Summary form only given. Recent advances in the design of broadband parametric down-conversion (PDC) sources have opened the possibility to attain a regime of high squeezing previously unacessible in the pulsed domain [1]. However, characterising a PDC source is a challenging task when multiple spectral modes are being squeezed simultaneously and one wants to determine the number of squeezers and their relative strengths. Moreover, as one approaches the high squeezing regime, a number of nonlinear effects that are not usually considered when the source is operated at low pump power become relevant [2, 3].Here we present a technique to perform a complete and self-referenced characterisation of a broadband PDC source using only classical measurements. Often, PDC sources are described by their joint spectral amplitude, which conveys the frequency correlations between the generated photons. Our method complements the information contained in the joint spectrum with a measurement of a second-order process that to our knowledge has not been directly measured until now. Generally, a PDC process can be described as a Bogoliuvov transformation of the bosonic operators of the formaouts (ω) = f dω'Us,s(ω,ω') ains + f dω''Us,i(ω,ω'')(ain i (ω''))† for the signal and analogously for the idler mode. In our work we show that these transfer functions, Us,s(i,i) and Us,i(i,s), can be measured in the stimulated regime [4,5], by scanning the wavelength of a narrowband seed laser and performing a frequency resolved intensity measurement of the generated light.
Summary form only given. Recent advances in the design of broadband parametric down-conversion (PDC) sources have opened the possibility to attain a regime of high squeezing previously unacessible in the pulsed domain [1]. However, characterising a PDC source is a challenging task when multiple spectral modes are being squeezed simultaneously and one wants to determine the number of squeezers and their relative strengths. Moreover, as one approaches the high squeezing regime, a number of nonlinear effects that are not usually considered when the source is operated at low pump power become relevant [2, 3].Here we present a technique to perform a complete and self-referenced characterisation of a broadband PDC source using only classical measurements. Often, PDC sources are described by their joint spectral amplitude, which conveys the frequency correlations between the generated photons. Our method complements the information contained in the joint spectrum with a measurement of a second-order process that to our knowledge has not been directly measured until now. Generally, a PDC process can be described as a Bogoliuvov transformation of the bosonic operators of the formaouts (ω) = f dω'Us,s(ω,ω') ains + f dω''Us,i(ω,ω'')(ain i (ω''))† for the signal and analogously for the idler mode. In our work we show that these transfer functions, Us,s(i,i) and Us,i(i,s), can be measured in the stimulated regime [4,5], by scanning the wavelength of a narrowband seed laser and performing a frequency resolved intensity measurement of the generated light.
Reliable verification of squeezed-light sources is essential for photonic quantum technologies. High-dimensional quantum optical networks demand single-mode, pure squeezed states which, in principle, can be generated through careful engineering of parametric down-conversion-based (PDC) sources. However, due to the imperfections of optical components, the generated state is never pure and commonly contains internal mode structure. Existing characterisation techniques, based on either joint spectral intensity or normalized second-order correlation functions, work under the assumption that the probed state is pure, and therefore can result in incomplete or misleading assessment of the source quality. Here, we develop a device-agnostic characterisation framework for PDC-based sources with distinguishable signal and idler fields. Treating the source as a black box producing a mixed multimode Gaussian state, we find a lower bound for the state purity, which can be experimentally determined via mode-unresolved measurements. Our approach enables a holistic assessment of realistic squeezed-light source quality without requiring a detailed model of the nonlinear device and its surrounding optical network, providing practical benchmarks for optimizing sources for state-of-the-art quantum 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 , ], 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.
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.
