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Quadrature properties of high harmonics emitted by two-level atom

Ákos Gombkötő

Published May 12, 2020• 0 citations
OpenAlex

Abstract

We analyse the quadrature mean values and variances of high harmonic photons, emitted by a classically driven elementary quantum source of radiation. This fundamental system is modelled with a two-level atom. The quadrature mean values and variances are calculated for harmonic modes in the near-field. Numerical results imply the presence of weak squeezing in each harmonic mode, more pronounced in even harmonics. Approximate time-evolution of the collective electromagnetic field is calculated, and the electric field-variance of the scattered pulse-train is given.

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We analyse the quadrature mean values and variances of high harmonic photons, emitted by a classically driven elementary quantum source of radiation. This fundamental system is modelled with a two-level atom. The quadrature mean values and variances are calculated for harmonic modes in the near-field. Numerical results imply the presence of weak squeezing in each harmonic mode, more pronounced in even harmonics. Approximate time-evolution of the collective electromagnetic field is calculated, and the electric field-variance of the scattered pulse-train is given.
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.
We investigate a two-level atom in the field of a strong laser pulse. The resulting time-dependent polarization is the source of a radiation the frequency components of which are essentially harmonics of the driving field's carrier frequency. The time evolution of this secondary radiation is analyzed in terms of the expectation values of the photon-number operators for a large number of electromagnetic modes that are initially in the vacuum state. Our method is based on a multimode version of the Jaynes-Cummings-Paul model and can be generalized to different radiating systems as well. We show that, after the exciting pulse, the final distribution of the photon numbers is close to the conventional (Fourier-transform-based) power spectrum of the secondary radiation. The details of the high-order-harmonic spectra (HHG spectra) are also analyzed; for many-cycle excitations a clear physical interpretation is given in terms of the Floquet quasienergies. A first step towards the determination of the photon statistics of the high-order-harmonic modes reveals states with slightly super-Poissonian distribution.
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.
The dynamics of a coherently driven two-level atom with parametric amplifier and coupled to a vacuum reservoir is analyzed. The combination of the master equation and the quantum Langevin equation is presented to study the quantum properties of light. By using these equations, we have determined the time evolution of the expectation values of the cavity mode and atomic operators. Moreover, with the aid of these results, the correlation properties of noise operators, and the large-time approximation scheme, we calculate the mean photon number, power spectrum, second-order correlation function, and quadrature variances for the cavity-mode light and fluorescence. It is found that the half-width of the power spectrum for the fluorescent light in the presence of a parametric amplifier increases, while it decreases for the cavity-mode light. Moreover, we have found the probability for the atom to be in the upper level in the presence of a parametric amplifier.
In this work the statistical and squeezing properties of light-driven by sub-harmonic generation with two-mode coherent light are studied. With interaction Hamiltonian of both two-mode coherent and sub harmonic generation, we have driven master equation of system under consideration. From the master equation, the solution of the C-number Langevin equation is derived. It helps us to solve quadrature variance, quadrature squeezing, mean, and variance of photon number for light produced by sub-harmonic generation with the two-mode coherent light state. And the result shows that; the squeezing occurs in plus quadrature with the maximum squeezing of 87%. The photon statistics of the system under consideration is subpoissonian in which both mean & variance are increasing as kappa increase.
We have studied the statistical and squeezing properties of the cavity light generated by a two-level laser. This optical system contains N two-level atoms available in a cavity coupled to a single-mode vacuum reservoir. They are pumped to the top level from the bottom level by means of the electron bombardment. Applying the steady-state solutions of the equations of evolution of the expectation values of the atomic operators and the quantum Langevin equation, we obtained the global and local photon statistics of the single-mode light beam. We have found that, for the two-level laser operating well above the threshold, the uncertainties in the plus and minus quadratures are equal and satisfy the minimum uncertainty relation. In view of this, we have identified the light generated by the laser operating well above threshold to be coherent. On the other hand, the light generated by the laser operating at threshold is found to be chaotic. From the obtained results, we have also observed that a large part of the local mean photon number, the local photon number variance, and the local quadrature variance are confined in a relatively narrow frequency interval.