In this work, quantum-optical radiative recombinations between electrons and ions are analyzed using a semiclassical approach without losing their specific quantum-optical nature. Under moderately strong driving field conditions, the results of the quantum-optical model are consistent with the semiclassically derived results in terms of both the spectral intensity and phase. Deviations between the two models, which are observed under extremely strong driving field conditions, are investigated in the time and frequency domains to clarify the underlying reasons. In addition, the radiative recombination dynamics between a free electron and a bare ion can be simulated using our quantum model. In recent decades, the semiclassical model combined with the classical equations of light has been used as an intuitive and powerful tool to study the macroscopic buildup of nonlinearly generated light. In this macroscopic approach, the phase information of individual atomic radiations plays an essential role. Since our model can provide spectral phases of quantum-optical lights generated from individual atoms, it is now feasible to pursue the macroscopic buildup of specific quantum-optical radiations and relevant phenomena by using the conventional approach used for the semiclassical model.
In this work, quantum-optical radiative recombinations between electrons and ions are analyzed using a semiclassical approach without losing their specific quantum-optical nature. Under moderately strong driving field conditions, the results of the quantum-optical model are consistent with the semiclassically derived results in terms of both the spectral intensity and phase. Deviations between the two models, which are observed under extremely strong driving field conditions, are investigated in the time and frequency domains to clarify the underlying reasons. In addition, the radiative recombination dynamics between a free electron and a bare ion can be simulated using our quantum model. In recent decades, the semiclassical model combined with the classical equations of light has been used as an intuitive and powerful tool to study the macroscopic buildup of nonlinearly generated light. In this macroscopic approach, the phase information of individual atomic radiations plays an essential role. Since our model can provide spectral phases of quantum-optical lights generated from individual atoms, it is now feasible to pursue the macroscopic buildup of specific quantum-optical radiations and relevant phenomena by using the conventional approach used for the semiclassical model.
For decades, ultrafast light-matter interactions have provided a powerful means to observe electrons in motion across a wide range of physical systems. This dissertation builds new theoretical frameworks to make sense of the emergent phenomena that arise when light drives matter into the strong-field regime, spanning atomic, molecular, and condensed-matter systems. The resulting dynamics leave their fingerprints on a variety of observables, such as photoionization spectra, high-harmonic generation, and nonlinear spectroscopic signals, each of which provides a different window onto the underlying electronic motion. The work is organized into two parts.The first part focuses on the electric-field observables of nonlinear optical signals. Because both the amplitude and phase of the emitted field are experimentally accessible through techniques such as spectral interferometry and electro-optic sampling, the full field itself serves as a rich observable for characterizing nonlinear responses in atomic, molecular, and condensed-matter systems. Leveraging this, the simulations presented here uncover novel and largely unexplored physical phenomena encoded in these field observables. The second part turns to optical spectroscopy with quantum light. Although nonlinear optical processes are conventionally modeled within a semiclassical framework, treating the matter quantum mechanically while the driving ultrafast fields remain classical, the resulting signals can nonetheless exhibit intrinsically non-classical properties. Building on this insight, a framework for interpreting experimental data is introduced and used to show that four-wave mixing driven by ultrafast femtosecond laser pulses generates bright squeezed light. Beyond squeezed light, strong field-matter interactions can also produce attosecond entangled photons, a distinct form of quantum light. Several strategies are proposed to enhance the efficiency of their generation, with the developed theory predicting rates of energy-time entangled biphoton production orders of magnitude beyond those achievable with conventional spontaneous parametric down-conversion (SPDC) sources. The studies presented here are initial steps toward investigating quantum properties of these systems through quantum phynonlinear spectroscopy, which is not achievable with classical light.
The interaction of electrons with strong laser fields is usually treated with semiclassical theory, where the laser is represented by an external field. There are analytic solutions for the free electron wave functions, which incorporate the interaction with the laser field exactly, but the joint effect of the atomic binding potential presents an obstacle for the analysis. Moreover, the radiation is a dynamical system, the number of photons changes during the interactions. Thus, it is legitimate to ask how can one treat the high order processes nonperturbatively, in such a way that the electron-atom interaction and the quantized nature of radiation be simultaneously taken into account? An analytic method is proposed to answer this question in the framework of nonrelativistic quantum electrodynamics. As an application, a quantum optical generalization of the strong-field Kramers-Heisenberg formula is derived for describing high-harmonic generation. Our formalism is suitable to analyse, among various quantal effects, the possible role of arbitrary photon statistics of the incoming field. The present paper is dedicated to the memory of Prof. Dr. Fritz Ehlotzky, who had significantly contributed to the theory of strong-field phenomena over many decades.
