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Physical review. B./Physical review. B

Sensing quantum fluctuations via forbidden harmonics in quantum materials

Anonymous, Gopal Dixit

Published Aug 17, 2026• 0 citations
Publisher

Abstract

High-harmonic generation in solids provides a powerful window into light-driven electron dynamics on attosecond timescales, yet the role of quantum fluctuations of the driving field remains largely unexplored. Here, we show that the quantum state of light offers a nonclassical degree of freedom for controlling strong-field dynamics in quantum materials. Using graphene driven by bicircular quantum light composed of counterrotating ω and 2 ω components, we theoretically predict that squeezing-induced fluctuations break the dynamical symmetry of the classical bicircular field and activate otherwise forbidden harmonics. By analyzing the helicity-resolved harmonic spectra, we uncover robust polarization signatures uniquely dictated by the squeezed mode's profile, including a relative-phase-controlled helicity switching in the lowest orders. Crucially, second-order intensity correlations reveal that these forbidden harmonics exhibit strongly enhanced, super-Poissonian photon-number fluctuations, confirming that they inherit and directly transduce the nonclassical statistics of the squeezed driving vacuum. Our findings establish forbidden harmonics as high-fidelity optical probes of the quantum state of light and provide additional opportunities at the intersection of quantum optics, strong-field physics, and lightwave engineering in quantum materials.

DOI
10.1103/v886-ypf7

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High-harmonic generation in solids provides a powerful window into light-driven electron dynamics on attosecond timescales, yet the role of quantum fluctuations of the driving field remains largely unexplored. Here, we show that the quantum state of light offers a nonclassical degree of freedom for controlling strong-field dynamics in quantum materials. Using graphene driven by bicircular quantum light composed of counterrotating ω and 2 ω components, we theoretically predict that squeezing-induced fluctuations break the dynamical symmetry of the classical bicircular field and activate otherwise forbidden harmonics. By analyzing the helicity-resolved harmonic spectra, we uncover robust polarization signatures uniquely dictated by the squeezed mode's profile, including a relative-phase-controlled helicity switching in the lowest orders. Crucially, second-order intensity correlations reveal that these forbidden harmonics exhibit strongly enhanced, super-Poissonian photon-number fluctuations, confirming that they inherit and directly transduce the nonclassical statistics of the squeezed driving vacuum. Our findings establish forbidden harmonics as high-fidelity optical probes of the quantum state of light and provide additional opportunities at the intersection of quantum optics, strong-field physics, and lightwave engineering in quantum materials.
Symmetries are ubiquitous in physics and play a pivotal role in light-matter interactions, where they determine the selection rules governing allowed atomic transitions and define the associated conserved quantities. For the up-conversion process of high harmonic generation, the symmetries of the driving field determine the allowed frequencies and the polarization properties of the resulting harmonics. As a consequence, it is possible to establish classical selection rules when the process is driven by coherent radiation. In this work, we show that fluctuation-induced symmetry breaking in the driving field leads to the appearance of otherwise forbidden harmonics. This is achieved by considering bicircular quantum light, and demonstrate that the enhanced quantum fluctuations due to squeezing in the driving field break the classical selection rules. To this end, we develop a quantum optical description of the dynamical symmetries in the process of high harmonic generation, revealing corrections to the classical selection rules. Moreover, we show that the new harmonics show squeezing-like signatures in their photon statistics, allowing them to be clearly distinguished from classical thermal fluctuations.
High-harmonic generation (HHG) driven by intense quantum light has recently emerged as a new frontier in strong-field physics. Yet, the mechanism underlying HHG with nonclassical fields such as bright squeezed vacuum (BSV) light—characterized by a vanishing mean electric field—remains elusive. In this work, we develop a fully quantum theory for HHG under arbitrary quantum driving fields. We show that the fluctuation component of the dipole correlation operator plays a central role in HHG with quantum light and is essential for BSV-driven HHG. Furthermore, our framework reveals the photon statistics distribution within individual harmonics and across different harmonics, demonstrating that the statistics inherit the statistical properties of the driving field. This theory overcomes key limitations of existing approaches and uncovers new quantum features of HHG in the presence of nonclassical light.
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.
The atomic response to an ultra-intense driving field produces a characteristic high-harmonic spectrum featuring a rapid drop in intensity for the lower harmonics, followed by a plateau and a sharp cutoff. This response vanishes for circularly polarized classical drivers -- a limitation that can be overcome by introducing quantum features into the driving field. In this work, we show that squeezed highly elliptically polarized drivers not only enable the high-harmonic generation (HHG) process in classically forbidden regimes of large ellipticity, but also yield highly elliptical harmonic radiation with pronounced super-Poissonian photon statistics. Moreover, we show that the HHG spectral features encode information about the quantum nature of the driving field, revealing the presence of its squeezed field fluctuations. By analyzing the HHG spectral intensity dependence as a function of the driver's ellipticity and squeezing orientation, we identify a means to probe the driving field's quantum properties that intrinsically lie in the high-photon number regime.
High harmonic generation (HHG) is a highly nonlinear optical process in which radiation from a strong driving field is up-converted into its high-order harmonics. In atomic systems, this nonlinearity manifests itself through the intensity scaling of the emitted harmonics with the driving field strength. Despite the highly nonlinear nature of HHG, when the driving field is prepared in a classical Gaussian state and atomic depletion remains negligible, the quantum statistical properties of the generated harmonics retains classical Gaussian quantum statistics. Driving HHG with bright squeezed vacuum (BSV) light challenges this paradigm, as its enhanced field fluctuations can modify the statistical properties of the generated harmonics. In this work, we investigate the conditions under which BSV-driven HHG gives rise to non-classical Gaussian states, and identify the regimes where this Gaussian description breaks down. For bichromatic driving by a strong coherent field at frequency ωωω and a perturbative BSV field at 2ω2ω2ω, the even-harmonic response is approximately linear in the BSV quadrature, leading to non-classical multimode Gaussian entanglement in the harmonic field. We show that this state can be described as a distributed collective squeezed mode over the even-harmonic manifold, and characterize its covariance matrix, entanglement structure, and quantum teleportation fidelity as an operational benchmark. Our results highlight the potential of non-classically driven HHG as a platform for engineering Gaussian and non-Gaussian states of light in the extreme ultraviolet regime.
Recently, the intersection of quantum optics and attosecond physics has attracted growing interest. Here, we study the quantum optical signatures of high-harmonic generation (HHG) from solid-state material driven by squeezed coherent states. We find that squeezed coherent states can either enhance or suppress the HHG yields compared to that driven by coherent light, depending on the photon bunching or antibunching characteristics of driving light. The analysis on semiclassical trajectories indicates that the amplitude fluctuation alters the recombination energy, while the phase fluctuation affects the birth and recombination time of electron-hole pairs. By calculating the Husimi Q distributions of HHG, we demonstrate that the squeezing of the two conjugate quadratures of driving light asymmetrically influence the squeezing phase of harmonics. Surprisingly, we find that even under coherent driving, the harmonics still exhibit squeezing due to the highly nonlinear response of solid-state HHG, which was overlooked previously. Numerical calculations of the Mandel parameter are performed to characterize the photon statistics of emitted HHG arising from different microscopic mechanisms. The results indicate that intraband radiation can exhibit a super-Poissonian distribution, while interband emission exhibits sub-Poissonian distribution under coherent driving.