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Quantum Optics Journal of the European Optical Society Part B

The problem of propagation in quantum optics, with applications to amplification, coupling of EM modes and distributed feedback lasers

M Toren, Y. Ben-Aryeh

Published Oct 1, 1994• 38 citations
Publisher

Abstract

Theoretical methods for treating propagation in quantum optics are developed, in which the momentum operator is used in addition to the Hamiltonian. A quantum mechanical analysis is given for various physical systems which include amplification and coupling between electromagnetic modes. A quantum mechanical theory for distributed feedback lasers (DFBL) is described.

DOI
10.1088/0954-8998/6/5/006

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Theoretical methods for treating propagation in quantum optics are developed, in which the momentum operator is used in addition to the Hamiltonian. A quantum mechanical analysis is given for various physical systems which include amplification and coupling between electromagnetic modes. A quantum mechanical theory for distributed feedback lasers (DFBL) is described.
Starting with the canonical quantization procedure for the electromagnetic field inside an effective (linear or nonlinear) medium, we present a direct-space formulation of the theory of quantum optics. This approach does not use the conventional modal decomposition of the field, but relies on the electromagnetic momentum operator defined in terms of local electric- and magnetic-field operators. The momentum operator contains all the information on the spatial characteristics of the field, and can describe the translation of a short light pulse in a nonlinear medium, without a modal analysis of the pulse. Propagation is described through an operatorial wave equation that relates the temporal evolution of an electromagnetic pulse to its spatial progression. Through this equation, the direct-space approach to quantum optics can treat traveling-wave nonlinear-optical phenomena and, at the same time, account for their quantum statistics. The theory is applied to squeezed-light generation by the parametric down-conversion of a short laser pulse, as an illustration.
A quantum mechanical analysis of the propagation of coupled modes in integrated optical waveguides is given. The modal orthonormalization property on a cross-section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time symmetry are taken into account to derive the quantum momentum operator and Heisenberg's equations giving a quantum-consistent formulation of the coupled mode propagation as a function of forward and backward creation and annihilation operators.
The amplification of electromagnetic fields is analyzed in a quantum-mechanical context by discussing the behavior of a simple theoretical model of the parametric amplifier. The statistical properties of the amplifier fields are described by means of the time-dependent density operator for the system. In doing this, extensive use is made of the coherent states and the PPP representation of the density operator, which provide a quantum-mechanical description of the fields closely resembling their classical description. Explicit solutions are obtained for the density operator for either of the two field modes for a variety of initial states of the modes. Initial states considered include combinations of coherent states, chaotic mixtures, and nnn-quantum states. Particular attention is given the behavior of the amplifier fields in the limit of large amplification. The conditions are established under which the amplification process leads in this limit to the existence of a non-negative PPP representation for the density operator for a single mode of oscillation.
The subject of this book is based on the compulsory course "Quantum Optics and Lasers" of the Department of "Solid State Physics" of the Faculty of Physics of the Natural Sciences School of the National and Kapodistrian University of Athens. 1. Introduction to the quantum nature of light. 2. Mechanisms of interaction of electromagnetic (EM) radiation and matter (two-level system). 3. Semiclassical approach of the interaction of EM radiation and matter. EM field: classically. Two-level system e.g. atom: quantum mechanically. 4. Quantum mechanical approach of the interaction of EM radiation and matter. EM field quantization. 5. Lasers. 6. Density matrix. 7. Some other issues for the properties and the operation of Lasers.
This paper gives a unified approach to feedback control theory of quantum mechanical systems of bosonic modes described by noncommutative operators. A quantum optical closed-loop, including a plant and controller, is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view, in order to facilitate the use of control theory in microscopic world described by quantum theory. In particular, an input-output description of quantum mechanical systems which is essential in describing the behavior of the feedback systems is fully formulated and developed. This would then provide a powerful tool for quantum control and pave an avenue that connects control theory to quantum dynamics. This paper is divided into two parts. The first part is devoted to the basic formulation of quantum feedback control via quantum communication and local operations on an optical device, cavity, that can be regarded as a unit of quantum dynamics of bosonic modes. The formulation introduced in this paper presents the feature intrinsic in quantum feedback systems based on quantum stochastic differential equations. The input-output description provides a basis for developing quantum feedback control through the transfer function representation of quantum feedback systems. In the follow-up paper, the quantum mechanical representation of feedback is further elaborated to yield the control theoretical representation of fundamental notions of quantum theory, uncertainty principle, e.g., and some applications are presented.