Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2405.03868 · Physical Review A

Tunable linear-optical phase amplification

Christopher R. Schwarze, David S. Simon, Abdoulaye Ndao, Alexander V. Sergienko

Published May 6, 2024• 2 citations
arXivHTMLPDF

Abstract

We combine lossless, phase-only transformations with fully transmitting linear-optical scatterers to define the principle of linear-optical phase amplification. This enables a physical phase shift $\ensuremath{\phi}$ to be nonlinearly mapped to a new space $\ensuremath{\gamma}(\ensuremath{\phi})$ using linear optics, resulting in a completely general and enhanced phase shifter that can replace any standard one. A particular phase amplifier is experimentally realized, allowing the phase enhancement parameter $d\ensuremath{\gamma}/d\ensuremath{\phi}$ to be continuously tuned. Placing this enhanced phase shifter in one arm of a Mach-Zehnder interferometer led to an intensity-phase slope more than 20 times steeper than what can be obtained with its unamplified counterpart.

DOI
10.1103/physreva.109.053508

Related papers

Enhancing Phase Sensitivity in Mach–Zehnder Interferometers for Arbitrary Input States

Hongbin Liang, Jiancheng Pei, Xiaoguang Wang

To enhance the phase sensitivity of Mach–Zehnder interferometers, we use a tunable phase shift before the light beams are injected into the interferometer. The analytical result of the optimal phase shift is obtained, which only depends on the initial input states. For a non-zero optimal phase shift, the phase sensitivity of the interferometers in the output ports is always enhanced. We can achieve this enhancement for most states, including entangled and mixed states. The optimal phase shift is exhibited in three examples. Compared to previous methods, this scheme provides a general way to improve phase sensitivity and could find wide applications in optical phase estimations.

Chinese Physics Letters•Jul 1, 2020•1 citation

Universal optical amplification without a nonlinearity

Metin Sabuncu, Vincent Josse, Nicolas J. Cerf +2 more

We propose and realize a novel universal phase insensitive optical amplifier operating at the quantum limit in the low gain regime. The amplifier consists only of linear optics and detectors thus circumventing a nonlinear interaction.

Conference on Lasers and Electro-Optics•Jan 1, 2006•12 citations

Demonstration of a Low-Depth Universal Linear Optical Circuit

Tomofumi Odagawa, Kazuki Sakaino, Shogo Kimura +8 more

Universal linear optical (ULO) circuit is a versatile device that plays a fundamental role in quantum computation, optical machine learning, and MIMO processing for optical communications. The design of the ULO, i.e., a universal multiport interferometer, was initially proposed by Reck et al. in 1994 [1] and improved in terms of circuit depth and robustness to optical losses by Clements et al. in 2016 [2]. Recently, a further compactified circuit design was proposed Bell and Walmsley [3]. In Bell's scheme, the circuit layout consists of a network of symmetric Mach-Zehnder interferometers (MZI) with two variable phase shifters in each arm. The design significantly reduces the whole device length compared to the conventional designs, where the circuit consists of a network of asymmetric MZIs, each of which has a phase shifter in one arm and an external phase shifter outside of itself. This downsizing becomes significantly important toward the realization of large-scale ULOs in the limited chip area, particularly when each phase shifter is long or when the spacing between phase shifters cannot be made small. This time we experimentally demonstrate that Bell's scheme can express arbitrary unitary matrices as well as Clements' scheme.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 26, 2023•0 citations

