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arXiv:1704.07066 · Physical Review A

Superradiance with local phase-breaking effects

Nathan Shammah, Neill Lambert, Franco Nori, Simone De Liberato

Published Aug 30, 2017• 66 citations
arXivHTMLPDF

Abstract

We study the superradiant evolution of a set of $N$ two-level systems spontaneously radiating under the effect of phase-breaking mechanisms. We investigate the dynamics generated by nonradiative losses and pure dephasing, and their interplay with spontaneous emission. Our results show that in the parameter region relevant to many solid-state cavity quantum electrodynamics experiments, even with a dephasing rate much faster than the radiative lifetime of a single two-level system, a suboptimal collective superfluorescent burst is still observable. We also apply our theory to the dilute excitation regime, often used to describe optical excitations in solid-state systems. In this regime, excitations can be described in terms of bright and dark bosonic quasiparticles. We show how the effect of dephasing and losses in this regime translate into intermode scattering rates and quasiparticle lifetimes.

DOI
10.1103/physreva.96.023863

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We study the superradiant evolution of a set of NNN two-level systems spontaneously radiating under the effect of phase-breaking mechanisms. We investigate the dynamics generated by nonradiative losses and pure dephasing, and their interplay with spontaneous emission. Our results show that in the parameter region relevant to many solid-state cavity quantum electrodynamics experiments, even with a dephasing rate much faster than the radiative lifetime of a single two-level system, a suboptimal collective superfluorescent burst is still observable. We also apply our theory to the dilute excitation regime, often used to describe optical excitations in solid-state systems. In this regime, excitations can be described in terms of bright and dark bosonic quasiparticles. We show how the effect of dephasing and losses in this regime translate into intermode scattering rates and quasiparticle lifetimes.
Abstract The electrodynamics of active continuous media is applied to theoretically examine collective spontaneous emission regimes of dipole oscillator ensembles. Recent experiments in which the superfluorescence phenomenon has been observed are reviewed. The focus is on propagation and interaction effects experienced by the inhomogeneous waves of active center polarization and electromagnetic fields. The superradiant laser dynamics is examined and prospects for the realization of superradiant lasers using low-Q cavities are discussed.
Abstract The electrodynamics of active continuous media is applied to theoretically examine collective spontaneous emission regimes of dipole oscillator ensembles. Recent experiments in which the superfluorescence phenomenon has been observed are reviewed. The focus is on propagation and interaction effects experienced by the inhomogeneous waves of active center polarization and electromagnetic fields. The superradiant laser dynamics is examined and prospects for the realization of superradiant lasers using low- Q cavities are discussed.
We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to 10310^3103 emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.
Spontaneous decay is a phenomenon that has been described for the first time by Dirac, Wigner and Weisskopf, at the early ages of the development of quantum electrodynamics. The theory is applicable to a multi-body system only when atoms don’t interact during their decay. Dicke introduces in his seminal paper the case where this assumption doesn’t hold. The results he obtains not only tell that the system emits pulses, but the pulse duration now depends on 1/N, where N is the number of participating atoms to the process. The pulses temporal profile is described by a squared hyperbolic secant function. The resulting emission intensity scales as N^2. The atomic system radiates more intensively than the ordinary fluorescent emission, this is the reason why the process is called superradiance, or by a generalization to extended systems, superfluorescence. The superradiant emission has preferential escape directions, depending on the atomic sample shape. Superradiance is a collective process and it takes place when the group of excited atoms is left unper- turbed during the formation of of the macroscopic dipole. A fundamental difference compared to the spontaneous and stimulated emission processes is that all atoms act together as a single entity and it isn’t possible to identify single atoms involved. This remarkable behaviour is manifest when the atomic coherence of the system, while influenced by environmental interactions that cause dephasing in atoms, persists for a sufficient interval of time. Typical dephasing mechanisms, such as collisions in gases or lattice phonon interactions in crystals, make its experimental observation difficult. A possible solution to this problem is the use of optical crystals doped with rare-earths that are characterized by long and narrow levels lifetimes.
The present state of theoretical and experimental research on collective spontaneous emission (superradiance) in a system of radiators (atoms, molecules, or nuclei) is reviewed. The distinction between superradiance and the amplification of spontaneous emission is discussed. There is also a discussion of conditions under which the effect can be observed and of various theoretical methods for describing superradiance: the quantum single-mode and multimode models and the semiclassical approach. Theoretical papers on superradiance in systems with dimensions smaller than the wavelength of the radiation and also in extended systems are reviewed. It is shown that superradiance may occur in weakly amplifying media. A situation in which the superradiance is oscillatory is described. The possible use of superradiance to generate coherent emission in the x-ray and ? ranges is discussed. The superradiance accompanying Raman scattering of light in atomic and molecular media is studied. The theoretical results are compared with experimental observations of superradiance in the optical range. In an appendix, the nature of the phase transition in a system of radiators interacting through an electromagnetic field is discussed.
We introduce a straightforward quantum-electrodynamic approach to the problem of superradiant spontaneous emission from a system of two-level atoms, and also discuss two classical superradiant systems. The same physical concepts underlie our treatment of both the quantum and classical cases. Explicit expressions are found which describe the time evolution and directional character of the radiated power. Our approach applies to an arbitrary number of atoms which are confined to a region with linear dimensions which may be large compared with the mean wavelength of the emitted radiation. The radiative decay half-life of a large many-atom system is found to be much shorter than the natural lifetime of a single atom, but not as short as the half-life of a small atomic system with the same number of atoms. The far-field radiation pattern appropriate to the case of a circular cylinder of emitters which have been excited by a plane-wave pulse is considered in detail. Polar plots are presented of the radiation patterns produced when the atoms are excited by a plane-wave pulse. Exciting pulses traveling in directions both parallel and at an angle of 10\ifmmode^\circ\else\textdegree\fi{} to the axis of the cylinder are considered. A discussion and generalization of Dicke's "coherence-brightening" criterion is given.