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Europhysics Letters (EPL)

Correlation Between Counterpropagating Pulses in Superfluorescence

D Jansen, A Stahl

Published Feb 14, 1992• 8 citations
Publisher

Abstract

In superfluorescence (SF) with pencil-shaped excitation volume, two pulses are emitted in opposite directions. While the two pulses are independent in all known gas experiments, they are found to be strongly correlated in some solid-state systems. A model, in which a distributed-feedback (DFB) structure is formed starting from density fluctuations of the SF centres, is shown to explain the correlation between the counterpropagating waves.

DOI
10.1209/0295-5075/18/1/007

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Technical Physics Letters•Jun 1, 2002•0 citations
In superfluorescence (SF) with pencil-shaped excitation volume, two pulses are emitted in opposite directions. While the two pulses are independent in all known gas experiments, they are found to be strongly correlated in some solid-state systems. A model, in which a distributed-feedback (DFB) structure is formed starting from density fluctuations of the SF centres, is shown to explain the correlation between the counterpropagating waves.
Recent experiments on superfluorescence from O 2 - centres in KCl host crystals, with quasi-one-dimensional active volumes, have shown identically shaped and perfectly synchronized forward and backward pulses in each run. This is in blatant contrast to previous experiments on atomic beams and gases in which no forward-backward correlation beyond energy conservation had been found. We argue that a linear coupling due to backscattering from the bulk or the surface of the active volume, a phenomenon much weaker in gases than in solids, is responsible for the effect.
We discuss from first principles the cooperative decay of a system of two-level atoms, initially prepared in an uncorrelated excited state with population inversion NNN, and we give the conditions under which the superfluorescence effect occurs. Describing the atomic system in terms of collective variables, we derive a master equation for the reduced atomic density operator, which gives rise both to a damping and to a time-dependent frequency shift in the dynamics of collective modes. The coupled equations of motion are solved with a self-consistent approach. It is found that the system goes through a nonexponential decay if the maximum length of the active volume is smaller than a "cooperation range" and larger than a "threshold length," in agreement with the one-mode theory. The radiation burst has a time width proportional to ${N}^{\ensuremath{-}1}$, and its intensity is proportional to N2{N}^{2}N2. Specializing to a pencil-shaped volume, we find that only two atomic modes need to be considered; in this case, the average emitted radiation is all condensed in the two diffraction patterns of the opposite axial modes.
Measurements are reported of the quantum fluctuations in superfluorescence delay times. The fluctuations depend strongly on the Fresnel number FFF of the sample. For $F\ensuremath{\approx}1$ fair agreement with recent theories is obtained, while for larger FFF the fluctuations are smaller. A qualitative explanation for this FFF dependence is proposed. No correlation has been found between the delay times of pulses emitted from opposite ends of the same sample.
Recent advances in optical studies of condensed matter systems have led to the emergence of a variety of phenomena that have conventionally been studied in the realm of quantum optics. These studies have not only deepened our understanding of light–matter interactions but have also introduced aspects of many-body correlations inherent in optical processes in condensed matter systems. This paper is concerned with the phenomenon of superradiance (SR), a profound quantum optical process originally predicted by Dicke in 1954. The basic concept of SR applies to a general N body system, where constituent oscillating dipoles couple together through interaction with a common light field and accelerate the radiative decay of the whole system. Hence, the term SR ubiquitously appears in order to describe radiative coupling of an arbitrary number of oscillators in many situations in modern science of both classical and quantum description. In the most fascinating manifestation of SR, known as superfluorescence (SF), an incoherently prepared system of N inverted atoms spontaneously develops macroscopic coherence from vacuum fluctuations and produces a delayed pulse of coherent light whose peak intensity ∝N2. Such SF pulses have been observed in atomic and molecular gases, and their intriguing quantum nature has been unambiguously demonstrated. In this review, we focus on the rapidly developing field of research on SR phenomena in solids, where not only photon-mediated coupling (as in atoms) but also strong Coulomb interactions and ultrafast scattering processes exist. We describe SR and SF in molecular centers in solids, molecular aggregates and crystals, quantum dots, and quantum wells. In particular, we will summarize a series of studies we have recently performed on semiconductor quantum wells in the presence of a strong magnetic field. In one type of experiment, electron-hole pairs were incoherently prepared, but a macroscopic polarization spontaneously emerged and cooperatively decayed, emitting an intense SF burst. In another type of experiment, we observed the SR decay of coherent cyclotron resonance of ultrahigh-mobility 2D electron gases, leading to a decay rate that is proportional to the electron density. These results show that cooperative effects in solid-state systems are not merely small corrections that require exotic conditions to be observed; rather, they can dominate the nonequilibrium dynamics and light emission processes of the entire system of interacting electrons.
Correlation of the parameters (delay times, peak intensities) of counterpropagating superfluorescence pulses is studied within the framework of a one-dimensional theoretical model depending on the sharpness of boundaries of the excitation region. The concentration N 0 of the initially excited active centers is described by a smoothed profile (decaying to zero within the h − and h + wide intervals at the left-and right-hand ends of the sample, respectively), rather than by a rectangular profile. It is established that variation of the excitation region boundary widths h ± does not eliminate the observed correlations. Moreover, the correlations can significantly increase for the samples with a length of L = n λ/2, where n is any natural number and λ is the resonance light wavelength. The oscillating dependence of the parameters of counterpropagating superfluorescence pulses on the h ± values and a significant asymmetry of these pulses for h − ≠ h + are discussed.