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Physical Review A

Squeezing-enhanced and -reduced atomic-level splitting in two-photon dynamics

Weiping Zhang

Published Jun 1, 1990• 3 citations
Publisher

Abstract

In this paper, the two-photon Bloch equations of a two-level atom in broadband squeezed light are derived. On this basis, we discuss two-photon dynamic Stark splitting of atomic levels and the time evolution of atomic variables. The phenomena of squeezing-induced enhancement and reduction of dynamic Stark splitting of the atomic levels and overdamping of atomic time evolution are obtained.

DOI
10.1103/physreva.41.6393

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In this paper, the two-photon Bloch equations of a two-level atom in broadband squeezed light are derived. On this basis, we discuss two-photon dynamic Stark splitting of atomic levels and the time evolution of atomic variables. The phenomena of squeezing-induced enhancement and reduction of dynamic Stark splitting of the atomic levels and overdamping of atomic time evolution are obtained.
The dynamic Stark effect on the dynamical behaviors of atom and squeezed state field in-two-photon processes is studied by a model consisting of an effective two-level atom with multiple levels and quantized field with single mode. The dynamic Stark effect will cause the decreasing of the revival amplitude and the shortening of the period of the atomic Rabi osoillation of inversion, and the increasing the speed of energy exchange of an atom with the field. This is favorable to the enhancement of the photon antibunching and the narrowing of the Poisson distribution of photons. However, it will make the squeezing of field to decrease, even disappear.
In this thesis, we investigate the effect of the dynamical Stark shift on the quantum electrodynamics of an atom undergoing two-photon transitions, interacting with a quantized radiation field in an ideal cavity. To begin with, we discuss the dynamics of the electromagnetic field and the atom in the presence of the Stark shift. We derive closed expressions for the second-order coherence function, quadrature variances, atomic population inversion and dipole squeezing under the approximation of a large initial photon number and coherent or squeezed field input. We show that for an atom initially in the ground state, the inclusion of Stark shift reduces the field squeezing as well as the antibunching. Both the population inversion and the dipole squeezing exhibit phase sensitivity in the presence of Stark shift and for a particular choice of the relative phase of the two atomic levels "trapping" occurs in a two-level atom and the dipole is modified in such a way that it is permanently squeezed. We then discuss the effect of the stark shift on the emission spectrum of an atom and the cavity field spectrum. The inclusion of Stark shift results in asymmetric vacuum field Rabi splitting. We also study the dynamics of the combined atom-field wave function in the presence of the Stark shift and show that both the electromagnetic field and the atom periodically evolve to pure states which are radically different from those in the absence of the Stark shift. Finally, we study the nondegenerate two-photon Jaynes-Cummings model (NTPJCM) in the presence of the Stark shift and show that the dynamics of the NTPJCM in the presence of Stark shift is qualitatively different from the case of the absence of the Stark shift and radically different from the case of degenerate two-photon JCM in the presence of Stark shift.
We analyse the effects of the external coherent radiation and squeezed input on a two-level atom placed in a cavity applying the corresponding master equation. We study the atomic dynamics as well as the squeezing and statistical properties of the cavity radiation by analytically solving the associated differential equations. It is found that the atom stays in the lower energy level more often at steady state irrespective of the strength of the coherent and squeezed input. However, a strong external coherent radiation splits the line of the emission spectrum, whereas the squeezing broadens the width and significantly decreases the height of the spectrum. It is also found that the emitted radiation exhibits photon anti-bunching, super-Poissonian photon statistics and squeezing.
Multiphoton interaction of single-mode squeezed-state light and a two-level atom is considered based on the K-photon Jaynes–Cummings model. Time evolution of quantum fluctuation and photon statistical properties of the initial squeezing light are discussed. It is found that through interaction with a two-level atom, larger squeezing levels cannot be achieved in one-photon or multiphoton processes. For photon antibunching behavior of the light field, it is shown that a smaller initial squeezing level and an appropriately larger coherent part of the initial average photon number of the radiation field favor the generation of this nonclassical behavior, especially in the lower-order interaction processes.
A cavity QED system is analysed which duplicates the dynamics of a two-level atom in free space interacting exclusively with broadband squeezed light. We consider atoms in a three-or four-level Λ configuration coupled to a high-finesse optical cavity which is driven by a squeezed light field. Raman transitions are induced between a pair of stable atomic ground states via the squeezed cavity mode and coherent driving fields. An analysis of the reduced master equation for the atomic ground states shows that a three-level atomic system has insufficient parameter flexibility to act as an effective two-level atom interacting exclusively with a squeezed reservoir. However, the inclusion of a fourth atomic level, coupled dispersively to one of the two ground states by an auxiliary laser field, introduces an extra degree of freedom and enables the desired interaction to be realized. As a means of detecting the reduced quadrature decay rate of the effective two-level system, we examine the transmission spectrum of a weak coherent probe field incident upon the cavity. The extension to multiple atoms is also considered and we show that such a cavity QED system may also duplicate the dynamics of an ensemble of two-level atoms collectively coupled to broadband squeezed light.
The effects of the Stark interaction in the collective radiation of an ensemble of atoms in the field of a broadband electromagnetic field in a squeezed quantum state have been considered. It has been shown that the inclusion of the conditions for the formation of the squeezed field allows one to describe the dynamics of atoms in terms of random quantum creating, annihilating, and counting processes. The latter process is the Stark interaction of atoms and the field and manifests itself in the form of a trigger superradiance pulse generated by an ensemble of identical atoms excited by a quantized resonant squeezed electromagnetic field. The description is based on the kinetic equation derived for an open localized quantum system in a broadband squeezed quantized electromagnetic field. The resulting equation differs from the known ones, but agrees with them in particular and limiting cases.