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International Journal of Modern Physics B

Resonant enhancement of an X-ray laser electric field inside an atom

Şerban Mişicu

Published Mar 13, 2023• 0 citations
Publisher

Abstract

In the frame of a time-dependent oscillator model, the field induced by the coupling between the atomic electric dipole and an external X-ray laser field is investigated. The aim of the paper is to asses if in the resonant case (the frequency of the incoming field matches the frequency of the atom’s collective dipole oscillation) the damped collective oscillation induced by the external time-varying electric field can produce a significant amplification of the total electric field at the nucleus position.

DOI
10.1142/s0217979224500607

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In the frame of a time-dependent oscillator model, the field induced by the coupling between the atomic electric dipole and an external X-ray laser field is investigated. The aim of the paper is to asses if in the resonant case (the frequency of the incoming field matches the frequency of the atom’s collective dipole oscillation) the damped collective oscillation induced by the external time-varying electric field can produce a significant amplification of the total electric field at the nucleus position.
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We develop a nonperturbative model for the response of atomic electrons to oscillating external electric fields, valid in the physical regime where the central electric force is well described by an inverse square law and where the driven oscillations preserve the principal quantum number. We use the model to calculate the odd-harmonic electric-dipole radiation from a single atom driven by a laser field. The exact time-dependent eigensolutions of the model illustrate Zel’dovich’s concept of quasi-energy for sinusoidally time-dependent Hamiltonians. The validity and applicability of the model and suggested improvements are briefly discussed.
Treating the laser medium quantum mechanically and the laser electric field classically, a mathematical model was developed to study a laser field inside a single mode optical cavity by numerical and analytical techniques. The simulations for threshold population, population inversion and average population with electric field frequency for 500 kHz resonance frequency of the atom are presented. The gain coefficient and the pump parameter with the frequency of the cavity electric field for 1000 kHz resonance frequency of the atom were simulated. The threshold population is a minimum when the frequency of electric field is equal to the resonance frequency of the atom. The population inversion varies sinusoidal with time and the frequency of the electric field and is a maximum at the threshold frequency of the atom. The saturated laser intensity at steady state increases linearly with the pump parameter and for larger values of the pump parameter, a smaller time is needed to reach the saturation of the laser field.
To understand the time-dependent process in quantum mechanics, an exact expression for the dynamical change of the transition probability and the expectation value of the oscillation energy are presented for the system of the charged harmonic oscillator interacting with an external field through the electric dipole interaction of either type A・p or E・r. The oscillating wave packet is shown to be made from an eigenfunction of the free oscillator Hamiltonian by the interaction during some time. The off-resonance, difference between the field frequency and the proper frequency of the oscillator, controls the number of basis states significant in the transient process. Even on complete resonance, the golden rule holds true only for a short duration and all other nonresonant basis states participate in turn as the interaction time elapses. The difference between two types of dipole interaction exists certainly in the probability distribution in the basis states and the oscillation energy, though it does not in the total current of the oscillator.
Rydberg atoms excited in microwave resonators are ideal systems to test quantum electrodynamics on an unusual scale.1 Owing to their very large electric dipole sizes, these atoms are indeed coupled so strongly to infrared and millimeter-wave radiation that the field of a few photons—ultimately the one of a single photon—stored in a cavity is large enough to induce important transition rates during the atomic time of flight across the cavity. As a result quantum radiative effects are observed in a range of frequencies where usual atomic systems behave as purely classical radiators. The enhancement of the spontaneous emission rate of a single atom prepared in a tuned cavity has already been observed.2 For a resonant cavity with very small losses, a point should be reached where the atom can no longer decay but instead reversibly oscillates between the two states involved in the transition resonant with the cavity mode. Experiments aimed at the observation of this new regime of quantum electrodynamics evolution are under way