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Algorithms

Adaptive-Step Perturb-and-Observe Algorithm for Multidimensional Phase Noise Stabilization in Fiber-Based Multi-Arm Mach–Zehnder Interferometers

H. Abarzúa, C. Melo, Silvia Restrepo, S. Vergara, Daniel G. Sbarbaro, Gustavo Cañas, G. Lima, Gabriel Saavedra, Jaime Cariñe

Published Nov 21, 2024• 3 citations
Publisher

Abstract

Fiber-optic Mach-Zehnder interferometers are widely used in research areas such as telecommunications, spectroscopy, and quantum information. These optical structures are known to be affected by phase fluctuations that are usually modeled as multiparametric noise.This multidimensional noise must be stabilized or compensated for to enable fiber-optic Mach-Zehnder architectures for practical applications. In this work, we study the effectiveness of a modified Perturb-and-Observe (P&O) algorithm to control multidimensional phase noise in fiber-based multi-arm Mach-Zehnder interferometers. We demonstrate the feasibility of stabilizing multidimensional phase noise by numerical simulations using a simple feedback control scheme and analyze the algorithm’s performance for systems up to dimension 8x8. We achieved minimal steady-state errors that guarantee high optical visibility in complex optical systems with N×N matrices (with N=[2,3,4,5,6,7,8]).

DOI
10.3390/a17120534

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Fiber-optic Mach-Zehnder interferometers are widely used in research areas such as telecommunications, spectroscopy, and quantum information. These optical structures are known to be affected by phase fluctuations that are usually modeled as multiparametric noise.This multidimensional noise must be stabilized or compensated for to enable fiber-optic Mach-Zehnder architectures for practical applications. In this work, we study the effectiveness of a modified Perturb-and-Observe (P&O) algorithm to control multidimensional phase noise in fiber-based multi-arm Mach-Zehnder interferometers. We demonstrate the feasibility of stabilizing multidimensional phase noise by numerical simulations using a simple feedback control scheme and analyze the algorithm’s performance for systems up to dimension 8x8. We achieved minimal steady-state errors that guarantee high optical visibility in complex optical systems with N×N matrices (with N=[2,3,4,5,6,7,8]).
An experimental study was carried out on the performance of a feedback stabilization scheme for optical interferometers. Optical interferometers are susceptible to acoustic noise which translates into path length fluctuations in the interferometer arms. These fluctuations induce phase noise, resulting in amplitude fluctuations on the interferometer output. The experiment was performed on a Mach-Zehnder homodyne interferometer where a RMS noise reduction of 23 dB was observed. The stabilization scheme has application to other interferometer configurations. In the future, it will be applied to stabilize cavities used in the squeezed state generation of light. (Author)
This thesis investigates the phenomena of phase stability in a fiber-optical MZI (Mach-Zehnder Interferometer). The MZI is a key building block of optical systems for use in experiments with both continuous-wave light and with single photons. By splitting incoming light into two beams and allowing it to interfere with itself, an interference pattern is visible at the output, and this phenomena can be used to code information. This is the operating principle in, for example, QKD (Quantum Key Distribution) experiments. This interference requires coherence that is higher than the length difference between the beams that the incoming light is split into. Particularly the phase of the beams must be equal to achieve constructive interference. If one beam is phase-shifted (with respect to the other) due to the light having traversed a longer path, only partially constructive interference is achieved. If the phase shift also varies with time this leads to a system where experiments can no longer reliably be performed. Sources of these fluctuations are thermal, acoustic or mechanical. Fiber-optical interferometers are particularly sensitive to path length fluctuations of the waveguides as the fiber-optic medium contracts and elongates with temperature, and also has a larger surface area for circulating air to mechanically disturb the waveguides than bulk optics interferometers. In this thesis, a solution to environment-induced phase drift is presented by evaluating implementations of feedback algorithms for automatic control. The algorithms PID (Proportional-, Integral-, Derivative controller) and an ICA (IncrementalControl Algorithm) have been investigated and the performance of these controllers has been compared when used with, and without, optical enclosures. The algorithms are implemented in an FPGA (Field-Programmable Gate Array) and the controller actuates an electro-optical phase modulator that can add a phase shift to one of the light beams in the MZI. This thesis shows that significant improvement in the optical stability can be achieved with active control compared to an interferometer without active phase control.
Many protocols for long distance quantum communication require interferometric phase stability over long distances of optical fibers. In this paper we investigate the phase noise in long optical fibers both in laboratory environment and in installed commercial fibers in an urban environment over short time scales (up to hundreds of $\ensuremath{\mu}\text{s}$). We show that the phase fluctuations during the travel time of optical pulses in long-fiber loops are small enough to obtain high visibility first-order interference fringes in a Sagnac interferometer configuration for fiber lengths up to 75 km. We also measure phase fluctuations in a Mach-Zehnder interferometer in installed fibers with arm length 36.5 km. We verify that the phase noise respects Gaussian distribution and measure the mean phase change as a function of time difference. The typical time needed for a mean phase change of 0.1 rad is of order of $100\text{ }\ensuremath{\mu}\text{s}$, which provides information about the time scale available for active phase stabilization. Our results are relevant for future implementations of quantum repeaters in installed optical fiber networks.
The suppression of laser excess noise using a cascaded imbalanced Mach-Zehnder interferometer with fiber optic components was proposed and demonstrated in the experiment.By developing an automatic phase control system,the phase of the fiber interferometer with a large path imbalance(127m)can be stabilized in a long term,and the laser excess noise around 800 kHz and its integer multiples can be efficiently suppressed by more than 45 dB.The effective frequency bands of the noise filter can be controlled by adjusting the arm-length difference of the interferometer.The approach provides an effective solution for achieving compact and cost-effective laser noise reduction,and can be applied directly to the quantum optomechanical system where shot-noise-limited laser can be required.
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 demonstrate stable and user-adjustable single-photon interference in a 1 km long fiber-optic Mach-Zehnder interferometer, using an active phase control system with the feedback provided by a classical laser. We are able to continuously tune the single-photon phase difference between the interferometer arms using a phase modulator, which is synchronized with the gate window of the single-photon detectors. The phase control system employs a piezoelectric fiber stretcher to stabilize the phase drift in the interferometer. A single-photon net visibility of 0.97 is obtained, yielding future possibilities for experimental realizations of quantum repeaters in optical fibers and violation of Bell's inequalities using genuine energy-time entanglement.