Observation of a Multimode Displaced Squeezed State in High-Harmonic Generation

High harmonic generation is a resource of extremely broad frequency combs of ultrashort light pulses. The non-classical nature of this new quantum source has been recently evidenced in semiconductors by showing that high harmonic generation generates multimode squeezed states of light. Applications in quantum information science require the knowledge of the mode structure of the created states, defining how the quantum properties distribute over the spectral modes. To achieve that, an effective Schmidt decomposition of the reduced photonic state is performed on a tripartite harmonic set by simultaneously measuring the second- and third-order intensity correlation function. The Schmidt number is estimated which indicates an almost single-mode structure for each harmonic, a useful resource in quantum technology. By modelling our data with a displaced squeezed state, we retrieve the dependencies of the measured correlation as a function of the high harmonic driving laser intensity. The effective high-harmonic mode distribution is retrieved, and the strength of the contributing squeezing modes is estimated. Additionally, we demonstrate a significant violation of a Cauchy-Schwarz-type inequality for three biseparable partitions by multiple standard deviations. Our results confirm non-classicality of the high-harmonic generation process in semiconductors. The source operates at room temperature with compact lasers, and it could become a useful resource for future applications in quantum technologies.