In this study, we investigate the time–frequency-resolved resonant photon emission from a molecular vibrational oscillator driven by a monochromatic coherent external field. Using the complex spectral analysis of the Liouvillian, which integrates irreversible dissipative phenomena into quantum theory, we elucidate the fundamental processes of photon emission. Indeed, our analytical approach successfully decomposes the emission spectrum into two intrinsic contributions: one from a resonance eigenmode and another from continuous eigenmodes. These components are responsible for incoherent luminescence and coherent scattering photon emission processes, respectively. Our results show that while spontaneous emission dominates in the early stages of the emission process, coherent scattering gradually becomes more pronounced with time. Furthermore, destructive quantum interference between the two components plays a key role in determining the overall shape of the emission spectrum.
In this study, we investigate the time–frequency-resolved resonant photon emission from a molecular vibrational oscillator driven by a monochromatic coherent external field. Using the complex spectral analysis of the Liouvillian, which integrates irreversible dissipative phenomena into quantum theory, we elucidate the fundamental processes of photon emission. Indeed, our analytical approach successfully decomposes the emission spectrum into two intrinsic contributions: one from a resonance eigenmode and another from continuous eigenmodes. These components are responsible for incoherent luminescence and coherent scattering photon emission processes, respectively. Our results show that while spontaneous emission dominates in the early stages of the emission process, coherent scattering gradually becomes more pronounced with time. Furthermore, destructive quantum interference between the two components plays a key role in determining the overall shape of the emission spectrum.
We show how the properties of photon emission to a continuous field from a parametric oscillator relate to the behavior of the complex eigenfrequencies of the oscillator. The parametric oscillator has complex eigenfrequencies due to non-Hermiticity with two origins: parametric amplification and dissipation resulting from the loss of photons to a continuous field. In situations where the oscillator is close to the parametric resonance, and the coupling to the driving field is strong enough for a complex eigenfrequency to lie in the upper half of the first Riemann sheet, the number of photons of the parametric oscillator and the continuous field increases exponentially. The parametric amplification is counteracted by dissipation due to the coupling of the parametric oscillator to the continuous field, and if the dissipation is sufficiently strong relative to the amplification, the exponential growth is suppressed. The suppression occurs when the complex eigenfrequency responsible for the exponential growth moves into the second Riemann sheet analytically continued beyond the branch cut of the Green function on the real axis along the continuum of frequency. As a result, there appears a stationary photon emission, where creation of photons balance with dissipation due to emission of the photons to the continuous field. Then there is a constant flux of photons, with the number of photons in the continuous field increasing in proportion to time, while the number of photons in the parametric oscillator remains constant.
Recent developments on intense laser sources is opening a new field of optical sciences. An intense coherent light beam strongly interacting with the matter causes a coherent motion of a particle, forming a strongly dressed excited particle. A photon emission from this dressed excited particle is a strong nonlinear process causing high-harmonic generation (HHG), where the perturbation analysis is broken down. In this work, we study a coherent photon emission from a strongly dressed excited atom in terms of complex spectral analysis in the extended Floquet-Hilbert-space. We have obtained the eigenstates of the total Hamiltonian with use of Feshbach-Brilloiun-Wigner projection method. In this extended space, the eigenstates of the total Hamiltonian consisting of the radiation field and the atom system have complex eigenvalues whose imaginary part represents the decay rate. Time evolution of the system is represented by the complex eigenvector expansion so that the correlation dynamics between the photon and the atom is fully taken into account. The HHG is interpreted as the irreversible spontaneous photon emission due to the resonance singularity in terms of the multiple Floquet states that are generated by periodic external field. We have found that the interference between the emitted photons over the different Floquet states causes spatial pulse emission correlated with the decay process of the excited atom.
The perturbative density matrix formalism is used to study the time-dependent resonance Raman scattering (RRS) and resonance hot luminescence (RHL) components of the light-induced spontaneous emission process that has been called resonance secondary radiation (RSR). A three-level system coupled in a stochastic way to a bath is used to study the RSR emission driven by a coherent laser pulse with a variable Gaussian width in time. The spectral filter in a light detection system is explicitly included in the detection step of the problem. Observable time and frequency resolved RSR spectra are then calculated numerically. The spectral and temporal properties of the time-dependent RSR spectrum are very sensitive to the width of the driving pulse when the pulse width is of the same order of magnitude as the important system dephasing constants. In this domain the RRS contribution to the RSR spectrum weakens relative to the RHL as the light pulse is shortened. In the limit that the laser pulse becomes ‘‘delta function-like’’ the RSR spectrum consists essentially of RHL. When appropriate, the numerical results are compared to the stationary RSR problem as well as to the case where the RSR emission is driven by an exponential pulse. The analytical solutions to both of these cases are presented.
