Gauge-invariant boundary conditions in Euclidean quantum gravity can be obtained by setting to zero at the boundary the spatial components of metric perturbations, and a suitable class of gauge-averaging functionals. This paper shows that, on choosing the de Donder functional, the resulting boundary operator involves projection operators jointly with a nilpotent operator. Moreover, the elliptic operator acting on metric perturbations is symmetric. Other choices of mixed boundary conditions, for which the normal components of metric perturbations can be set to zero at the boundary, are then analysed in detail. Lastly, the evaluation of the 1-loop divergence in the axial gauge for gravity is obtained. Interestingly, such a divergence turns out to coincide with the one resulting from transverse-traceless perturbations.
This paper shows that it is theoretically possible for a medium to generate two copies of an incoming probe pulse as a result of the successive action of two control pulses under conditions of electromagnetically induced transparency. The medium is treated in the model of two-level atoms with threefold degeneration of the lower level (tripod configuration). The three laser-radiation pulses differ in polarization, and the propagation directions of the probe pulse and the two control pulses are orthogonal. The calculation uses a semiclassical approach, the slow-amplitude approximation, and the fixed-field approximation of the control pulses.
The general expression of the output-light Mandel parameter out 5 obtained in case of purely absorptive bistability, for arbitrary value of of incident light (theparameter measures the deviation of the photon-flow statistics from Poisson statistics). Calculations are based on stochastic rate equations. No adiabatic elimination of atomic variables is made; the coherent nature of "incoming" of incident photons into a cavity is correctly taken into account. On condition of bistability, although the strongly sub-Poisson input-photon statistics ( = -1) generally reduces the output noise as compared to the case of coherent input ( = 0), the inequality tout > 0 still holds near the switching points.
For the known, experimentally realised conditions', the detailed analysis of the field-induced transparency and formation of exceptionally low group velocity of probe light is performed. The secondary fields being due to the atomic polarization induced by the two propagating light pulses -coupling (or dressing) and probe ones, resonant to the adjoining transitions in a three-level scheme, are explicitly taken into account. Partly linear (relative to the probe pulse field) and completely non-linear regimes are considered. Particularly, the outputting coupled wave is shown to be slightly amplified, when the probe light pulse "disappears" inside the medium.
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