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Nuclear Physics A

Phase-consistent time development of an ensemble of quantum systems by one-photon emission processes

H. J. Rose

Published Sep 1, 1975• 0 citations
Publisher
DOI
10.1016/0375-9474(75)90528-x

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We study the properties of atom-photon bound states and single-photon cooperative dynamics in a waveguide system which consists of a finite-bandwidth channel with model dispersion and an ensemble of two-level atoms whose size is ignorable when compared with the lattice constant. The bound states are formed by all atoms and a localized photonic excitation. We find that the effect of atomic collection is equivalent to the case of one atom by rescaling the coupling strength with the square root of the atom number, as far as the eigenenergy equation is concerned. Besides, it is found there is a quantum phase transition when more than one type of atom are present. The characteristic lengths and wave functions are analyzed near the phase transition point. The exact analytical results for the cooperative dynamics at the single excitation level are obtained and we point out the dark state in this system leads to a universal population trapping in the time evolution process. This type of trapping obeys a simple law that is only associated with the atom number. A direct conclusion that results from the trapping law is that the single-photon cooperative emission is suppressed when the number of atoms is large enough.
In this work, we consider a quantum memory formed by an ensemble of 3-level atoms to study the emission of light in a Fock state for one and two excitations, exhibiting the superradiant character in these processes. In this setup, a writing laser beam may induce quantum transitions between pairs of levels, leaving either one or two of these atoms excited in an appropriate coherently distributed state across the cloud, thus storing quantum information. After that, a reading laser beam extracts this information in the form of one or two photons, respectively, in a superradiant emission at a specific mode of the electromagnetic field that depends on the details of the stored state. Then, we can certify the quantum nature of light, making sure that a semi-classical approach is inadequate to describe this phenomenon. The central point is the development of an analytical theory for the interaction between atoms and light in this context. We find the beam’s spatio-temporal profile, showing that the modes in which the generated read and write photons are counterpropagating. Following the theory, the two-photon wavepacket is consistent with the profile obtained for two independent photons, each identical to the one achieved for a single superradiant emission. These conclusions match with experimental studies of quantum information storage by a cloud of cold atoms realized by the quantum optics group at UFPE, where we notice a good agreement between theory and experiment. These studies allowed the first characterizations of the superradiant emission of two photons by an atomic ensemble.
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.