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Education and Training in Optics and Photonics

Teaching the foundations of quantum imaging through Mach-Zehnder interferometry

Dustin-Philipp Preissler, Timo Mappes, Maria Dienerowitz, Holger Cartarius

Published Jul 7, 2025• 0 citations
Publisher
DOI
10.1117/12.3076844

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Quantum imaging is an emerging field in quantum optics with a wide range of applications including microscopy, secure communication and medical imaging. To foster knowledge and attract public attention and understanding, these applications are of high interest for teaching and science communication. The field of quantum imaging in particular has an appealing goal, the transmission of images. Quantum imaging setups use single photon sources and detectors, which are hard to adjust, easily damaged, and yet expensive. However, the basic approach of quantum imaging methods can be explained in a much simpler way. We use a Mach-Zehnder interferometer with laser beams to demonstrate how to obtain the properties of the imaged object. The setup is highly stable and well-suited for student laboratory courses.
Phase-shifting interferometry (PSI) promises excellent performance for quantitative phase measurement. However, the PSI is commonly realized by utilizing the Mach-Zehnder interferometer (MZI) fed with classical resources, and hence its phase sensitivity is hindered by the photon shot noise. In this paper, we propose to introduce specific phase-shifting algorithms into the well-established quantum-enhanced MZI, seeded by coherent and squeezed vacuum states and followed by single-mode intensity detection and difference intensity detection, to achieve quantitative phase measurement with sensitivity beyond that achieved by the corresponding Mach-Zehnder-type PSI with classical input. We show that when the average photon number of the coherent state is dominant, the optimal phase sensitivity of the Mach-Zehnder-type PSI with coherent plus squeezed vacuum input is better than the phase sensitivity of the Mach-Zehnder-type PSI with single coherent input under the same phase-sensing intensity condition in both of detection setups. We also show that for the typical MZI seeded with a high-power coherent state and a finitely squeezed vacuum state, the combination of intensity detection and phase-shifting algorithm can still improve the sensitivity of quantitative phase measurement. Furthermore, we derive the phase sensitivity of the fixed MZI as well as the quantum Cramér-Rao bound for two detection schemes. Finally, we explore the impacts of photon losses on the phase sensitivity enhancements of the Mach-Zehnder-type PSI and the fixed MZI in the high-intensity regime for each detection setup. The robustness to losses is compared between the Mach-Zehnder-type PSI and the fixed MZI. Our results may be helpful to promote the exploration of quantum-enhanced quantitative phase sensing.