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Exact theory of cooperative spontaneous emission by a concentrated system of two-level atoms: Bethe Ansatz method

V. I. Rupasov, Vladimir I. Yudson

Published Nov 1, 1984• 0 citations
OpenAlex

Abstract

It is shown that a concentrated system of two-level atoms interacting with a quantum electromagnetic field can be described by a one-dimensional, completely integrable model in quantum field theory. Exact multiparticle eigen states of a field+atoms system are found by the Bethe Ansatz method. The eigen states are used to solve the problem of spontaneous decay of the excited state of the atomic subsystem (Dicke superradiance problem).

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An exact analysis of spontaneous emission by a single two level atom in the rotating wave approximation II. Numerical results

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In this paper we investigate the dynamics of a model for a three-level atom in interaction with a radiation field. The exact solution to the spontaneous-emission problem is derived using methods developed earlier by the authors, and expressions are obtained for the probabilities of the atom’s being in the first or second excited states at any time t. For the special case that the strengths of the coupling between each of the excited states and the λth mode of the field are proportional, detailed conclusions can be drawn concerning the effects of such factors as system size, coupling function, and level splitting on the temporal evolution of the system. The evolution of excited quantum systems having one versus two modes of decay to the ground state is also compared, and similarities and differences in the temporal behavior are noted. Finally the relevance of the theory presented in this paper to experimental problems in radiation chemistry and physics is indicated in our concluding remarks.

Journal of Mathematical Physics•Sep 1, 1976•5 citations
It is shown that a concentrated system of two-level atoms interacting with a quantum electromagnetic field can be described by a one-dimensional, completely integrable model in quantum field theory. Exact multiparticle eigen states of a field+atoms system are found by the Bethe Ansatz method. The eigen states are used to solve the problem of spontaneous decay of the excited state of the atomic subsystem (Dicke superradiance problem).
The process of cooperative spontaneous emission in a system of two-level emitters interacting via electromagnetic field is analyzed using the Bogolyubov reduced description method, which provides the possibility of studying the state of the generated field. Field macrostates are described with electric and magnetic field amplitudes and binary correlation functions of their components. Since the previously obtained set of differential equations describing the Dicke system evolution with considering field correlations is very cumbersome, we must find some way of simplifying the model to make it accessible for numerical modeling. The general picture of correlation development can be elucidated with using one- and two-dimensional models. The paper presents the set of evolution equations for Dicke system with fixed orientation of dipole moments of emitters forming a two-dimensional structure. The material equations and equilibrium correlations are discussed. The transition to the Cauchy problem for ordinary differential equations is proposed.
The spontaneous emission of a set of NNN identical two-level atoms interacting with a quantized electromagnetic field is studied. The atoms are assumed to be close together compared to the mean wavelength of the emitted radiation, and their initial state is either a Dicke state or a superposition of the ground and excited state for each atom. Approximate expressions are obtained for transition probabilities, expectation values, and correlations as functions of time. The spontaneous emission for a very large separation of the atoms is also studied. In this case the directional properties of the emitted radiation, as well as the time within which the atoms decay to their ground state, depend on the position of each atom.
Coherent spontaneous emission from a system of NNN two-level atoms interacting with a quantized radiation field is treated for the case in which Dicke's "cooperation number" rrr is macroscopically large. It is shown how to modify the quasiclassical approach to this problem to incorporate quantum effects that are lost in the self-consistent-field approximation. The statistics of the emitted radiation are found to vary markedly with the initial state of the system of atoms. The photon statistics tend to that typical of blackbody radiation when the initial state of the atomic system is that which would result from incoherent pumping ($m\ensuremath{\sim}r$). When, on the other hand, the atoms are initially in a superradiant state ($m\ensuremath{\ll}r$), the emitted radiation may be represented approximately by a coherent state.
The problem of a single two level atom in its excited state, placed in a cavity in which no photons are present initially, and interacting with N modes of the electromagnetic field is solved exactly in the electric dipole, rotating wave approximation. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time dependent wavefunction of the system is given. These quantities are evaluated analytically for N=1,2 and 3, and the time dependent properties of the system for these values of N are investigated and discussed.
In this paper we investigate the dynamics of a model for a three-level atom in interaction with a radiation field. The exact solution to the spontaneous-emission problem is derived using methods developed earlier by the authors, and expressions are obtained for the probabilities of the atom’s being in the first or second excited states at any time t. For the special case that the strengths of the coupling between each of the excited states and the λth mode of the field are proportional, detailed conclusions can be drawn concerning the effects of such factors as system size, coupling function, and level splitting on the temporal evolution of the system. The evolution of excited quantum systems having one versus two modes of decay to the ground state is also compared, and similarities and differences in the temporal behavior are noted. Finally the relevance of the theory presented in this paper to experimental problems in radiation chemistry and physics is indicated in our concluding remarks.