We investigate high harmonic generation (HHG) of an atom in the presence of squeezed vacuum of a single harmonic mode. Based on a fully quantum time-dependent Schrödinger equation, we derive an analytical formula for the harmonic amplitude. Our simulations of the HHG spectrum with this formula show that the harmonic amplitude of the corresponding squeezed mode can undergo significant changes with different parameters of the squeezed vacuum. Using the time-frequency analysis method, the physics underlying the effects of the vacuum quantum fluctuation (VQF) on the harmonic generation is revealed, which is found to be consistent with the explanation of Fermi's golden rule. Our work establishes a profound connection between harmonic generation and VQF, and may provide an unconventional approach to manipulating harmonic emission. Published by the American Physical Society 2024
We investigate high harmonic generation (HHG) of an atom in the presence of squeezed vacuum of a single harmonic mode. Based on a fully quantum time-dependent Schrödinger equation, we derive an analytical formula for the harmonic amplitude. Our simulations of the HHG spectrum with this formula show that the harmonic amplitude of the corresponding squeezed mode can undergo significant changes with different parameters of the squeezed vacuum. Using the time-frequency analysis method, the physics underlying the effects of the vacuum quantum fluctuation (VQF) on the harmonic generation is revealed, which is found to be consistent with the explanation of Fermi's golden rule. Our work establishes a profound connection between harmonic generation and VQF, and may provide an unconventional approach to manipulating harmonic emission. Published by the American Physical Society 2024
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) 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.
Abstract We theoretically demonstrate ultra-wideband resonant high-order harmonic generation (HHG) driven by quantum light. The resonant HHG spectra generated by the bright squeezed vacuum (BSV) state exhibit nearly twice the bandwidth compared to typical non-resonant HHG driven by BSV, enabling the cutoff to approach approximately 400 eV. The underlying mechanism of this significant broadening is analyzed by examining the yield of fluctuation amplitude-dependent coherent harmonics. We find that this broadening results from the weak sensitivity of the coherent harmonic yield to the fluctuation amplitude of BSV. Furthermore, by analyzing the dependence of the cutoff energy of resonant HHG on the BSV intensity and wavelength, we propose a revised formula for estimating the cutoff energy of BSV-driven resonant HHG.
High-harmonic generation (HHG) has recently emerged as a promising method for generating nonclassical states of light with frequencies spanning from the infrared up to the extreme ultraviolet regime. In this work, we theoretically investigate the generation of squeezed states of light through HHG processes in atomic systems that were initially driven to their first excited state. Our study reveals significant single-mode squeezing in both the driving field and low-order harmonic modes. Additionally, we characterize two-mode squeezing features in the generated states, both between fundamental and harmonic modes, and among the harmonic modes themselves. Using these correlations, we demonstrate the generation of optical Schr\"odinger kitten states through heralding measurements, specifically via photon subtraction in one of the modes influenced by two-mode squeezing.
We analyse the quadrature variance of high harmonic photons, using a simplified quantum optical model associated with high-harmonic generation (HHG) in the case of an elementary quantum source, modelled with a two-level atom. Assuming classical excitation, we find weak, oscillating (anti-)squeezing in the scattered radiation, with the variance-spectrum following similar evolution to the photon-number spectrum. Investigating the phase-relations, we conclude that the squeezed states of each mode are {most of the time{ close to being amplitude-squeezed, and squeezed states appear periodically within each attosecond pulse. We have also defined an approximate single noise-ellipse based on the collective field, and its analysis shows that it is anti-squeezed.
Recent developments in quantum light engineering have enabled the use of infrared bright squeezed vacuum (BSV) femtosecond pulses in nonlinear optics, including strong-field physics and high-harmonic generation. However, theory has focused on single-atom interactions, neglecting the crucial macroscopic aspect of light propagation through media. This raises a key question: How does BSV propagate in nonlinear media, and how this affects the nonlinear signals and the radiation’s quantumness? We address this with a fully quantized framework for propagation in gas media undergoing high-harmonic generation. We find that ionization and the associated photon losses cause decoherence, which limits the propagation length, degrades radiation’s quantumness, and reduces the emitted harmonics. However, these effects are not detrimental. We identify conditions that minimize propagation-induced decoherence while preserving detectable harmonics with super-Poissonian photon statistics. Our results establish fully quantized basis for exploring BSV in nonlinear optics, strong-field-quantum optics, and ultrafast science in all states of matter. Recent developments in strong-field quantum optics are usually modelled with approaches neglecting the propagation dynamics inside the medium. Here, the authors introduce a fully quantized framework for bright squeezed vacuum states propagating inside atomic media undergoing high-harmonic generation, unveiling the role of decoherence effects.