Gain-induced spectral non-degeneracy in type-II parametric down-conversion - Taheri, Behnood; Kopylov, Denis; Hammer, Manfred; Meier, Torsten; Förstner, Jens; Sharapova, Polina R. (arXiv)

Characterization of spatial Schmidt modes in high-gain SU(1,1) interferometers - Scharwald, Dennis; Sharapova, Polina (Physical Review Research)
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.

Schmidt modes carrying orbital angular momentum generated by cascaded systems pumped with Laguerre–Gaussian beams - Scharwald, Dennis; Gehse, Lucas; Sharapova, Polina (APL Photonics)
Orbital angular momentum (OAM) modes are an important resource used in various branches of quantum science and technology due to their unique helical structure and countably infinite basis. Generating light that simultaneously carries high-order orbital angular momenta and exhibits quantum correlations is a challenging task. In this work, we present a theoretical approach to the generation of correlated Schmidt modes carrying OAM via parametric down-conversion (PDC) in cascaded nonlinear systems (nonlinear interferometers) pumped by Laguerre–Gaussian beams. We demonstrate how the number of generated modes and their population can be controlled by varying the pump parameters, the gain of the PDC process, and the distance between the crystals. We investigate the angular displacement measurement uncertainty of these interferometers and demonstrate that it can overcome the classical shot noise limit.

Simultaneous measurement of multimode squeezing through multimode phase-sensitive amplification - Barakat, Ismail; Kalash, Mahmoud; Scharwald, Dennis; Sharapova, Polina; Lindlein, Norbert; Chekhova, Maria (Optica Quantum)
Multimode squeezed light is an increasingly popular tool in photonic quantum technologies, including sensing, imaging, and computation. Meanwhile, the existing methods of its characterization are technically complicated, which reduces the level of squeezing, and mostly deal with a single mode at a time. Here, for the first time, to the best of our knowledge, we employ optical parametric amplification to characterize multiple squeezing eigenmodes simultaneously. We retrieve the shapes and squeezing degrees of all modes at once through direct detection followed by modal decomposition. This method is tolerant to inefficient detection and does not require a local oscillator. For a spectrally and spatially multimode squeezed vacuum, we characterize eight strongest spatial modes, obtaining squeezing and anti-squeezing values of up to −5.2 ± 0.2 dB and 8.6 ± 0.3 dB, respectively, despite the 50% detection loss. This work, being the first exploration of an optical parametric amplifier’s multimode capability for squeezing detection, paves the way for the real-time detection of multimode squeezing.

Theory of Multimode Squeezed Light Generation in Lossy Media - Kopylov, Denis A.; Meier, Torsten; Sharapova, Polina R. (Quantum)
A unified theoretical approach to describe the properties of multimode squeezed light generated in a lossy medium is presented. This approach is valid for Markovian environments and includes both a model of discrete losses based on the beamsplitter approach and a generalized continuous loss model based on the spatial Langevin equation. For an important class of Gaussian states, we derive master equations for the second-order correlation functions and illustrate their solution for both frequency-independent and frequency-dependent losses. Studying the mode structure, we demonstrate that in a lossy environment no broadband basis without quadrature correlations between the different broadband modes exists. Therefore, various techniques and strategies to introduce broadband modes can be considered. We show that the Mercer expansion and the Williamson-Euler decomposition do not provide modes in which the maximal squeezing contained in the system can be measured. In turn, we find a new broadband basis that maximizes squeezing in the lossy system and present an algorithm to construct it.

Spectral and temporal properties of type-II parametric down-conversion: The impact of losses during state generation - Kopylov, Denis A.; Stefszky, Michael; Meier, Torsten; Silberhorn, Christine; Sharapova, Polina R. (Physical Review Research)
In this paper, we theoretically study the spectral and temporal properties of pulsed spontaneous parametric down-conversion (SPDC) generated in lossy waveguides. Our theoretical approach is based on the formalism of Gaussian states and the Langevin equation, which is elaborated for weak parametric down-conversion and photon-number-unresolved click detection. Using the example of frequency-degenerate type-II SPDC generated under the pump-idler group-velocity-matching condition, we show how the joint-spectral intensity, mode structure, normalized second-order correlation function, and Hong-Ou-Mandel interference pattern depend on internal losses of the SPDC process. We found that the joint-spectral intensity is almost insensitive to internal losses, while the second-order correlation function shows a strong dependence on them, being different for the signal and idler beams in the presence of internal losses. Based on the sensitivity of the normalized second-order correlation function, we show how its measurement can be used to experimentally determine internal losses.

