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Research in Optical Sciences

Probing multimode squeezing with correlation functions

Andreas Christ, Kaisa Laiho, A. Eckstein, K. N. Cassemiro, Christine Silberhorn

Published Jan 1, 2012• 5 citations
Publisher

Abstract

We use broadband correlation functions to probe multimode squeezed states. Measuring the higher-order correlations enables loss independent access to the state characteristics which is less costly and time-consuming than standard tomographic methods.
DOI
10.1364/qim.2012.qt1b.4

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Broadband multimode squeezers constitute a powerful quantum resource with promising potential for different applications in quantum information technologies such as information coding in quantum communication networks or quantum simulations in higher-dimensional systems. However, the characterization of a large array of squeezers that coexist in a single spatial mode is challenging. In this paper, we address this problem and propose a straightforward method for determining the number of squeezers and their respective squeezing strengths by using broadband multimode correlation function measurements. These measurements employ the large detection windows of the state of the art avalanche photodiodes in order to simultaneously probe the full Hilbert space of the generated state, which enables us to benchmark the squeezed states. Moreover, due to the structure of correlation functions, our measurements are not affected by losses. This is a significant advantage, since detectors with low efficiencies are sufficient. Our approach is less costly than tomographic methods relying on multimode homodyne detection, which is based on much more demanding measurement and analysis tools and appear to be impractical for large Hilbert spaces.
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.
High-harmonic generation (HHG) is a prototypical strong-field process in which intense light drives matter to emit radiation at integer multiples of the driving frequency. Extending HHG into the quantum-optical regime offers new opportunities to probe and control strongly nonlinear light-matter interactions using nonclassical states of light. Yet describing this regime requires a fully quantum treatment of the correlated electron-photon dynamics, which becomes computationally challenging for broadband, strongly squeezed fields. Here we solve the quantum-electrodynamical dynamics of a two-level system driven by bright squeezed vacuum in a converged multimode Hilbert space. Both the driving field and emitted harmonics are fully quantized, with the light-matter interaction treated nonperturbatively. This enables direct access to the multimode quantum state and its higher-order correlations beyond semiclassical sampling or perturbative descriptions. We show that squeezed-vacuum driving produces harmonic emission with qualitatively distinct second- and third-order photon correlations compared with coherent excitation. Moreover, back-action from the driven emitter strongly reshapes the incident squeezed field, generating pronounced Wigner-function negativities that evolve on attosecond timescales. Our results establish a fully quantum framework for broadband strong-field dynamics with squeezed light and provide a route to predicting and interpreting quantum-HHG experiments and their extension to more complex emitters.