Further compactifying linear optical unitaries

B. A. Bell, I. A. Walmsley

Quantum integrated photonics requires large-scale linear optical circuitry, and for many applications, it is desirable to have a universally programmable circuit, able to implement an arbitrary unitary transformation on a number of modes. This has been achieved using the Reck scheme, consisting of a network of Mach–Zehnder interferometers containing a variable phase shifter in one path as well as an external phase shifter after each Mach–Zehnder. It subsequently became apparent that with symmetric Mach–Zehnders containing a phase shifter in both paths, the external phase shifters are redundant, resulting in a more compact circuit. The rectangular Clements scheme improves on the Reck scheme in terms of circuit depth, but it has been thought that an external phase-shifter was necessary after each Mach–Zehnder. Here, we show that the Clements scheme can be realized using symmetric Mach–Zehnders, requiring only a small number of external phase-shifters that do not contribute to the depth of the circuit. This will result in a significant saving in the length of these devices, allowing more complex circuits to fit onto a photonic chip, and reducing the propagation losses associated with these circuits. We also discuss how similar savings can be made to alternative schemes, which have robustness to imbalanced beam-splitters.

arXiv:2104.07561•APL Photonics•Jul 1, 2021•46 citations

Local Variance-Based Calibration of Programmable Photonic Interferometer Meshes

Gökhan Elmas, Igor A. Litvin, Janis Nötzel

Programmable photonic interferometer meshes enable reconfigurable linear optical transformations, but their performance depends critically on accurate calibration of Mach-Zehnder interferometers and phase shifters. Conventional methods often require node isolation, dedicated routing paths, orthogonal training states, reference channels, or prior phase-voltage characterization, which become increasingly difficult in large thermally tuned meshes. We introduce a local variance-based self-calibration method using intensity-only measurements. Controlled phase perturbations are applied, and calibration points are identified from minima of the measured output-power variance. For Mach-Zehnder interferometers, the variance follows a characteristic |sin(theta)| dependence, allowing bar and cross operating points to be found without conventional node isolation. For phase shifters, balanced interference produces a complementary |cos(phi)| variance signature, enabling quadrature calibration through the same statistical principle. We validate the method experimentally on an 8 x 8 silicon nitride programmable photonic processor using a fully automated two-stage procedure. Starting from random phase settings, all Mach-Zehnder interferometers are calibrated first, followed by phase-shifter calibration under balanced-interference conditions. As a system-level test, we implement an embedded 4 x 4 Hadamard transformation on the 8 x 8 processor using a Clements decomposition. These results establish local output variance as a simple calibration observable for programmable photonic meshes. The method is compatible with discrete random phase ensembles and requires neither conventional node isolation nor orthogonal training fields, making it a practical calibration primitive for scalable self-stabilizing photonic processors.

physics.opticsCross-listedarXiv:2607.14759•Jul 17, 2026

Advanced implementations of phase sensitive amplifiers

Francesca R. Parmigiani, Graham Hesketh, Kyle R. H. Bottrill +4 more

We review our recent results on different configurations of phase sensitive amplifiers that achieve all-optical phase regeneration and optical phase quantization at low nonlinear phase shifts.

