Photon Anti-Bunching and Quantum Non-Gaussianity from High-Harmonic Generation

TL;DR

The paper addresses whether high-harmonic generation in semiconductors can produce non-classical states of light suitable as quantum optical resources. The authors perform photon-counting measurements of harmonics H11, H12, H13 with a Hanbury-BrownTwiss setup to extract $g^{(2)}$ and use a non-classicality witness $W_{NC}$ and a quantum non-Gaussian (QNG) witness. They perform inter-order heralding (e.g., H(12|11)) to engineer heralded states, observe anti-bunching with $g^{(2)}_{h} < 1$, and certify QNG for certain herald configurations. A constrained numerical model based on a generalized two-mode Gaussian state, including beamsplitters, squeezing, and displacement, reproduces the data and reveals entanglement (nonzero $E_N$) between harmonics, suggesting SHHG as a scalable source of quantum resources.

Abstract

Quantum technologies are powered by platforms to generate complex non-classical states of matter or light to realize applications. We investigate the non-classical properties of high-harmonic generation in semiconductors, an emerging photonic platform. Measuring the click statistics of three double-digit orders, we evaluate witness operators to certify the non-classicality of the generated states. We show that higher-order harmonics driven by a coherent laser are squeezed and entangled. The properties of the emission are well retrieved with an entangled Gaussian state model, obtained by numerical state optimization to multiple observables. Additionally, we perform inter-order heralded measurements to engineer the quantum state of the emission. The heralded states have distinct properties, showing anti-bunched photon statistics. Further, we witness the generation of a quantum non-Gaussian state, a resource highly relevant for quantum information. With this, we establish high-harmonic generation as a platform for generating quantum optical resources.

Figures (7)

• Figure 1: Schematic of the experimental setup and properties of the emitted radiation. (a) Ultrashort laser pulses in the infrared spectral range interact with the electrons inside a semiconductor crystal. During the interaction, higher-order harmonics are generated as a frequency comb. After selecting three orders with spectral filters, single-photon detection is performed to acquire the mean number of photons as well as the number of simultaneous photon detection events between the detectors. One detector is used as a herald, to condition the measurement of the other detectors on successful detection of a herald photon. (b) From the HHG spectrum three orders (H11, H12, H13) are selected for analysis. The intensity is shown in logarithmic scaling. The colored region indicates the spectral width of the employed filters. (c) Measured normalized intensity correlation function $g^{(2)}_{\mathrm{H}(i,j)}$ calculated from single- and coincidence events produced from photons of single harmonic order ($i =j$). At low mean photon numbers, photon bunching is observed.
• Figure 2: Non-Classicality Criteria. (a) The heralded intensity correlation function $g^{(2)}_{\mathrm{H}(i|j)}$ of the state is shown over the mean photon number of harmonic $i$. Single detection events on the herald harmonic $j$ are used to condition the detection of simultaneous events on the signal harmonic order $i$. The heralded states have distinct photon statistics, showing anti-bunching with $g_{\mathrm{h}}^{(2)} < 1$. (b) Based on the photon detection probabilities a non-classicality witness can be derived. For all harmonics (H11, H12, H13) $W_{\mathrm{NC}} > 0$ certifies that the unheralded, initial harmonic state cannot be expressed as a mixture of coherent states.
• Figure 3: Quantum non-Gaussian Witness. The witness violation strength $\Delta W = W(a) - W_{\mathrm{G}}(a)$ is plotted as a function of signal count rate for the initial (top) and heralded (bottom) states across over the mean photon number. Data points above the dashed zero line with $\Delta W > 0$ certify the quantum non-Gaussian nature of the measured states.
• Figure 4: Properties of the effective state. The modelled state is found by optimizing a generalized two-mode Gaussian state to the experimentally recorded non-classicality observables. We depict the properties of the reduced states. For $\mathrm{H}(i|j)$, the harmonic order $j$ takes the role of the herald, to conditionally create the heralded state in harmonic order $i$. The modelled states shows squeezing (a) and displacement, scaling with the mean photon number. The initial unheralded states $\mathrm{H}(i, j)$ are entangled as quantified by the non-zero logarithmic negativity c).
• Figure S1: Technical Drawing of the Setup. The driving laser intensity is controlled using a pair of polarizers (P). The driving laser beam is focused onto the sample (S) and the generated high-harmonic emission collimated using off-axis parabolic mirrors. The pump light is filtered using a pinhole and a spectral filter. Luminescence from the sample is suppressed using a broadband polarizer. Three harmonic orders are selected and separated spatially using dichroic mirrors (DM). The single-photon sensitive detectors (SPAD) are arrange in a Hanbury-Brown and Twiss like geometry. Spectral filters with a bandwidth of 10 nm are placed in front of each detector. Single counts and coincidence events are recorded with a time to digital converter.