The interaction of intense light with matter gives rise to fascinating phenomena at the intersection of quantum optics and extreme nonlinear optics. High-harmonic generation (HHG) has attracted significant interest as a non-perturbative light-matter interaction process. Simultaneously, quantum optics explores the subtle interactions between light and matter at the level of individual quanta of light. Merging these two fields has led to the emergence of extreme nonlinear quantum optics, which challenges conventional assumptions about the quantum nature of light generated by nonlinear processes [1]–[3]. A recent experiment observed HHG from a solid driven by bright squeezed vacuum [2], but the created quantum state was not yet characterized. A central critical gap in the field remains measuring the quantum state of light generated by non-perturbative nonlinear processes, which requires a comprehensive sub-cycle quantum light tomography approach. It was so far unknown whether fragile quantum features like squeezing can survive in conditions of massive photon numbers and extreme nonlinearities.
The interaction of intense light with matter gives rise to fascinating phenomena at the intersection of quantum optics and extreme nonlinear optics. High-harmonic generation (HHG) has attracted significant interest as a non-perturbative light-matter interaction process. Simultaneously, quantum optics explores the subtle interactions between light and matter at the level of individual quanta of light. Merging these two fields has led to the emergence of extreme nonlinear quantum optics, which challenges conventional assumptions about the quantum nature of light generated by nonlinear processes [1]–[3]. A recent experiment observed HHG from a solid driven by bright squeezed vacuum [2], but the created quantum state was not yet characterized. A central critical gap in the field remains measuring the quantum state of light generated by non-perturbative nonlinear processes, which requires a comprehensive sub-cycle quantum light tomography approach. It was so far unknown whether fragile quantum features like squeezing can survive in conditions of massive photon numbers and extreme nonlinearities.
Abstract High-harmonic generation has been driving the development of attosecond science and sources. More recently, high-harmonic generation in solids has been adopted by other communities as a method to study material properties. However, so far high-harmonic generation has only been driven by classical light, despite theoretical proposals to do so with quantum states of light. Here we observe non-perturbative high-harmonic generation in solids driven by a macroscopic quantum state of light, a bright squeezed vacuum, which we generate in a single spatiotemporal mode. The process driven by a bright squeezed vacuum is considerably more efficient in the generation of high harmonics than classical light of the same mean intensity. Due to its broad photon-number distribution, covering states from 0 to 2 × 10 13 photons per pulse, and strong subcycle electric field fluctuations, a bright squeezed vacuum gives access to free carrier dynamics within a much broader range of peak intensities than accessible with classical light.
High harmonic generation (HHG) is an extremely nonlinear effect generating coherent broadband radiation and pulse durations reaching attosecond timescales. Conventional models of HHG that treat the driving and emitted fields classically are usually very successful but inherently cannot capture the quantum-optical nature of the process. Although prior work considered quantum HHG, it remains unknown in what conditions the spectral and statistical properties of the radiation depart considerably from the known phenomenology of HHG. The discovery of such conditions could lead to novel sources of attosecond light having squeezing and entanglement. Here, we present a fully-quantum theory of extreme nonlinear optics, predicting quantum effects that alter both the spectrum and photon statistics of HHG, thus departing from all previous approaches. We predict the emission of shifted frequency combs and identify spectral features arising from the breakdown of the dipole approximation for the emission. Our results show that each frequency component of HHG can be bunched and squeezed and that each emitted photon is a superposition of all frequencies in the spectrum, i.e., each photon is a comb. Our general approach is applicable to a wide range of nonlinear optical processes, paving the way towards novel quantum phenomena in extreme nonlinear optics.
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.
For decades, most research of high harmonic generation (HHG) considered matter as quantum but light as classical. Recently, HHG driven by quantum states of light such as bright squeezed vacuum was predicted to reach beyond the classical HHG cutoff. Moreover, in squeezed coherent illumination, it was shown that the underlying dynamics are significantly modified by the photon statistics effective force. Here we show that HHG driven by quantum light results in quantum high harmonics. We derive a formula for the quantum state of the high harmonics, when driven by arbitrary quantum light states, and then explore specific cases of experimental relevance. Specifically, for a moderately squeezed pump, HHG driven by squeezed coherent light results in squeezed high harmonics. Harmonic squeezing is optimized by syncing ionization times with the pump's squeezing phase. Beyond this regime, as pump squeezing is increased, the harmonics initially acquire squeezed thermal photon statistics, and then occupy an intricate quantum state which strongly depends on the semiclassical nonlinear response function of the interacting system. Our results pave the way for generation of squeezed extreme-ultraviolet ultrashort pulses, and more generally, quantum frequency conversion into previously inaccessible spectral ranges, which may enable ultrasensitive attosecond metrology. Published by the American Physical Society 2024
High-harmonic generation (HHG) has emerged as a pivotal process in strong-field physics, yielding extreme ultraviolet radiation and attosecond pulses for a wide range of applications. Furthermore, its emergent connection with the field of quantum optics has revealed its potential for generating nonclassical states of light. Here, we investigate the process of high-harmonic generation in semiconductors under a quantum optical perspective while using a Bloch-based solid-state description. Through the implementation of quantum operations based on the measurement of high-order harmonics, we demonstrate the generation of nonclassical light states similar to those found when driving atomic systems. These states are characterized using diverse quantum optical observables and quantum information measures, showing the influence of electron dynamics on their properties. Additionally, we analyze the dependence of their features on solid characteristics such as the dephasing time and crystal orientation, while also assessing their sensitivity to changes in driving field strength. This paper provides insights into HHG in semiconductors and its potential for generating nonclassical light sources.
Intense light-matter interaction largely relies on the use of high-power light sources, creating fields comparable to, or even stronger than, the field keeping the electrons bound in atoms. Under such conditions, the interaction induces highly nonlinear processes such as high harmonic generation, in which the low-frequency photons of a driving laser field are upconverted into higher-frequency photons. These processes have enabled numerous groundbreaking advances in atomic, molecular, and optical physics, and they form the foundation of attosecond science. Until recently, however, such processes were typically described using semi-classical approximations, since the quantum properties of the light field were not required to explain the observables. This has changed in the recent past. Ongoing theoretical and experimental advances show that fully quantized descriptions of intense light-matter interactions, which explicitly incorporate the quantum nature of the light field, open new avenues for both fundamental research and technological applications at the fully quantized level. These advances emerge from the convergence of quantum optics with strong-field physics and ultrafast science. Together, they have given rise to the field of quantum optics and quantum electrodynamics of strong-field processes.