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Journal of Modern Optics

Photon Conversion among Multichromatic Waves in Two-level Atom Systems

Y.B. Xie

Published Nov 1, 1995• 6 citations
Publisher

Abstract

In this paper, we shall discuss a generalized version of the Jaynes-Cummings model in which a two-level atom is coupled to multichromatic waves with general frequencies and coupling constants. We shall show that this two-level atom system can be mapped into an effective model in which a quantum particle moves in a lattice whose sites specify the number of photons in the multichromatic waves. In general, when the number L of modes is greater than two, large energy exchanges among different monochromatic waves are possible (L = 2 is a special case; exchanges of a large number of photons are possible only for degenerate modes). Depending on the frequencies of the elecromagnetic modes, we can classify the two-level systems in two categories. In one case, the eigenfunctions of the quantum particle are extended and thus exchange of a large number of photons is possible. In the other case, the eigenfunctions of the quantum particle are localized and exchange of a large number of photons is greatly suppressed.

DOI
10.1080/09500349514551941

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In this paper, we shall discuss a generalized version of the Jaynes-Cummings model in which a two-level atom is coupled to multichromatic waves with general frequencies and coupling constants. We shall show that this two-level atom system can be mapped into an effective model in which a quantum particle moves in a lattice whose sites specify the number of photons in the multichromatic waves. In general, when the number L of modes is greater than two, large energy exchanges among different monochromatic waves are possible (L = 2 is a special case; exchanges of a large number of photons are possible only for degenerate modes). Depending on the frequencies of the elecromagnetic modes, we can classify the two-level systems in two categories. In one case, the eigenfunctions of the quantum particle are extended and thus exchange of a large number of photons is possible. In the other case, the eigenfunctions of the quantum particle are localized and exchange of a large number of photons is greatly suppressed.
In this paper, we shall examine a generalized version of the Jaynes-Cummings model in which a two-level atom moves in a lossless cavity and is coupled to multichromatic waves with general frequencies and coupling constants. We shall show that both the motion of the atom and the photon conversion between multichromatic waves are dynamically correlated. Using the semiclassical approximations introduced in a previous paper, we obtain the equations which describe the dynamics of this quantum system and discuss the solutions in several special cases. In particular, we point out that the motion of the atom may be controlled by the electromagnetic modes, and vice versa, that is the amplitudes and phases of the electromagnetic fields in the cavity may also be determined by the position of the atom.
If a two-level atom is in the two-photon resonance with a quantized mode and simultaneously inter-acts with a quasi-resonance classical field, then a photon exchange is observed in this system between the quantized and classical modes. It is demonstrated that such a physical system can serve as a source of squeezed radiation in the quantized mode. The squeezing can be arbitrarily close to unity, while the radiation amplitude can be relatively large. A situation is discussed when N atoms are in the two-photon resonance with a quantized mode and simultaneously interact with a classical field. The phenomenon of exponential superradiation is described when the number of photons in the quantized mode exponentially depends on the number N of atoms.
A classical realization of the Jaynes-Cummings (JC) model, describing the interaction of a two-level atom with a quantized cavity mode, is proposed based on light transport in engineered waveguide superlattices. The optical setting enables us to visualize in Fock space dynamical regimes not yet accessible in quantum systems, providing new physical insights into the deep strong coupling regime of the JC model. In particular, bouncing of photon number wave packets in Hilbert space and revivals of populations are explained as generalized Bloch oscillations in an inhomogeneous tight-binding lattice.
The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically simulates the interaction of a single two-level system with a quantized field under field nonlinearities and nonlinear couplings as long as the quantum optics model conserves parity. We describe how to reconstruct the mean value of quantum optics measurements, such as photon number and atomic energy excitation, from the intensity and from the field, such as von Neumann entropy and fidelity, at the output of the photonic lattices. We discuss how typical initial states involving coherent or displaced Fock fields can be engineered from recently discussed Glauber-Fock lattices. As an example, the Buck-Sukumar model, where the coupling depends on the intensity of the field, is classically simulated for separable and entangled initial states.
An extension of the standard one-photon as well as the two-photon Jaynes-Cummings (JC) model has been done to include transient effects due to a modulation of the atom-field coupling coefficient. An explicit time dependence is given for the case of a linear sweep of the coupling parameter. We have shown the effects of such a sweep on the dynamical evolution of a two-level atom undergoing a one- or two-photon process in a single nondecaying mode of the field in a coherent state. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated and are found to be both qualitatively as well as quantitatively different from the standard JC models.