IEEE/LEOS Summer Topical Meetings•Jul 1, 2014•0 citations
We combine lossless, phase-only transformations with fully transmitting linear-optical scatterers to define the principle of linear-optical phase amplification. This enables a physical phase shift \ensuremathϕ\ensuremath{\phi}\ensuremathϕ to be nonlinearly mapped to a new space \ensuremathγ(\ensuremathϕ)\ensuremath{\gamma}(\ensuremath{\phi})\ensuremathγ(\ensuremathϕ) using linear optics, resulting in a completely general and enhanced phase shifter that can replace any standard one. A particular phase amplifier is experimentally realized, allowing the phase enhancement parameter d\ensuremathγ/d\ensuremathϕd\ensuremath{\gamma}/d\ensuremath{\phi}d\ensuremathγ/d\ensuremathϕ to be continuously tuned. Placing this enhanced phase shifter in one arm of a Mach-Zehnder interferometer led to an intensity-phase slope more than 20 times steeper than what can be obtained with its unamplified counterpart.
To enhance the phase sensitivity of Mach–Zehnder interferometers, we use a tunable phase shift before the light beams are injected into the interferometer. The analytical result of the optimal phase shift is obtained, which only depends on the initial input states. For a non-zero optimal phase shift, the phase sensitivity of the interferometers in the output ports is always enhanced. We can achieve this enhancement for most states, including entangled and mixed states. The optimal phase shift is exhibited in three examples. Compared to previous methods, this scheme provides a general way to improve phase sensitivity and could find wide applications in optical phase estimations.
Universal linear optical (ULO) circuit is a versatile device that plays a fundamental role in quantum computation, optical machine learning, and MIMO processing for optical communications. The design of the ULO, i.e., a universal multiport interferometer, was initially proposed by Reck et al. in 1994 [1] and improved in terms of circuit depth and robustness to optical losses by Clements et al. in 2016 [2]. Recently, a further compactified circuit design was proposed Bell and Walmsley [3]. In Bell's scheme, the circuit layout consists of a network of symmetric Mach-Zehnder interferometers (MZI) with two variable phase shifters in each arm. The design significantly reduces the whole device length compared to the conventional designs, where the circuit consists of a network of asymmetric MZIs, each of which has a phase shifter in one arm and an external phase shifter outside of itself. This downsizing becomes significantly important toward the realization of large-scale ULOs in the limited chip area, particularly when each phase shifter is long or when the spacing between phase shifters cannot be made small. This time we experimentally demonstrate that Bell's scheme can express arbitrary unitary matrices as well as Clements' scheme.
Quantum integrated photonics requires large-scale linear optical circuitry, and for many applications, it is desirable to have a universally programmable circuit, able to implement an arbitrary unitary transformation on a number of modes. This has been achieved using the Reck scheme, consisting of a network of Mach–Zehnder interferometers containing a variable phase shifter in one path as well as an external phase shifter after each Mach–Zehnder. It subsequently became apparent that with symmetric Mach–Zehnders containing a phase shifter in both paths, the external phase shifters are redundant, resulting in a more compact circuit. The rectangular Clements scheme improves on the Reck scheme in terms of circuit depth, but it has been thought that an external phase-shifter was necessary after each Mach–Zehnder. Here, we show that the Clements scheme can be realized using symmetric Mach–Zehnders, requiring only a small number of external phase-shifters that do not contribute to the depth of the circuit. This will result in a significant saving in the length of these devices, allowing more complex circuits to fit onto a photonic chip, and reducing the propagation losses associated with these circuits. We also discuss how similar savings can be made to alternative schemes, which have robustness to imbalanced beam-splitters.
Programmable photonic interferometer meshes enable reconfigurable linear optical transformations, but their performance depends critically on accurate calibration of Mach-Zehnder interferometers and phase shifters. Conventional methods often require node isolation, dedicated routing paths, orthogonal training states, reference channels, or prior phase-voltage characterization, which become increasingly difficult in large thermally tuned meshes. We introduce a local variance-based self-calibration method using intensity-only measurements. Controlled phase perturbations are applied, and calibration points are identified from minima of the measured output-power variance. For Mach-Zehnder interferometers, the variance follows a characteristic |sin(theta)| dependence, allowing bar and cross operating points to be found without conventional node isolation. For phase shifters, balanced interference produces a complementary |cos(phi)| variance signature, enabling quadrature calibration through the same statistical principle. We validate the method experimentally on an 8 x 8 silicon nitride programmable photonic processor using a fully automated two-stage procedure. Starting from random phase settings, all Mach-Zehnder interferometers are calibrated first, followed by phase-shifter calibration under balanced-interference conditions. As a system-level test, we implement an embedded 4 x 4 Hadamard transformation on the 8 x 8 processor using a Clements decomposition. These results establish local output variance as a simple calibration observable for programmable photonic meshes. The method is compatible with discrete random phase ensembles and requires neither conventional node isolation nor orthogonal training fields, making it a practical calibration primitive for scalable self-stabilizing photonic processors.