Multiphoton, multimode state classification for nonlinear optical circuits - Kopylov, Denis A.; Offen, Christian; Ares, Laura; Wembe Moafo, Boris Edgar; Ober-Blöbaum, Sina; Meier, Torsten; Sharapova, Polina R.; Sperling, Jan (Physical Review Research)
We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which is in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes.

Bipartite entanglement extracted from multimode squeezed light generated in lossy waveguides - Kopylov, Denis; Meier, Torsten; Sharapova, Polina R. (APL Quantum)
Entangled two-mode Gaussian states constitute an important building block for continuous variable quantum computing and communication protocols. In this work, we theoretically study two-mode bipartite states, which are extracted from multimode light generated via type-II parametric downconversion (PDC) in lossy waveguides. For these states, we demonstrate that the squeezing quantifies entanglement and we construct a measurement basis, which results in the maximal bipartite entanglement. We illustrate our findings by numerically solving the spatial master equation for PDC in a Markovian environment. The optimal measurement modes are compared with two widely used broadband bases: the Mercer–Wolf basis (the first-order coherence basis) and the Williamson–Euler basis.

Multiphoton, multimode state classification for nonlinear optical circuits - Kopylov, Denis; Offen, Christian; Ares, Laura; Wembe Moafo, Boris Edgar; Ober-Blöbaum, Sina; Meier, Torsten; Sharapova, Polina; Sperling, Jan
We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which being in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes.

Microscopic simulations of the dynamics of excitonic many-body correlations coupled to quantum light - Rose, Hendrik; Sharapova, Polina; Meier, Torsten
Dataset of the publication "Microscopic simulations of the dynamics of excitonic many-body correlations coupled to quantum light" H. Rose, P. R. Sharapova, and T. Meier, Proc. SPIE 12884, Ultrafast Phenomena and Nanophotonics XXVIII, 1288403 (2024). ( https://doi.org/10.1117/12.2690245 ). The zip file includes the data on which the plots shown in figures 1 and 2 are based.

Microscopic simulations of the dynamics of excitonic many-body correlations coupled to quantum light - Rose, Hendrik; Sharapova, Polina R.; Meier, Torsten (Ultrafast Phenomena and Nanophotonics XXVIII)

Quantum-optical excitations of semiconductor nanostructures in a microcavity using a two-band model and a single-mode quantum field - Rose, Hendrik; Vasil'ev, Andrey N.; Tikhonova, Olga V.; Meier, Torsten; Sharapova, Polina
Dataset of the publication "Quantum-optical excitations of semiconductor nanostructures in a microcavity using a two-band model and a single-mode quantum field" H. Rose, A. N. Vasil’ev, O. V. Tikhonova, T. Meier, and P. R. Sharapova, Phys. Rev. A 107, 013703 (2023). ( https://doi.org/10.1103/PhysRevA.107.013703 ). The zip file includes the data on which the plots shown in figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 are based.

Quantum-optical excitations of semiconductor nanostructures in a microcavity using a two-band model and a single-mode quantum field - Rose, Hendrik; Vasil'ev, A. N.; Tikhonova, O. V.; Meier, Torsten; Sharapova, Polina (Physical Review A)

Nonlinear Dielectric Nanoresonators and Metasurfaces: Toward Efficient Generation of Entangled Photons - Sharapova, Polina R.; Kruk, Sergey S.; Solntsev, Alexander S. (Laser & Photonics Reviews)
Keywords: Condensed Matter Physics; Atomic and Molecular Physics; and Optics; Electronic; Optical and Magnetic Materials

Steady states of Λ-type three-level systems excited by quantum light with various photon statistics in lossy cavities - Rose, Hendrik; Tikhonova, O V; Meier, Torsten; Sharapova, Polina (New Journal of Physics)
Abstract The interaction between quantum light and matter is being intensively studied for systems that are enclosed in high- Q cavities which strongly enhance the light–matter coupling. Cavities with low Q -factors are generally given less attention due to their high losses that quickly destroy quantum systems. However, bad cavities can be utilized for several applications, where lower Q -factors are required, e.g., to increase the spectral width of the cavity mode. In this work, we demonstrate that low- Q cavities can be beneficial for preparing specific electronic steady states when certain quantum states of light are applied. We investigate the interaction between quantum light with various statistics and matter represented by a Λ-type three-level system in lossy cavities, assuming that cavity losses are the dominant loss mechanism. We show that cavity losses lead to non-trivial electronic steady states that can be controlled by the loss rate and the initial statistics of the quantum fields. We discuss the mechanism of the formation of such steady states on the basis of the equations of motion and present both analytical expressions and numerical simulations for such steady states.
Keywords: General Physics and Astronomy

