Abstract We study the spatial mode content at the output of a wide-field interferometer, i.e. a nonlinear interferometer comprising two coherently-pumped spatially-multimode optical parametric amplifiers placed in sequence with a focusing element in between. This device is expected to provide a phase sensitivity below the shot-noise limit for multiple modes over a broad angular range. To reconstruct the spatial modes and their weights, we implement a simple method based on the acquisition of only intensity distributions. The eigenmode decomposition of the field is obtained through the measurement of the covariance of intensities at different spatial points. We investigate both the radial and azimuthal (orbital angular momentum) modes and show that their total number is large enough to enable applications of the interferometer in spatially-resolved phase measurements.
Abstract We study the spatial mode content at the output of a wide-field interferometer, i.e. a nonlinear interferometer comprising two coherently-pumped spatially-multimode optical parametric amplifiers placed in sequence with a focusing element in between. This device is expected to provide a phase sensitivity below the shot-noise limit for multiple modes over a broad angular range. To reconstruct the spatial modes and their weights, we implement a simple method based on the acquisition of only intensity distributions. The eigenmode decomposition of the field is obtained through the measurement of the covariance of intensities at different spatial points. We investigate both the radial and azimuthal (orbital angular momentum) modes and show that their total number is large enough to enable applications of the interferometer in spatially-resolved phase measurements.
An SU(1,1) interferometer uses a sequence of two optical parametric amplifiers for achieving sub-shot-noise sensitivity to a phase shift introduced in between. We present the first realization of a wide-field SU(1,1) interferometer, where the use of a focusing element enables spatially multimode operation within a broad angle. Over this angle, the interference phase is found to be flat. This property is important for the high sensitivity to the phase front disturbance. Further, −4.3±0.7 dB quadrature squeezing, an essential requirement to the high sensitivity, is experimentally demonstrated for plane-wave modes inside the interferometer. Such an interferometer is useful not only for quantum metrology, but also in remote sensing, enhanced sub-shot-noise imaging, and quantum information processing.
An SU(1,1) interferometer uses a sequence of two optical parametric amplifiers for achieving sub-shot-noise sensitivity to a phase shift introduced in between. We present the first realization of a wide-field SU(1,1) interferometer, where the use of a focusing element enables spatially multimode operation within a broad angle. Over this angle, the interference phase is found to be flat. This property is important for the high sensitivity to the phase front disturbance. Further, -4.3 +/- 0.7 dB quadrature squeezing, an essential requirement to the high sensitivity, is experimentally demonstrated for plane-wave modes inside the interferometer. Such an interferometer is useful not only for quantum metrology, but also in remote sensing, enhanced sub-shot-noise imaging, and quantum information processing. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Multimode quantum light has promising applications in many areas of physics, such as quantum communications and quantum computing. However, its multimode nature also makes it challenging to measure its properties. Recently [I. Barakat , ], a technique for the simultaneous measurement of squeezing of multiple broadband modes based on a phase-sensitive amplification approach was experimentally implemented using a setup that effectively corresponds to an SU(1,1) interferometer. Here, we aim to provide a complete theoretical analysis of the modal structure of (generally unbalanced) SU(1,1) interferometers and a detailed theoretical formal derivation of the framework for this technique. Utilizing the joint Schmidt decomposition of the transfer functions, we investigate the shape and phase profiles of the modes of the SU(1,1) interferometer and its components [parametric down-conversion (PDC) sections] for different parametric gain regimes. We discover a complicated interplay between the PDC modes and the modes of the entire interferometer, and analyze it by using their overlap coefficients as a similarity measure. Finally, we develop a rigorous processing method for the aforementioned multimode squeezing measurement technique and discuss necessary approximations to make this method experimentally feasible.
The existing methods for measuring the orbital-angular-momentum (OAM) spectrum suffer from issues such as poor efficiency, strict interferometric stability requirements, and too much loss. Furthermore, most techniques inevitably discard part of the field and measure only a post-selected portion of the true spectrum. Here, we propose and demonstrate an interferometric technique for measuring the true OAM spectrum of optical fields in a single-shot manner. Our technique directly encodes the OAM-spectrum information in the azimuthal intensity profile of the output interferogram. In the absence of noise, the spectrum can be fully decoded using a single acquisition of the output interferogram, and, in the presence of noise, acquisition of two suitable interferograms is sufficient for the purpose. As an important application of our technique, we demonstrate measurements of the angular Schmidt spectrum of the entangled photons produced by parametric down-conversion and report a broad spectrum with the angular Schmidt number 82.1.
We present a comprehensive framework for evaluating the phase sensitivity of spectrally multimode SU(1,1) interferometers probed with a coherent-vacuum input, under both number and homodyne detections. The optical parametric amplifiers (OPAs) are simulated using a periodically polled thin-film lithium niobate waveguide. The theoretical model incorporates the intrinsic multimode spectral nature of waveguide-based OPAs. Under the assumptions of identical OPAs and Schmidt-mode-independent phase shifts, we have shown that the multimode SU(1,1) interferometer is equivalent to a collection of independent single-mode interferometers in the Schmidt basis that operate in parallel, each associated with a Schmidt mode of the parametric process. We further present an optimized waveguide design based on asymmetric group-velocity matching to realize a practical OPA with nearly factorizable joint spectral amplitude (JSA). The Schmidt coefficients extracted from the numerically simulated JSA are incorporated into the theoretical model to evaluate the phase sensitivity. The results show that the sensitivity under a multimode condition depends strongly on the measurement scheme. For number detection, the degradation in sensitivity arises from the redistribution of the available nonlinear resource among the Schmidt modes, whereas homodyne detection exhibits an additional coherence penalty that can be substantially reduced by optimally shaping the local oscillator. Moreover, we show that the performance degradation can be to a large extent mitigated by optimizing the spectrum of the injected signal coherent state and, in the case of homodyne detection, the spectrum of the local oscillator. Altogether, this work provides a unified theoretical and numerical framework for analyzing and optimizing realistic multimode SU(1,1) interferometers with waveguide-based OPAs for quantum-enhanced sensing applications.
Multimode quantum light has promising applications in many areas of physics, such as quantum communications and quantum computing. However, its multimode nature also makes it challenging to measure its properties. Recently [I. Barakat et al., Optica Quantum 3, 36 (2025)], a technique for the simultaneous measurement of squeezing of multiple broadband modes based on a phase-sensitive amplification approach was experimentally implemented using a setup that effectively corresponds to an SU(1,1) interferometer. Here, we aim to provide a complete theoretical analysis of the modal structure of (generally unbalanced) SU(1,1) interferometers and a detailed theoretical formal derivation of the framework for this technique. Utilizing the joint Schmidt decomposition of the transfer functions, we investigate the shape and phase profiles of the modes of the SU(1,1) interferometer and its components [parametric down-conversion (PDC) sections] for different parametric gain regimes. We discover a complicated interplay between the PDC modes and the modes of the entire interferometer, and analyze it by using their overlap coefficients as a similarity measure. Finally, we develop a rigorous processing method for the aforementioned multimode squeezing measurement technique and discuss necessary approximations to make this method experimentally feasible.