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arXiv:1012.0262 · New Journal of Physics

Probing multimode squeezing with correlation functions

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

Published Mar 18, 2011• 283 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/13/3/033027

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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.
Multimode squeezed light is a key resource for high-dimensional quantum technologies, enhancing metrological sensitivity, boosting communication security, and enabling parallel processing in computation. Its practical potential, however, remains constrained by the inherent single-mode operation of homodyne detection, necessitating post-processing for multimode characterization. Here, we overcome this long-standing challenge by employing multimode optical parametric amplification, enabling loss-tolerant direct detection of squeezing in each mode, which in turn permits mode sorting after amplification. As a result, we demonstrate, for the first time to the best of our knowledge, the real-time monitoring of multimode squeezing. With a spatial light modulator sorting the modes, we simultaneously measure squeezing in nine spatial modes co-propagating within one beam. Although mode sorting and filtering reduce the detection efficiency to less than 0.3%, we observe high-purity squeezing of up to - 7.9 ± 0.6 dB - to the best of our knowledge, the highest squeezing recorded for pulsed light. Furthermore, we demonstrate real-time, loss-tolerant characterization of continuous-variable entanglement and extend it to the detection of cluster states. Similar methods can be applied in the frequency domain, facilitating a crucial capability for scalable quantum technologies.
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
Wigner function tomography is indispensable for characterizing quantum states, but its commonly used version, balanced homodyne detection, suffers from several weaknesses. First, it requires efficient detection, which is critical for measuring fragile non-Gaussian states, especially bright ones. Second, it needs a local oscillator, tailored to match the spatiotemporal properties of the state under test, and fails for multimode and broadband states. Here we propose Wigner function tomography based on optical parametric amplification followed by direct detection. The method is immune to detection inefficiency and loss, and suitable for broadband, spatially and temporally multimode quantum states. To prove the principle, we experimentally reconstruct the Wigner function of squeezed vacuum occupying a single mode of a strongly multimode state. We obtain a squeezing of −7.5±0.4dB and purity of 0.91 −0.08 +0.09 despite more than 97% loss caused mainly by filtering. Theoretically, we also consider the reconstruction of a squeezed single photon—a bright non-Gaussian state. Due to multimode parametric amplification, the method allows for simultaneous tomography of multiple modes. This makes it a powerful tool for optical quantum information processing.
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±0.2-5.2 \pm 0.2−5.2±0.2 dB and 8.6±0.38.6 \pm 0.38.6±0.3 dB, respectively.
Multimode entangled states of light are key resources for high-dimensional photonic quantum technologies, particularly for continuous-variable quantum computing and quantum information processing. Exploiting their full capabilities requires detection strategies that can efficiently and simultaneously access a large number of modes and their quantum correlations. Multimode optical parametric amplification (MOPA) provides a promising approach by amplifying multiple quadratures prior to detection, rendering the measurement robust against subsequent optical losses while enabling broadband operation. Here, we demonstrate the spectral multimode capability of MOPA by simultaneously characterizing a broadband 60-node dual-rail continuous-variable cluster state. We reconstruct the cluster-state nullifiers across the spectral modes and observe nearly uniform squeezing ranging from -7.2 to -6.5 dB. Furthermore, by evaluating the van Loock-Furusawa criterion across all relevant bipartitions, we verify genuine multipartite entanglement throughout the 60-node state. These results establish MOPA as a promising platform for scalable high-dimensional quantum information processing in the spectral domain.