Preparation of nonclassical light with special quantum properties is essential for quantum technologies. High-harmonic generation (HHG) is a process which not only enables the creation of attosecond pulses but also has the potential to generate light with intricate quantum properties. In a recent experiment [PRX Quantum 5. 040319], nonclassical inter-harmonic correlations have been measured from a HHG source between low-order harmonics. In this work, we theoretically investigate entanglement between different harmonics within an effective, phenomenological quantum optical model. This model implements a significant degree of simplification regarding the processes within the target material, treating the material through susceptibilities, as it is usual in quantum optics. Such an approach yields a general description of HHG in the few-harmonic generation regime, permitting the implications that can be derived within it to hold broadly within the domain of validity. We find that entanglement is produced as a result of the often neglected back-action. We can qualitatively reproduce experimentally measured nonclassicalities, which suggests that intermodal entanglement can, to an extent, be considered a universal phenomenon associated with HHG, rather than a result of using specific material targets.
Preparation of nonclassical light with special quantum properties is essential for quantum technologies. High-harmonic generation (HHG) is a process which not only enables the creation of attosecond pulses but also has the potential to generate light with intricate quantum properties. In a recent experiment [PRX Quantum 5. 040319], nonclassical inter-harmonic correlations have been measured from a HHG source between low-order harmonics. In this work, we theoretically investigate entanglement between different harmonics within an effective, phenomenological quantum optical model. This model implements a significant degree of simplification regarding the processes within the target material, treating the material through susceptibilities, as it is usual in quantum optics. Such an approach yields a general description of HHG in the few-harmonic generation regime, permitting the implications that can be derived within it to hold broadly within the domain of validity. We find that entanglement is produced as a result of the often neglected back-action. We can qualitatively reproduce experimentally measured nonclassicalities, which suggests that intermodal entanglement can, to an extent, be considered a universal phenomenon associated with HHG, rather than a result of using specific material targets.
High-order harmonic generation (HHG) is a significant nonlinear phenomenon triggered by the interaction of intense laser fields with matter. As a high-quality coherent light source, it has found extensive applications in areas such as attosecond pulse generation and ultrafast spectroscopy. Recent studies have revealed the prevalent existence of nonclassical effects in high-harmonic radiation, including nonclassical photon statistics, intermodal correlations, and entanglement. It holds broad development prospects in directions including the generation of nonclassical states with high photon numbers, precise control of entanglement in solid-state systems, and integration with cavity quantum electrodynamics. This review systematically summarizes the research progress concerning the nonclassical effects in HHG. It begins with an overview of the semiclassical model and strong-field quantum theory, clarifying the differences in the quantum properties of harmonic fields when driven by coherent states versus nonclassical states. Subsequently, it focuses on various physical schemes for generating nonclassical optical field states, such as optical cat states and squeezed states, via this process. Research on strong-field HHG not only deepens our understanding of the fundamental nature of intense laser physics but also opens new avenues for the generation and application of quantum light sources in the extreme ultraviolet to X-ray spectral regions.
We present a study of photon statistics associated with high-order harmonic generation (HHG) involving one-mode and intermodal correlations of the high harmonic photons. The aim of the paper is to give insight into the nonclassical properties of high-order harmonic modes. To this end, we use a simplified model describing an elementary quantum emitter: the model of a two-level atom. While the material system is extremely simplified in this description, the conclusions and the methods may be generalized for more complex cases. Our primary interest is an effective model of HHG in which the exciting pulse is classical and the harmonics are quantized, although we touch upon the more generalized, fully quantized model as well. Evolution of the Mandel parameter, photon antibunching, squeezing, and cross correlations are calculated. Results imply that with respect to a single quantized emitter, nonclassicality of the harmonics is present: sub-Poissonian photon statistic and squeezing can characterize certain optical modes, while strong anticorrelation can also be present.
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) is conventionally understood to produce attosecond pulse trains only when the emitted harmonics are mutually phase-locked, in accordance with the classical theory of mode-locking. Such locking is necessary for pulse synthesis when the harmonic field is in a separable multimode quantum state. This requirement, however, can be circumvented entirely for harmonic combs exhibiting intermodal entanglement. We introduce a novel family of multimode quantum states, termed attoquants: states associated with highly structured pulse trains that are inherently insensitive to relative phases. As a concrete example, we analyse the coherent permanent state, constructed as a completely symmetric superposition of products of coherent states over all permutations of a fixed parameter set. It is shown analytically that its electric-field expectation value is a locked Fourier superposition of the driving-field harmonics, yielding an attosecond pulse train without requiring mode-locking. We further calculate the photon statistics, the Wigner function, and the logarithmic negativity of this state, confirming it to be genuinely nonclassical and entangled. Finally, we offer a phenomenological interpretation for the generation of such entangled states during HHG, as a consequence of multi-atom effects. Since the coherence volume of the driving field greatly exceeds that of its harmonics, a collectively-driven cluster of atoms can radiate the individual harmonics as spatially resolved, but fundamentally indistinguishable sources. This can generate the permutation-symmetric entanglement structure of an attoquant.
Effects of extreme nonlinear optics, such as high harmonic generation (HHG), are conventionally modeled with classical electromagnetic fields: both the driving and emitted fields are treated classically. We present the fully quantum electrodynamical theory of extreme nonlinear optics and use it to predict new quantum effects in HHG. The quantum description shows new effects in both the spectral and statistical properties of HHG. We also describe how the HHG process changes in the single-atom regime and discuss experiments that can test our various predictions. Revealing the quantum-optical nature of HHG could lead to novel sources of attosecond light having intrinsically quantum statistics, such as squeezing and entanglement.
Quantum high-harmonic generation (HHG) is a prominent and growing field of research with potential capabilities of providing high photon-number entangled states of light. However, there is an open debate regarding the theory level required for correctly describing the quantum aspects of HHG, such as squeezing or entanglement. Previous approaches either semi-classically sampled the quantum electromagnetic field distribution, or employed perturbation theory utilizing the semi-classical simulations as a starting point. Both of these schemes miss out key quantum-optical features as self-consistent numerical simulations of the electron-photon wavefunction are not performed at any stage. In this Letter, we develop a full quantum theory for multipartite entanglement in HHG, solving exactly the light-matter interaction Hamiltonian in a given Hilbert space, and employ it for evaluating the quantum correlations of emitted photons. We show that HHG entanglement oscillates with the driving laser power and exhibits multiple local maxima, which allows fine-tuning HHG entanglement. Such features arise for both above-threshold harmonics and between above- and below-threshold harmonics. By analyzing different types of atomic targets, we find that the long-range behavior of driven electrons can qualitatively change the resulting entanglement, potentially leading to non-universal behavior across systems. Lastly, we show that focal averaging over classical degrees of freedom in fact plays a key role in entanglement measures and can change the qualitative behavior of observables. Our work establishes the state-of-the art in exploring entanglement features in HHG, and paves way for analysis and engineering of entangled multi-photon states in the XUV and ultrafast regime for more complex matter systems.