Elettra | Q4Q Laboratory Turning noise into insight: Ultrafast pump-probe phase-randomized tomography It may sound counterintuitive, but sometimes noise can actually improve a measurement. In the quantum world, noise is not just a disturbance, it also carries valuable statistical information about a system’s behavior. Our team has developed a technique called ultrafast pump-probe phase-randomized tomography, which harnesses the intrinsic randomness of light to track quantum fluctuations in materials at ultrafast timescales. This approach provides a new way to explore quantum materials in non-equilibrium states, revealing statistical properties that traditional methods might overlook. While common spectroscopic techniques treat light as a classical wave, this work combines quantum optical tomography with ultrafast pumpprobe spectroscopy and leverages the statistical properties of light to study fluctuations in light-driven materials. Ultrafast photoexcitation has recently emerged as a powerful means to control and induce new coherent phenomena, such as light-induced superconductivity, light-induced ferroelectricity and vibrational light-induced transparency, which are otherwise not accessible under thermodynamic equilibrium. In our experimental scheme, strong classical pump pulses generate the non-equilibrium state, while weak, few-photon probe pulses measure the response of the sample. The quantum properties of light emerge especially in the weak intensity regime, where the quantized nature of photons comes into play. By accessing light-matter interactions in the quantum regime, we can reveal the intrinsic quantum fluctuations of the sample, which are imprinted onto the statistical properties of the probe (Fig. 1 a). Quantum optical tomography is a widely explored method to study the quantum state of light, but it is difficult to adapt to non-equilibrium optical spectroscopies of materials. It relies on delicate and slow phase-resolved measurements of the interference obtained by mixing the quantum probe with a classical reference beam. Leveraging the intrinsic randomness of the Carrier-EnvelopePhase (CEP) of ultrashort laser pulses, we devise an ideal phase-randomized tomography protocol, which overcomes the limitations due to interferometer instabilities and enables a fast and robust reconstruction of the statistical distribution of phase-averaged optical observables, such as the photon number. This novel phase-randomized scheme allows us to reliably detect small pumpinduced changes in the full photon number distribution as a function of the time delay between pump and probe. In Fig. 1 (b), we benchmark the method studying the interaction of photons with a coherent phonon excitation in α-quartz. The equilibrium photon number distribution of the transmitted probe is well fitted by the Poissonian statistics, typical of a coherent optical state. As a result of the optical excitation, the initial distribution is modulated as a function of time following the phonon oscillations. In Fig. 1 (c), we detail how both the mean-value and variance of the transmitted probe light are phonondependent, demonstrating the capability to measure non-equilibrium changes in the photon number statistics with ultrafast resolution. To understand whether the variance of the photon number carries valuable insight about the phonon properties, we model the light-phonon interaction using a Raman Hamiltonian and calculate the expected optical response for different phonon states (coherent, thermal, squeezed). As illustrated in Fig. 1 (d), the variance of the phonon displacement shows different noise levels and periodicities, peculiar to each phonon state, which are mapped in the optical degrees of freedom by the photon-phonon interaction. This shows theoretically that the material fluctuations imprint distinctive signatures in the optical statistics. The comparison between model and experiment sets a bound on the amount of squeezing or thermal excitations present in the system. We characterize the probe photon distributions in terms of the Mandel parameter Q, which quantifies the deviations from the standard Poissonian statistics of a coherent laser state (i.e. deviations of the photon number variance from its expectation value). For instance, negative values of Q are indicative of a purely quantum state, exhibiting fluctuations below the vacuum level. Experimentally, we observe a small super Poissonian character (Q >0), which is due to the classical experimental noise. If we correct the Mandel parameter considering the excess noise which affects the detection response, our results are compatible with Poissonian statistics, which validates the coherent phonon description for the vibrational excitation in transparent quartz. In conclusion, the technique provides an optimal scheme to perform the reconstruction of optical phaseaveraged observables (i.e. photon number) with ultrafast resolution. The application to pump-probe experiments opens a new way to reveal the ultrafast dynamics of fluctuations in nonequilibrium light-induced states in complex quantum materials. Going beyond a mean-value description is key to measure the microscopic statistical properties which can be indicative of competing phases or quantum phenomena, like squeezing and entanglement, which rule, for instance, unconventional superconductors or quantum spin liquids. The capability to access the statistical degrees of freedom of matter on the femtosecond timescale via light-matter interaction will be useful both for the spectroscopy of the quantum properties of materials and to explore new routes to manipulate and characterize light pulses in quantum optics. Elettra Highlights 2024–2025 80
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