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 , ], 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.
Nonlinear interferometers are promising tools for quantum metrology, as they are characterized by an improved phase sensitivity scaling compared to linear interferometers operating with classical light. However, the multimodeness of the light generated in these interferometers results in the destruction of their phase sensitivity, requiring advanced interferometric configurations for multimode light. Moreover, in contrast to the single-mode case, time-ordering effects play an important role for the high-gain regime in the multimode scenario and must be taken into account for a correct estimation of the phase sensitivity. In this paper, we present a theoretical description of spatially multimode SU(1,1) interferometers operating at low and high parametric gains. Our approach is based on a step-by-step solution of a system of integro-differential equations for each nonlinear interaction region. We focus on interferometers with diffraction compensation, where focusing elements such as a parabolic mirror are used to compensate for the divergence of the light. We investigate plane-wave and Gaussian pumping and show that for any parametric gain, there exists a region of phases for which the phase sensitivity surpasses the standard shot-noise scaling and discuss the regimes where it approaches the Heisenberg scale. Finally, we arrive at insightful analytical expressions for the phase sensitivity that are valid for both low and high parametric gain and demonstrate how it depends on the number of spatial modes of the system.
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, and in the best case, deal with a single mode at a time. Here, we demonstrate experimentally how the squeezing can be measured in multiple spatial modes simultaneously, using optical parametric amplification and direct detection followed by modal decomposition based on spatial intensity correlations. We apply this method to a multimode squeezed vacuum generated via high-gain parametric down-conversion. We measure the degrees of squeezing and anti-squeezing for eight strongest spatial modes, obtaining highest squeezing and anti-squeezing values of −5.2±0.2 dB and 8.6±0.3 dB, respectively.
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.
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.
Nowadays, the realization of quantum computations and communications based on continuous variables has attracted a significant attention due to a substantial expansion of the system dimensionality. The main progress in this area is attributed to the implementation of multimode systems based on squeezed states of light. One of the simplest ways to generate such states relies upon their producing in a single-pass optical parametric amplifier (OPA) using ultrafast pumping. However, for homodyne detection of such multimode states, the profile of the local oscillator (LO) must perfectly match the profile of the measured mode. Usually, this is not the case; therefore a proper treatment of multimode squeezing is required. In this work, we study both theoretically and experimentally the multimode squeezed light generated in type-0 and type-II OPA. We characterize such sources and investigate the degree of squeezing in dependence on the LO spectral profile, employing a pulse shaping technique. The theoretical analysis is performed using the Schmidt-mode theory. This work might have a significant impact on the realization of multimode quantum protocols