Spontaneous light emission is central to a vast range of physical systems and is a founding pillar for the theory of light–matter interactions. In the presence of complex photonic media, the description of spontaneous light emission usually requires advanced theoretical quantum optics tools such as macroscopic quantum electrodynamics, involving quantized electromagnetic fields. Although rigorous and comprehensive, the complexity of such models can obscure the intuitive understanding of many quantum-optical phenomena. Here, we review a method for calculating spontaneous emission and other quantum-optical processes without making explicit use of quantized electromagnetic fields. Instead, we introduce the concept of transition currents, comprising charges in matter that undergo transitions between initial and final quantum states. We show how predictions that usually demand advanced methods in quantum electrodynamics or quantum optics can be reproduced by feeding these transition currents as sources to the classical Maxwell equations. One then obtains the relevant quantum observables from the resulting classical field amplitudes, without washing out quantum optical effects. We show that this procedure allows for a straightforward description of quantum phenomena, even when going beyond the dipole approximation and single emitters. As illustrative examples, we calculate emission patterns and Purcell-enhanced emission rates in both bound-electron and free-electron systems. For the latter, we derive cathodoluminescence emission and energy-loss probabilities of free electrons interacting with nanostructured samples. In addition, we calculate quantum-beat phenomena in bound-electron systems and wave function-dependent optical coherence in free-electron systems. Remarkably, the transition-current formalism captures more complex phenomena, such as many-body interference effects and super-radiance of both bound- and free-electron systems, second-order processes such as two-photon emission, and quantum recoil corrections to free-electron radiation. We review a variety of light–matter interactions in fields ranging from electron microscopy to nanophotonics and quantum optics, for which the transition-current theoretical formalism facilitates practical simulations and a deeper understanding of novel applications.
Ultrafast ionization dynamics within the field half cycle is shown to be the key physical factor that controls the properties of optical nonlinearity as a function of the carrier wavelength and intensity of a driving laser field. The Schrödinger-equation analysis of a generic hydrogen quantum system reveals universal tendencies in the wavelength dependence of optical nonlinearity, shedding light on unusual properties of optical nonlinearities in the midinfrared. For high-intensity low-frequency fields, free-state electrons are shown to dominate over bound electrons in the overall nonlinear response of a quantum system. In this regime, semiclassical models are shown to offer useful insights into the physics behind optical nonlinearity.
Quantum-optical descriptions of strong-field processes have attracted significant attention in recent years. Typically, the theoretical modeling has been conducted in the Schrödinger picture, where results are only obtainable under certain approximations, while, in contrast, the Heisenberg picture has remained relatively unexplored. In this work, we develop an accurately controlled perturbative expansion of the time-evolution operator in the Heisenberg picture and derive beyond-semiclassical corrections to the emitter dynamics due to the coupling to the quantized electromagnetic field, capturing effects of the quantum fluctuations present in the latter. We focus on high-order harmonic generation (HHG), where the approach is accurate in parameter regimes of current interest and it gives closed-form expressions for key observables. This formulation not only simplifies numerical calculations compared to the Schrödinger-picture approach but also provides a clear correspondence between nonclassical features of the emitted light and the underlying induced dynamics of the generating medium including quantum fluctuations. Moreover, the Heisenberg framework naturally yields scaling relations with the number of independent emitters, enabling us to assess whether nonclassical behavior should persist under typical experimental conditions involving large emitter ensembles. Interestingly, we find that the degree of squeezing increases with the number of emitters, whereas the photon statistics approaches a classical Poissonian distribution in the many-emitter limit. We also find that the beyond-semiclassical emitter dynamics significantly enhances the degree of squeezing of the emitted light. Our work advances the theoretical understanding of quantum-optical HHG and introduces an accessible and well-controlled framework to describe realistic experiments.
A semiclassical treatment of the radiation loss in a laser, previously investigated by Baseia and Nussenzveig [Opt. Acta 31, 39 (1984)], is extended to the quantum-theory level. The model employs an optical cavity having an output coupling that includes the radiation loss due to the beam extraction through appropriate boundary conditions, instead of the unrealistic loss reservoir of the conventional treatment. This allows one to work entirely within the continuous spectrum and obtain the equation for the radiation field both inside and outside the cavity. Inside the cavity the results agree, in the coherent representation and absence of quantum noise, with those of the previous semiclassical theory. Also, the results of both treatments for the field inside the cavity coincide with those of the conventional theory, since we reinterpret its ``mode amplitude'' as a collective variable. Outside the cavity (an inaccessible region for a standard approach) the explicit solution for the laser field exhibits a natural relationship between the intensities inside and outside the cavity. Further considerations, such as those concerning the role played by the noise term in the field buildup, are also discussed.