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Journal of Mathematical Physics

Multipoles and excitons in higher-order coherence

Andrei N. Weiszmann

Published Jun 1, 1980• 1 citation
Publisher

Abstract

Considering the coherence properties of an inelastically scattered quantum radiation by an ensemble of N identical three level atoms in a solid-like array, we addressed the question whether this process is actually mediated by a series of multipole interactions and/or a series of virtual intermediate-exciton transitions and how the type of the considered mediation is reflected in the higher order coherence properties of the scattered radiation. Using a projector technique the reduced field density operator, the atomic and field correlation functions were found, the higher order coherence properties were studied and the arrival-time and phase correlation conditions of the light quanta were obtained and analysed. The results suggest that not only the arrival-time and phase correlation conditions are mathematically independent from the type of the considered mediating process, but that the multipole interaction approximation of a resonant Raman scattering, in the above considered system, is physically equivalent with the virtual intermediate-exciton transitions too.

DOI
10.1063/1.524594

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Considering the coherence properties of an inelastically scattered quantum radiation by an ensemble of N identical three level atoms in a solid-like array, we addressed the question whether this process is actually mediated by a series of multipole interactions and/or a series of virtual intermediate-exciton transitions and how the type of the considered mediation is reflected in the higher order coherence properties of the scattered radiation. Using a projector technique the reduced field density operator, the atomic and field correlation functions were found, the higher order coherence properties were studied and the arrival-time and phase correlation conditions of the light quanta were obtained and analysed. The results suggest that not only the arrival-time and phase correlation conditions are mathematically independent from the type of the considered mediating process, but that the multipole interaction approximation of a resonant Raman scattering, in the above considered system, is physically equivalent with the virtual intermediate-exciton transitions too.
The concept of coherence is analyzed in a system of interacting radiation and matter. Using the projection technique, the reduced field density operator is found, and with it the first and higher order field correlation functions are computed. It is proved that the inelastically scattered field is, for the most part, incoherent in any order at any time interval after collision with an atomic ensemble, except some specific time intervals and positions, where the order of coherence is determined by the atomic correlations considered.
We have studied a mathematical framework of higher-order multipole fields in the vicinity of optical nanoantennas. We have exemplified at suitably chosen Nanoantennas i.e. a Nano antenna which strongly enhances the quadruple field. The modification of excitation rates in quantum mechanical systems due to this quadrupolar enhancement was studied. The hybrid system consisting of an optical Nano antenna and a quantum mechanical three level system was studied in detail. A properly designed Nano-antenna can excite dipole for bidden transitions in three level systems due to the enhanced higher order multipole fields. The dynamics of the system is strongly altered by the presence of the nanoantenna and cannot be done by the quadrupolar enhancement alone. This can be achieved by enhancing higher order multipole fields near the antenna. A quadrupole transition as the dominant excitation channel in a three level system was considered. It was found that the enhancement of this transition significantly intensify subsequent emission processes with respect to altered emission characteristics. The effects depend on geometrical parameters; the properties of the optical nanoantenna can be tailored and hence allowed for direct implementations in spectroscopies schemes. The obtained results were found in good agreement with previously obtained results.
Quantum theoretical treatment of coherent forward scattering of light in a polarized atomic ensemble with an arbitrary angular momentum is developed. We consider coherent forward scattering of a weak radiation field interacting with a realistic multilevel atomic transition. Based on the concept of an effective Hamiltonian and on the Heisenberg formalism, we discuss the coupled dynamics of the quantum fluctuations of the polarization Stokes components of propagating light and of the collective spin fluctuations of the scattering atoms. We show that in the process of coherent forward scattering, this dynamics can be described in terms of a polariton-type spin wave created in the atomic sample. Our work presents a general example of an entangling process in the system of collective quantum states of light and atomic angular momenta, previously considered only for the case of spin-12\frac{1}{2}21​ atoms. We use the developed general formalism to test the applicability of the spin-12\frac{1}{2}21​ approximation for modeling the quantum nondemolishing measurement of atoms with a higher angular momentum.
After the sequence of introductory chapters that collected the necessary tools, we are now ready to discuss complete experiments. The first type of experiment we consider is the creation and detection of order in multilevel atoms through coherent Raman processes. The atoms that we use to study these processes are rare earth ions in a crystal matrix. Enclosing them in a crystal allows long interaction times, but also makes it necessary to consider their interaction with neighbouring atoms. Overview Raman processes Introduction In the preceding chapters, we mentioned several types of Raman processes. Their common feature is a resonant change of the energy of the photons that interact with the material system. The energy of the scattered photons may be lower (Stokes process) or higher (anti-Stokes) than that of the incident photons. The energy difference is transferred to the material system, where it must match an energy level separation. The photon energy itself, however, does not have to match exactly a transition frequency of the medium. This is commonly expressed by the statement that the Raman scattering proceeds through a virtual state, represented by the dashed line in Figure 7.1. The presence of a real state of the atom, indicated by the full line, nevertheless increases the coupling efficiency, as discussed in Chapter 3. The earlier sections on three-level effects and optical anisotropy dealt with the mathematical formalism of Raman processes, using generic level systems to describe them.
The two types of cooperative effects between the converted photons in the multiple steps of Raman lasing are proposed. The first type involves the cooperative process between the photons of one of the steps of Raman conversion. The second cooperative effect appears between the photons belonging to different steps of multiple conversions. This new type of generated coherent state is proposed by novel bimodal entangled sources, which take into consideration both the coherence and collective phenomena between the photons belonging to the system of the bimodal field obtained in multiple Raman emissions. For this, the creation and annihilation operators of the new resonator quasi-particle ware introduced taking into consideration the Hilbert space of field vectors at frequency differences, ωp+1−ωp between the anti-Stokes components of multiple Raman lasing. The application of higher-order multiple Roman bimodal coherent field quantum information is described in accordance with the definition of quantum amplitude and phase of such entangled states of light. The cooperative properties of the bimodal field in the multiple scattering processes of Raman lasing in the cavity/fiber and its interaction with ensemble of atoms prepared in coherent state are proposed. We introduced the new characteristics of bi-modes field in which the multiple Raman scattering takes into consideration the interaction with coherent excitation and non-stationary quantum fluctuations of the generation rate of the introduced quasi particles. Here, we represent the rate moments through the annihilation and generation operators of the cavity quasi-parties.
Summary form only given. Effects of exciton-exciton correlations (e.g. bound biexciton, exciton-exciton scatterings) have been amply demonstrated in the /spl chi//sup (3)/ contributions to experiments measuring the interband polarization in semiconductor quantum wells. Increasing attention is currently being focussed on higher order excitonic correlation effects. One higher-order quantity is the incoherent exciton density (defined as total exciton density minus the interband polarization squared) which is created by excitons scattering each other out of the coherent component. Other than its role in the dephasing and relaxation of the system, the incoherent exciton density has not received much attention. In this contribution, we present results of our theoretical study on the behavior of this quantity and related correlation functions under conditions that inhibit relaxation. Our theory follows the general formulation of bosonic theories for excitons: the basic degrees of freedom are exact bosons, and the fermionic exchange effects are incorporated into the boson-boson and boson-photon effective Hamiltonians. We truncate the effective interaction at the two-boson level. No formal bosonization procedure is used: the matrix elements of our effective Hamiltonian are chosen in such a way that in the coherent /spl chi//sup (3)/ limit, our boson theory yields formally identical results as the standard fermionic dynamics controlled truncation formalism. Standard many-body techniques are used to derive equations of motion for densities, correlation functions, and measurable quantities such as the interband polarization.