Squeezed light is expected to enable new quantum metrology and quantum computation applications, but the very high degree of experimental control required in practice places severe demands on the physical devices used to generate it. As ultrafast squeezed light sources are reaching an unprecedented degree of brightness and modal control, there is a strong interest in developing methods for their experimental characterization and theoretical understanding. In this thesis, we demonstrate both a new application and a new characterization technique for pulsed squeezed light. In the first part of the thesis, we present a new metrological application of pulsed squeezed light: quantum-enhanced label-free nonlinear microscopy. Stimulated emission microscopy (SEM) is a state-of-the-art pump-probe microscopy technique whose sensitivity is ultimately limited by shot noise in the probe beam. We propose to overcome this fundamental limitation by using a sub-Poissonian probe generated via optical parametric amplification. We demonstrate an intensity-squeezed sub-picosecond pulsed probe, and a simple stimulated emission microscope. Using this squeezed probe, sub-Poissonian statistics are observed in the SEM signal. After this proof-of-principle experiment, we aim to provide an improved design for a source of intensity-squeezed light. First, we develop a theoretical framework to simulate the photon statistics of a general sub-Poissonian source, considering pulsed and focused pump and seed fields in a unified spatio-temporal description. Next, we use this framework to suggest possible improvements to our previous squeezed probe. In the second part of this thesis, we provide new theoretical and experimental tools to analyze the high gain regime of pulsed spontaneous parametric down-conversion (SPDC). We study a waveguided source capable of generating twin-beams with tens of photons in a single spatio-temporal mode. We develop a framework to efficiently simulate SPDC for an arbitrary nonlinear gain, including the effect of parasitic nonlinearities such as self-phase modulation (SPM) of the pump and cross-phase modulation (XPM) between pump and twin-beams. We experimentally characterize our source using a new technique based on stimulated difference-frequency generation (DFG). In a type-II down-conversion process, we measure the frequency generation produced not only in the orthogonal polarization to the seeding beam, but also in its same polarization, which we interpret as cascaded difference-frequency generation. We argue that the additional information obtained in this measurement allows for a self-referenced estimation of the squeezing gain. Using these measurements, we accurately fit our theoretical model, revealing that, in the high gain regime, parasitic nonlinearities strongly affect the spectral structure of the twin-beams. We propose a simple strategy to reduce the impact of these nonlinearities on the modal structure of SPDC.
Parametric down-conversion (PDC) is the established standard for the practical generation of a multiplicity of quantum optical states. These include two-mode squeezed vacuum, heralded non-Gaussian states and entangled photon pairs. Detailed theoretical studies provide insight into the time-frequency (TF) structure of PDC, which are governed by the complex-valued joint spectral amplitude (JSA) function. However in experiments, the TF structure of PDC is mostly characterised by intensity measurementsthat forbid access to the important phase of the JSA. In this paper, we present an amplitude-sensitive quantum process tomography technique that combines methods from ultrafast optics and classical three-wave mixing. Our approach facilitates a direct and phase-sensitive time-frequency tomography of PDC with high spectral resolution and excellent signal-to-noise ratio. This is important for all quantum optical applications, which rely on engineered parametric processes and base on minute knowledge of the quantum wave-function for the generation of tailored photonic quantum states.
We study theoretically how high-gain effects affect the measurement outcome of visible signal spectra in undetected photon measurement schemes. We consider two interferometric configurations: firstly, the SU(1,1) interferometer where the idler incurs loss and additional dispersion in between two identical, lossless, squeezers; secondly, the induced coherence interferometer where the idler incurs loss and additional dispersion in between two identical, lossless, squeezers and where the second squeezer is seeded by the idler and a vacuum ancilla mode. Furthermore, we consider a distributed loss configuration where the idler incurs loss as it propagates in the nonlinear medium. Motivated by experimental evidence and due to the fact that broadband sources are ideal for these measurement schemes, we use the dispersive data of a third-order dispersion engineered integrated waveguide parametric down conversion (PDC) source presented in New Journal of Physics 26, 123025 (2024) to model the PDC spectra in the three configurations. For each configuration we consider the case of idler-only (i) absorption, (ii) additional dispersion, and (iii) the combined effects. We obtain results which outline the strength and weaknesses of the different configurations at different operation points.