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arXiv:1606.00956 · Physics Letters A

Unified quantum density matrix description of coherence and polarization

Bertúlio de Lima Bernardo

Published May 17, 2017• 18 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2017.05.018

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A density-matrix approach is developed to provide a theoretical description of the intensity, angular distribution, and polarization of superradiative emission from an ensemble of many-electron atomic systems. The many-electron atomic systems are described as cooperatively interacting by means of forces that can be long range. Particular emphasis is given to the coherent excitation of the collective atomic-ensemble states, which may be produced by incident laser radiation. The initial excitation and spontaneous emission processes may be described as independent. Both frequency-domain and time-domain formulations of the density-matrix approach are developed. The collective atomic-ensemble states are specified in a detailed hyperfine representation, corresponding to successively coupling the individual hyperfine angular momenta F pertaining to the many-electron atoms. A less detailed fine-structure angular-momentum representation may also be used. In the density-operator approach, account can be taken of the coherent excitation of a particular subspace of the initial atomic-ensemble states. For a comprehensive and unified development of time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations, a reduced-density-matrix (quantum-open-systems) approach is introduced. The non-equilibrium atomic-ensemble-state kinetics and the homogeneous spectral-line shapes can thereby be systematically and self-consistently determined. The collective atomic-ensemble states may be obtained using a variety of different methods. These states can be determined using a dressed-state approach, in which the required states are calculated in the presence of an electromagnetic field.
We present a theoretical study of the evolution of polarization entanglement and quantum coherence in 511 keV photon pairs produced by para-positronium decay during successive Compton scattering events. We start with a maximally entangled Bell state and employ the generalized Stokes-Mueller formalism to derive the two-photon density matrix following single-, double-, and triple-Compton scattering, explicitly considering both polar and azimuthal scattering geometries. Using this framework, we quantify the degradation of quantum correlations through concurrence (as a measure of entanglement) and the l1l_1l1​-norm (as a measure of coherence). Our results demonstrate that entanglement is highly sensitive to the scattering geometry and disappears near right-angle scattering, while quantum coherence remains finite even in regimes where entanglement vanishes completely. These findings provide a unified description of polarization-dependent decoherence in annihilation photon pairs and clarify the distinct roles of entanglement and coherence in realistic two-photon interactions. These results are relevant for quantum-enhanced positron emission tomography and highlight the persistence of quantum resources in scattering-dominated media.
Abstract Despite the enormous technological interest in micro and nanolasers, surprisingly, no class‐B quantum density‐matrix model is available to date, capable of accurately describing coherence and photon correlations within a unified theory. In class‐B lasers—applicable for most solid‐state lasers at room temperature—, the macroscopic polarization decay rate is larger than the cavity damping rate which, in turn, exceeds the upper level population decay rate. Here, a density‐matrix theoretical approach for generic class‐B lasers is carried out, and closed equations are provided for the photonic and atomic reduced density matrix in the Fock basis of photons. Such a relatively simple model can be numerically integrated in a straightforward way, and exhibits all the expected phenomena, from one‐atom photon antibunching, to the well‐known S‐shaped input–output laser emission and super‐Poissonian autocorrelation for many atoms (), and from few photons (large spontaneous emission factors, ) to the thermodynamic limit ( and ). Based on the analysis of , it is concluded that super‐Poissonian fluctuations are clearly related to relaxation oscillations in the photon number. A strong damping of relaxation oscillations with an atom number as small as is predicted. This model enables the study of few‐photon bifurcations and nonclassical photon correlations in class‐B laser devices, also leveraging quantum descriptions of coherently coupled nanolaser arrays.