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Physical Review A

Observation of two-photon noise-initiated fluctuations in far-infrared Dicke’s superradiance

Joseph S. Bakos, Damien P. Scherrer, Fritz Kurt Kneubühl

Published Jul 1, 1992• 33 citations
Publisher

Abstract

The anticorrelated fluctuation of the intensity of a driver beam pumping a \ensuremath{\Lambda}-like three-level system in the first transition from the initial to the intermediate level and that of the intensity of the radiation generated in the second transition from the intermediate to the final level initiated by noise is observed in an experimental arrangement designed for the investigation of far-infrared Dicke's superradiance. The fluctuation is interpreted as the result of a two-photon back-and-forth transition between the initial and the final level, emitting (absorbing) and absorbing (emitting) photons in the first and the second transition depending on the direction of the two-photon transition. The influence of this two-photon back-and-forth transition on the Dicke's superradiance is discussed.

DOI
10.1103/physreva.46.410

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The anticorrelated fluctuation of the intensity of a driver beam pumping a \ensuremath{\Lambda}-like three-level system in the first transition from the initial to the intermediate level and that of the intensity of the radiation generated in the second transition from the intermediate to the final level initiated by noise is observed in an experimental arrangement designed for the investigation of far-infrared Dicke's superradiance. The fluctuation is interpreted as the result of a two-photon back-and-forth transition between the initial and the final level, emitting (absorbing) and absorbing (emitting) photons in the first and the second transition depending on the direction of the two-photon transition. The influence of this two-photon back-and-forth transition on the Dicke's superradiance is discussed.
Dicke superradiance, a single-mode burst of radiation emitted by an ensemble of two-level atoms, has garnered tremendous attention within the physics community. Its extension to multi-level systems introduces additional degrees of freedom, such as mode-selective control over well-known Dicke superradiant behaviors. However, previous work on the extension to two-mode superradiance in three-level atoms has been largely overlooked for over five decades. In this study, we revisit the two-mode superradiance model for a Λ-type three-level system, where two modes couple to a common excited state and two separate lower levels, offering new insights. For the first time, we obtain exact numerical solutions of the two-mode rate equations for this model. We analyze the temporal evolution of two-mode intensities, superradiance time delays, and quantum noise in the time domain as the number of atoms varies. We believe this work will enable external mode-selective control over superradiance processes—a capability unattainable in the single-mode case.
Photon statistics are obtained from exact closed-form solutions for both spontaneous and stimulated coherent emissions by a large number of two-level atoms in a Dicke state. Depending on the initial excitation level of the atoms, three types of photon statistics are obtained for the emitted radiation field. Moments of the photon number of the emitted field are calculated in the case of initial atomic coherent states as well as Dicke states, and in the case of n-photon stimulating pulses as well as coherent stimulating pulses. In the particular case of an initial "superradiant" Dicke state stimulated by a coherent-radiation field, the emitted radiation pulse is also fully coherent. In other cases the photon distributions undergo large fluctuations.
Fully excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954 [Phys. Rev. 93, 99 (1954)]. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength $\ensuremath{\lambda}$ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of distant noninteracting atoms with mutual separations much larger than $\ensuremath{\lambda}$. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.
Superradiance has been observed in the far infrared on a pure-rotational transition in optically pumped methyl fluoride. Observed behavior included single pulses, shot-to-shot fluctuation, dependence on the pump pulse length, preferential polarization, and longitudinally asymmetric emission (the onset of swept-gain superradiance). A numerical solution of the Maxwell-Bloch equations including degeneracy, Doppler broadening, and population and polarization source terms, and taking into account all the transitions which might possibly contribute, produces results which agree well with the observations. To do this, only a single free parameter is used; this is a factor of about 10 multiplying the expected initial tipping angle (which is of the order of ${N}^{\frac{\ensuremath{-}1}{2}}$).