can eliminate the bias drift of at arbitrary working point within a long time range. Besides, there is no need of any feedback mechanisms in the scheme. This means our scheme will not lead to any increasement in system complexity, making it more suitable for a QKD system.