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Physical Review A

Theory of atomic correlations and line shape in microwave multiphoton processes

Franco Persico

Published Nov 1, 1976• 1 citation
Publisher

Abstract

Absorption of a microwave photon by a system of $N$ two-level atoms followed by reemission, and absorption of two microwave photons followed by emission of a single photon of double frequency are considered. Interatomic correlations and dephasing effects are taken into account, and it is shown that they have different relative importance in different parts of the cross-section curve: On resonance, dephasing effects are expected to prevail, while far from resonance the opposite is true. This behavior is shown to be reflected in a different angular and $N$ dependence of the emission curve in the center and in wings of the line. These predictions are compared with the experimental results on second-harmonic generation of the preceding paper by Boscaino, and shown to be in at least qualitative agreement.

DOI
10.1103/physreva.14.1695

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Absorption of a microwave photon by a system of NNN two-level atoms followed by reemission, and absorption of two microwave photons followed by emission of a single photon of double frequency are considered. Interatomic correlations and dephasing effects are taken into account, and it is shown that they have different relative importance in different parts of the cross-section curve: On resonance, dephasing effects are expected to prevail, while far from resonance the opposite is true. This behavior is shown to be reflected in a different angular and NNN dependence of the emission curve in the center and in wings of the line. These predictions are compared with the experimental results on second-harmonic generation of the preceding paper by Boscaino, and shown to be in at least qualitative agreement.
Second-harmonic (SH) generation by paramagnetic samples at microwave frequency is considered, and the dependence of its intensity on the total number NNN of active centers is experimentally investigated. The reported results show a N2{N}^{2}N2 dependence of the SH intensity near the resonance condition and a higher NNN dependence in the far wings of the SH line. A qualitative explanation is suggested in which the observed effect is related to the internal correlations established among the spins during the SH generation process, as theoretically investigated in the following paper by Persico.
Multiphoton emitters are a sought-after resource in quantum photonics. Nonlinear interactions between a multilevel atomic system and a coherent drive can lead to resonant two-photon emission, but harvesting light from this process has remained a challenge due to the small oscillator strengths involved. Here we present a study of two-photon resonance fluorescence at microwave frequencies, using a superconducting, ladder-type artificial atom, a transmon, strongly coupled to a waveguide. We drive the two-photon transition between the ground and second-excited states at increasingly high powers and observe a resonance fluorescence peak whose intensity becomes comparable to single-photon emission until it splits into a Mollow-like triplet. We measure photon correlations of frequency-filtered spectral lines and find that while emission at the fundamental frequency stays antibunched, the resonance fluorescence peak at the two-photon transition is superbunched. Our results provide a route towards the realization of multiphoton sources in the microwave domain.
Cross correlation refers to the situation in which the fluctuations in the fields of two or more lasers are correlated in some way. Recently, Thomas et al. [ Opt. Lett.6, 298 ( 1981); Phys. Rev. Lett.48, 867 ( 1982)] proposed the generation of cross correlation between two laser fields interacting with a three-level system as a means of reducing noise and went on to exploit this property in the observation of narrow Ramsay fringes. Dalton and Knight [ J. Phy. B15, 3997 ( 1982)] discussed the theoretical aspects of cross correlation and showed that it produced interesting effects in population trapping for example. We have demonstrated that it has significant effects on the optical double-resonance (ODR) spectra [ J. Phys. B17, L389 ( 1984)]. On the other hand, the effects of non-Lorentzian laser line shapes have been shown by various workers to have significant effects on a wide range of phenomena, such as multiphoton ionization, resonance fluorescence, and ODR. In this paper we present a theory of the interactions of lasers whose fluctuations are governed by the phase-diffusion process with atomic systems that includes the effects of cross correlation and non-Lorentzian line shapes. We derive the basic equations (which in general have to be solved numerically) and obtain analytic results in the case in which the line shape is approximately Lorentzian near line center but falls off faster than a Lorentzian in the wings. We believe that this analytic model shows all the essential features of the interplay between cross correlation and non-Lorentzian line shapes. The theory is applied to the ODR experiment. In particular, we find that the asymmetry of the spectra is strongly affected by these two features, and so is the ODR spectral line shape when the saturating laser intensity is close to the threshold for producing two peaks.
We have considered the induced processes that occur in a driven two-level atom, where a laser photon is absorbed and emitted by the ground and by the excited states of the atom, respectively. In the low-intensity limit of the laser field, the induced spectra arising when a laser photon is absorbed by the ground state of the atom consist of two peaks describing induced-absorption and stimulated-emission processes, respectively, where the former prevails over the latter. Asymmetry of the spectral lines occurs at off-resonance and its extent depends on the detuning of the laser field. The physical, process where a laser photon is emitted by the excited state is the reverse of that arising from the absorption of a laser photon by the ground state of the atom. The former differs from the latter in that the emission of a laser photon by the excited state occurs in the low-frequency regime and that the stimulated-emission process prevails over that of the induced absorption. In this case, amplification of ultrashort pulses is likely to occur without the need of population inversion between the optical transitions. The computed spectra are graphically presented and discussed.
The author derives an expression for the spectrum of the radiation scattered by an atom that suffers binary collisions in the weak-field limit. The frequency of the incident radiation is in near-resonance with a multiplet transition. The authors accounts for strong atom-perturber correlations that are induced when the incident or the detected frequency is in the far wing of an absorption line. For an isolated transition between two degenerate atomic levels the model picture of quasistatic absorption followed by adiabatic reorientation of the excited state predicts a redistributed fluorescence line with a polarisation that is determined by geometrical factors.
We investigate theoretically the spatial quantum correlations of the light produced by spontaneous emission in type-I second-harmonic generation in the traveling-wave configuration. It is first shown that spontaneous emission occurs at both fundamental and second-harmonic frequency. Considering the quantum fluctuations of the intensities collected in symmetrical parts of the far-field plane, nonclassical correlations below the shot noise are predicted not only at fundamental frequency, but also at second-harmonic frequency. The latter cannot be traced back to any twin-photon emission mechanism, but are generated by a secondary process acting on twin photons. This mechanism also creates correlations between fundamental and second-harmonic field, at a given transverse wave number, and at opposite wave numbers. The analysis of a simplified few-mode model, on a quantum level, provides a good qualitative understanding of these correlations.