Multimode squeezing: generation and characterization

Multimode squeezed light is an increasingly popular tool in photonic quantum technologies, including sensing, imaging, and computing [1]. In metrology, it provides the measurement of the phase beyond the classical sensitivity limit [2,3], its role was crucial for the first observation of gravitational waves [4]. At the same time, multiple squeezed modes are promising tools for continuous-variable quantum computing, quantum information processing and quantum communication, where each mode (qumode) serves as an information carrier and a large set of modes can be used for the cluster sates generation and measurement-based quantum computation [5]. With numerous applications of multimode squeezed light, it is important to characterize squeezing in multiple spatial and temporal modes taking into account internal losses in the system: When PDC is generated in transparent bulk nonlinear crystals the absorption is small enough to be neglected, however, internal losses can be significant for structured media like waveguides, where the guided light can be lost due to scattering from surface roughness. We investigate the mode structure of lossy broadband multimode squeezed light and show how the maximal possible squeezing can be extracted and measured. In opposite to an ideal multimode squeezed states, where the unique basis of Schmidt modes can be found via Bloch-Messiah reduction of Bogoliubov transformation [6], the broadband basis of Schmidt modes for lossy squeezed states cannot be uniquely defined. We introduce a new type of broadband basis for lossy systems in which the squeezing is maximized, i.e., the upper bound for squeezing is reached, and show how these modes can be constructed [7]. Furthermore, the existing experimental methods of multimode squeezed vacuum characterization (homodyne detection, projective filtering) are technically complicated, and in the best case, deal with a single mode at a time. We present a method [8] based on a cascaded system of nonlinear crystals to simultaneously measure squeezing in different spatial modes. In such a system, the second crystal serves as an amplifier/deamplifier for the squeezed light generated in the first crystal (squeezer). The direct intensity measurement of light after the amplifier allows us to reconstruct the squeezing of the light generated in the first crystal.
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