A recently introduced theoretical framework for modeling the dynamics of X-ray amplified spontaneous emission is based on stochastic sampling of the density matrix of quantum emitters and the ...radiation field, similarly to other phase-space sampling techniques. While based on first principles and providing valuable theoretical insights, the original stochastic differential equations exhibit divergences and numerical instabilities. Here, we resolve this issue by accounting the stochastic components perturbatively. The refined formalism accurately reproduces the properties of spontaneous emission and proves universally applicable for describing all stages of collective X-ray emission in paraxial geometry, including spontaneous emission, amplified spontaneous emission, and the non-linear regime. Through numerical examples, we analyze key features of superfluorescence in one-dimensional approximation. Importantly, single realizations of the underlying stochastic equations can be fully interpreted as individual experimental observations of superfluorescence.
We propose an approach based on stochastic differential equations to describe superfluorescence in compact ensembles of multi-level emitters in the presence of various incoherent processes. This ...approach has a numerical complexity that does not depend on the number of emitters. The stochastic differential equations are derived directly from the quantum master equation. In this study, we present a series of numerical examples, comparing our solution to exact calculations and discussing the limits of applicability. For many relevant cases, the proposed stochastic differential equations provide accurate results and correctly capture quantum many-body correlation effects.
In this work we introduce a phase-space description based on the positive P representation for bosonic fields interacting with a system of quantum emitters. The formalism is applicable to collective ...light-matter interactions and open quantum systems with decoherence. Conservation of particle numbers is considered, and a Jordan-Schwinger transformation enables the representation of multi-level quantum emitters. The evolution of the phase-space description of the combined system of emitters and field is formulated in terms of stochastic trajectories and we derive the rules of mapping from traditional quantum mechanics to this stochastic formalism. The resulting equations of motion encode deterministic, classical evolution with quantum effects incorporated by stochastic noise terms. The framework's equations and properties are provided without specifying the Hamiltonian, aiming for broad applicability in diverse research domains. A potential future application is the quantum mechanical description of collective spontaneous emission of an incoherently pumped ensemble of atoms.
An approach to modeling the dynamics of x-ray amplified spontaneous emission and superfluorescence -- the phenomenon of collective x-ray emission initiated by intense pulses of X-ray Free Electron ...Lasers -- is developed based on stochastic partial differential equations. The equations are derived from first principles, and the relevant approximations, derivation steps, and extensions specific to stimulated x-ray emission are presented. The resulting equations take the form of three-dimensional generalized Maxwell-Bloch equations augmented with noise terms for both field and atomic variables. The derived noise terms possess specific correlation properties that enable the correct reconstruction of spontaneous emission. Consequently, the developed theoretical formalism is universally suitable for describing all stages of stimulated x-ray emission: spontaneous emission, amplified spontaneous emission, and superfluorescence. We present numerical examples that illustrate various properties of the emitted field, including spatio-temporal coherence, spectral-angular and polarization characteristics. We anticipate that the proposed theoretical framework will establish a robust foundation for interpreting measurements in stimulated x-ray emission spectroscopy, modeling x-ray laser oscillators, and describing other experiments leveraging x-ray superfluorescence.
X-ray radiation of relativistic electrons passing through the crystal lattice (in case of channeling radiation) requires electrons with energies just from tens up to hundreds MeV, but has a drawback: ...low number of emitted X-ray quanta. However, the brightness of such a source could be potentially increased if the current density of the electron bunch is high enough to initiate the self amplified spontaneous emission (SASE) process. The conditions at which this phenomenon could take place for the case of axial channeling are analyzed in the present paper within the first order perturbation theory. The transition from spontaneous to SASE regime is described, the requirements for bunch current parameters initiating SASE process are determined taking into account the periodic structure of the crystal medium. It is also shown that satisfying Bragg diffraction conditions could enhance self amplification. Numerical results for the case of axial channeling in Si, Ge and C crystals are presented as an example.