Theoretical analysis of correlations between two quantum fields exciting a three-level system using the cluster-expansion approach - Rose, Hendrik; Tikhonova, Olga V.; Meier, Torsten; Sharapova, Polina (Ultrafast Phenomena and Nanophotonics XXVI)

Two-Mode Photon-Number Correlations Created by Measurement-Induced Nonlinearity - Meier, Torsten; Hoepker, Jan Philipp; Protte, Maximilian; Eigner, Christof; Silberhorn, Christine; Sharapova, Polina R.; Sperling, Jan; Bartley, Tim (Conference on Lasers and Electro-Optics: Applications and Technology)
We demonstrate theoretically and experimentally complex correlations in the photon numbers of two-mode quantum states using measurement-induced nonlinearity. For this, we combine the interference of coherent states and single photons with photon sub-traction.

Two-Colour Spectrally Multimode Integrated SU(1,1) Interferometer - Ferreri, Alessandro; Sharapova, Polina R. (Symmetry)
Multimode integrated interferometers have great potential for both spectral engineering and metrological applications. However, the material dispersion of integrated platforms constitutes an obstacle that limits the performance and precision of such interferometers. At the same time, two-colour nonlinear interferometers present an important tool for metrological applications, when measurements in a certain frequency range are difficult. In this manuscript, we theoretically developed and investigated an integrated multimode two-colour SU(1,1) interferometer operating in a supersensitive mode. By ensuring the proper design of the integrated platform, we suppressed the dispersion, thereby significantly increasing the visibility of the interference pattern. The use of a continuous wave pump laser provided the symmetry between the spectral shapes of the signal and idler photons concerning half the pump frequency, despite different photon colours. We demonstrate that such an interferometer overcomes the classical phase sensitivity limit for wide parametric gain ranges, when up to 3×104 photons are generated.
Keywords: Physics and Astronomy (miscellaneous); General Mathematics; Chemistry (miscellaneous); Computer Science (miscellaneous)

Flexible source of correlated photons based on LNOI rib waveguides - Ebers, Lena; Ferreri, Alessandro; Hammer, Manfred; Albert, Maximilian; Meier, Cedrik; Förstner, Jens; Sharapova, Polina R. (Journal of Physics: Photonics)
Lithium niobate on insulator (LNOI) has a great potential for photonic integrated circuits, providing substantial versatility in design of various integrated components. To properly use these components in the implementation of different quantum protocols, photons with different properties are required. In this paper, we theoretically demonstrate a flexible source of correlated photons built on the LNOI waveguide of a special geometry. This source is based on the parametric down-conversion (PDC) process, in which the signal and idler photons are generated at the telecom wavelength and have different spatial profiles and polarizations, but the same group velocities. Distinguishability in polarizations and spatial profiles facilitates the routing and manipulating individual photons, while the equality of their group velocities leads to the absence of temporal walk-off between photons. We show how the spectral properties of the generated photons and the number of their frequency modes can be controlled depending on the pump characteristics and the waveguide length. Finally, we discuss special regimes, in which narrowband light with strong frequency correlations and polarization-entangled Bell states are generated at the telecom wavelength.
Keywords: tet_topic_waveguide

Excitation of an electronic band structure by a single-photon Fock state - Rose, H.; Vasil'ev, A.N.; Tikhonova, O.V.; Meier, Torsten; Sharapova, Polina R.
In this report, we consider a semiconductor nanostructure in an optical cavity that is coupled to quantum light. We describe the semiconductor nanostructure with a parabolic band structure in a 1D k-space, while we assume a single-mode quantum field. The 1D system is chosen for simplicity in both the analytical and the numerical treatment and paves the way for the description of 2D structures in the future. Therefore, instead of using parameters which are realistic for 1D systems, we rather use parameters which qualitatively correspond to 2D GaAs structures.