Resonance fluorescence from a two-level emitter is a standard route to single-photon generation, where the emitter produces only one photon at a time, and multiphoton emission or scattering is inherently suppressed. In this study, we challenge this paradigm in the weak-excitation limit, where coherent scattering dominates. Using a single quantum dot in a microcavity, we show that the incoherent component exhibits pronounced superbunching, revealing simultaneous multiphoton scattering from a single emitter. In contrast, the total reflected field—comprising the reflected driving field and incoherent scattering—displays perfect antibunching, arising from quantum interference that cancels two-photon probability amplitudes. By spectrally filtering the reflected field, we tune the relative contributions of coherent and incoherent components, observing transitions in photon statistics from antibunching to superbunching, or to Poissonian light. Supported by master-equation simulations and an interference-based model, these results uncover the hidden but fundamental role of multiphoton dynamics in resonance fluorescence, and open avenues for generating nonclassical light in cavity and waveguide quantum electrodynamics.
The nature of resonance emission of light, which appears as a mixture of (coherent) resonance scattering and (incoherent) resonance fluorescence, is considered. The basic conceptual elements which distinguish the scattering and fluorescence components for the linear excitation limit are developed in terms of a simple formulation whereby a molecule interacts with a coherent Lorentzian light pulse which increases exponentially with time for t<0 and is turned off at t = 0. These results together with the ideas, currently existing in the literature, that stochastic modulation of a molecule by its medium is essential for the appearance of fluorescence provide the basis for the further formulation of a theory which does not require the ad hoc introduction of a random potential. The theory developed considers the microscopic origins of manifest stochastic modulation effects in terms of a bath potential for the molecule–medium (bath) degrees of freedom. This potential, termed the sudden potential, is associated with the change in interaction with the medium that a molecule experiences upon intramolecular state transitions which are induced by external interactions (e.g., by light). Development of the reduced molecule–field density operator leads naturally to a separation of terms which describes scattering and (the propensity for) fluorescence. Critical to the theory is a four-time correlation function for the bath (sudden) potential. The difficulties inherent in defining absorption (spectrum) resonances and the corresponding distinctions between resonance and relaxed emission are discussed. Implications are considered for the further understanding of experimental results on molecular excitation dynamics in the gas phase and in supersonic jets. Sources of stochastic modulation other than material media are mentioned. In particular, the possibility is suggested of the pervasive existence of stochastic modulation through interaction of a molecule with the vacuum state of the radiation field. This raises questions concerning the fundamental relations between quantum mechanics and thermodynamics.
In the previous articles of this series, dealing with the interaction between a number of molecules and the electromagnetic field in a resonant cavity, both the molecules and the field were treated by perturbation theory. The perturbation restriction on the field is removed in the present article, allowing large changes in the field, but the molecules are still assumed to undergo a small change during the time under consideration. The justification for this type of analysis, involving the generalization of the conventional concepts of induced and spontaneous emission, the applicability to a molecular amplifier during the buildup period, and the re-examination of a calculation by Serber and Townes concerning the fundamental limits of molecular amplification, is discussed.Two different molecular distributions are considered. In one (the resonant case) all molecules have the same frequency as the cavity, and in the other (the nonresonant case) there is a uniform frequency distribution. The molecules are assumed to be initially in an emissive state. Several types of driving fields are considered. Expressions are obtained for the field operators by the solution of a Volterra integral equation, and expectation values are obtained for the field strength and field energy.In the resonant case, both the coherent and incoherent fields increase exponentially after a sufficiently long time, no matter how small the initial gain is. Their ratio becomes constant and is equal to the number of photons in the driving field only in the absence of dissipation. An interesting related result is the fact that the signal-to-noise ratio for constant signal input power increases as the cavity dissipation increases. An estimate of the total time for which the theory is valid is obtained from a consideration of the energy emitted by the molecules. Contact is made with perturbation theory for sufficiently small gain and short time.In the nonresonant case the effect of the molecules is shown to be that of a negative dissipation. In contrast to the resonant case, the gain becomes exponential only if the negative dissipation exceeds, in absolute value, the true dissipation. The ratio of induced to spontaneous emission is, in this case also, equal to the number of photons in the driving field only in the absence of disipation. However, the signal-to-noise ratio for constant input power drops with increasing cavity dissipation.