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arXiv:2004.07327 · Monthly Notices of the Royal Astronomical Society

Astronomical masers and Dicke’s superradiance

Fereshteh Rajabi, Martin Houde

Published Apr 23, 2020• 10 citations
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Abstract

ABSTRACT We consider the radiation properties and processes of a gas with a population inversion using the formalism based on the Maxwell–Bloch equations. We focus on the maser action and Dicke’s superradiance to establish their relationship in the overall radiation process during the temporal evolution of the system as a function of position. We show that the maser action and superradiance are not competing phenomena but are rather complementary and define two distinct limits for the intensity of radiation. Masers characterize the quasi-steady state limit, when the population inversion density and the polarization amplitude vary on time-scales longer than those of non-coherent processes affecting their evolution (e.g. collisions), while superradiance defines the fast transient regime taking place when these conditions are reversed. We show how a transition from a maser regime to superradiance will take place whenever a critical threshold for the column density of the population inversion is reached, at which point a strong level of coherence is established in the system and a powerful burst of radiation can ensue during the transient regime. This critical level also determines the spatial region where a transition from the unsaturated to the saturated maser regimes will take place; superradiance can thus be seen as the intermediary between the two. We also quantify the gain in radiation intensity attained during the superradiance phase relative to the two maser regimes and show how the strong coherence level during superradiance is well suited to explain observations that reveal intense and fast radiation flares in maser-hosting regions.

DOI
10.1093/mnras/staa1067

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ABSTRACT We consider the radiation properties and processes of a gas with a population inversion using the formalism based on the Maxwell–Bloch equations. We focus on the maser action and Dicke’s superradiance to establish their relationship in the overall radiation process during the temporal evolution of the system as a function of position. We show that the maser action and superradiance are not competing phenomena but are rather complementary and define two distinct limits for the intensity of radiation. Masers characterize the quasi-steady state limit, when the population inversion density and the polarization amplitude vary on time-scales longer than those of non-coherent processes affecting their evolution (e.g. collisions), while superradiance defines the fast transient regime taking place when these conditions are reversed. We show how a transition from a maser regime to superradiance will take place whenever a critical threshold for the column density of the population inversion is reached, at which point a strong level of coherence is established in the system and a powerful burst of radiation can ensue during the transient regime. This critical level also determines the spatial region where a transition from the unsaturated to the saturated maser regimes will take place; superradiance can thus be seen as the intermediary between the two. We also quantify the gain in radiation intensity attained during the superradiance phase relative to the two maser regimes and show how the strong coherence level during superradiance is well suited to explain observations that reveal intense and fast radiation flares in maser-hosting regions.
We derive relativistic Maxwell-Bloch equations for potential applications in astronomical environments, where various radiative processes are known to occur, including the maser action and Dicke's superradiance. We show that for both phenomena a radiating system's response is preserved at different relative velocities between the system's rest frame and the observer, while the relevant timescales and the radiation intensity transform as expected from relativistic considerations. We verify that the level of coherence between groups of emitters travelling at different speeds is unchanged in all reference frames. We also derive relativistic versions of the maser equations applicable in the steady-state regime.
ABSTRACT We have applied the concept of superradiance introduced by Dicke in 1954 to astrophysics by extending the corresponding analysis to the magnetic dipole interaction characterizing the atomic hydrogen 21 cm line. Although it is unlikely that superradiance could take place in thermally relaxed regions and that the lack of observational evidence of masers for this transition reduces the probability of detecting superradiance, in situations where the conditions necessary for superradiance are met (close atomic spacing, high velocity coherence, population inversion, and long dephasing timescales compared to those related to coherent behavior), our results suggest that relatively low levels of population inversion over short astronomical length-scales (e.g., as compared to those required for maser amplification) can lead to the cooperative behavior required for superradiance in the interstellar medium. Given the results of our analysis, we expect the observational properties of 21 cm superradiance to be characterized by the emission of high-intensity, spatially compact, burst-like features potentially taking place over short periods ranging from minutes to days.
ABSTRACT We investigate the application of the conventional quasi-steady state maser modelling algorithm of Menegozzi & Lamb (ML) to the high field transient regime of the one-dimensional Maxwell-Bloch (MB) equations for a velocity distribution of atoms or molecules. We quantify the performance of a first order perturbation approximation available within the ML framework when modelling regions of increasing electric field strength, and we show that the ML algorithm is unable to accurately describe the key transient features of R. H. Dicke’s superradiance (SR). We extend the existing approximation to one of variable fidelity, and we derive a generalization of the ML algorithm convergent in the transient SR regime by performing an integration on the MB equations prior to their Fourier representation. We obtain a manifestly unique integral Fourier representation of the MB equations which is O(N)\mathcal {O}\left(N\right)O(N) complex in the number of velocity channels N and which is capable of simulating transient SR processes at varying degrees of fidelity. As a proof of operation, we demonstrate our algorithm’s accuracy against reference time domain simulations of the MB equations for transient SR responses to the sudden inversion of a sample possessing a velocity distribution of moderate width. We investigate the performance of our algorithm at varying degrees of approximation fidelity, and we prescribe fidelity requirements for future work simulating SR processes across wider velocity distributions.
The reflection of short optical pulses from the boundary of a resonant medium is investigated theoretically by the coupled system of the Maxwell and optical Bloch equations. In order to describe the reflected wave, the slowly-varying-envelope approximation in space is not exploited. The coherent reflection is shown to be in connection with Dicke superradiance. It takes place if the relaxation time of the polarization is longer than the superradiation time of the atoms in an optically thin boundary layer of the medium. That is why much of the relevant information can be obtained already in the thin-medium limit, which is considered separately. The conditions of strong reflection from an extended medium are similar to the ones found for a thin sample. The transition into the incoherent and stationary regime is discussed.
Amplification of maser radiation involves an interaction between the radiation and the response function of the molecules that exhibit the population inversion. If the molecular response is taken to be quantum-mechanical, it is shown that the matter–radiation interaction must involve both amplitude and phase if a correct treatment of saturation of the population inversion is to be determined. The semi-classical treatment is compared with a fully quantum-mechanical approach, in which the radiation field is also quantized. Amplification and saturation of the maser radiation are accompanied by a partial locking of the phase across the lineshape. Significant variation of the phase under strongly saturated conditions occurs only over frequency intervals much larger than the homogeneous linewidth. The fully quantum-mechanical treatment of the radiation may have important consequences for the initiation of maser action.
We discuss the problem of calculating the superradiant behavior in samples small compared to a radiation wavelength. Difficulties associated with the analysis of Dicke are considered in the framework of quantum electrodynamics and equivalently from a classical point of view. The evolution of superradiance in a small sphere is followed numerically with attention to spatial variation of the Bloch dipole density. Coherence is maintained except in the region ${(\mathrm{kR})}^{\ensuremath{-}1}|cos\ensuremath{\theta}|\ensuremath{\lesssim}2$ which is at the Bloch equator, where it suddenly disappears. Away from the equator, the spatial variations of dipole density oscillate with amplitude $\ensuremath{\sim}{(\mathrm{kR})}^{2}sin\ensuremath{\theta}$ and frequency $\ensuremath{\sim}{(\mathrm{kR})}^{\ensuremath{-}3}|cos\ensuremath{\theta}|$. All these results agree with the predictions of a theoretical discussion previously published.