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Quantum 2.0 Conference and Exhibition

Unbalanced Interferometer beyond Coherence Length by Amplitude Measurement

Yunxiao Zhang, Xuan Tang, Xueshi Guo, Liang Cui, Xiaoying Li, Z. Y. Ou

Published Jan 1, 2024• 0 citations
Publisher

Abstract

We report the recovery of interference in an interferometer with path imbalance well beyond coherence length of the input field. This is achieved by direct amplitude measurement via homodyne detection.
DOI
10.1364/quantum.2024.qtu3a.48

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Interference effects are usually observed by intensity measurement. Path indistinguishability by the quantum complementarity principle requires projection of the interfering fields into a common indistinguishable mode before detection. On the other hand, the essence of wave interference is the addition of amplitudes of the interfering fields. Therefore, if amplitudes can be directly measured and added, interference can occur even though the interfering fields are in well-distinguishable modes. Here, we make a comprehensive study in both theory and experiment of a technique by homodyne measurement of field amplitudes to reveal interference. This works for both classical and quantum fields even though there exists distinguishability in the interfering paths of light. This directly challenges the complementarity principle. We present a resolution of this issue from the viewpoint of measurement that emphasizes either particle or wave. This technique is particularly useful for recovering interference in unbalanced interferometers with path imbalance beyond a coherence length of the input field and can be applied to remote sensing to extend the applicable range. Since the amplitude-based interference phenomena studied here are fundamentally different from the traditional intensity-based interference phenomena, our approach leads to a new paradigm to study coherence between optical fields.
Optical interference usually requires two interfering paths to be balanced within the coherence length. For the case of unbalanced paths, interference effects can be recovered in the frequency-domain analysis of the superposed resultant optical field because optical frequency filtering in the spectral analysis of the optical field lengthens the coherence length to overcome the path imbalance. However, since optical detection usually is intensity measurement that loses the phase information of the detected optical field, the output photocurrent of intensity measurement cannot recover the lost interference effect in the postprocessing of the data such as electronic spectral analysis. On the other hand, if amplitude measurement can be used to measure the resultant optical field from the path-unbalanced superposition of two fields, the output photocurrent carries complete information of two fields and can restore interference in postdetection processing, even though no interference shows up in direct intensity measurement. In this paper, we use homodyne detection method for amplitude measurement to analyze the output of a path-unbalanced interferometer in the spectral domain. Since complete information about the superposed optical field is contained in the photocurrent, spectral analysis shows interference fringes in frequency that reveal information about the path imbalance. It is found that shot noise is the limiting factor in the visibility of interference but can be reduced with a squeezed state input in the unused port of the unbalanced interferometer. This approach is a different paradigm from the traditional one for studying the coherence between optical fields and should find wide application in remote sensing and precision measurement.