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Annual Meeting Optical Society of America

Interaction of a three-level atom with squeezed light

Reeta Vyas, Surendra Singh

Published Jan 1, 1989• 0 citations
Publisher

Abstract

Dynamics of a three-level atom interacting with one- and two-mode radiation fields is studied when the initial state of the field is a squeezed coherent state. All the three types of level configurations cascade; V and Lambda are considered. A model similar to the Jaynes-Cumming type developed by Yoo and Eberly1 is used. Various parameter ranges including the one in which the photon number distribution for the squeezed state exhibits oscillatory behavior2 are considered. Interesting revival structures are seen. Curves are presented to illustrate the behavior.

DOI
10.1364/oam.1989.thii3

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Dynamics of a three-level atom interacting with one- and two-mode radiation fields is studied when the initial state of the field is a squeezed coherent state. All the three types of level configurations cascade; V and Lambda are considered. A model similar to the Jaynes-Cumming type developed by Yoo and Eberly1 is used. Various parameter ranges including the one in which the photon number distribution for the squeezed state exhibits oscillatory behavior2 are considered. Interesting revival structures are seen. Curves are presented to illustrate the behavior.
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.
The Jaynes–Cummings interaction of a two-level atom with the radiation field is studied when the radiation is initially in a strongly squeezed coherent state. The dynamic response of the atomic inversion shows echoes after each revival when the squeezed coherent state exhibits an oscillatory photon-counting distribution due to the phase-space interference effect. The sensitivity of the dynamic behavior to approximations used in computing the atomic inversion is discussed. Comparison is made with the intensity-dependent interaction model of Buck and Sukumar [ Phys. Lett.81A, 132 ( 1981)]; this model does not exhibit echoes. The mean, variance, and entropy for the photon-number distribution are calculated and found to show behavior similar to that of the atomic inversion.
The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of the radiation field is investigated, as the state of the field is gradually changed from a coherent state to a squeezed coherent state. The effect of mild squeezing on the coherent light is shown to be striking: the photon number distribution gets localized and it peaks maximally for a particular value of squeezing. The atomic inversion retains its structure for a longer time. The mean linear entropy shows that the atom has a tendency to get disentangled from field within the collapse region and also in the revival region, for mild squeezing. These properties are absent for the case of a coherent state or for an excessively squeezed coherent state. We also elucidate a connection between these properties and the photon statistics of the mildly squeezed coherent state; these states have the minimum variance and are also maximally sub-Poissonian.
We investigate some of the fundamental features of the interaction of squeezed light with two-level atoms in the framework of the Jaynes-Cummings model. We start our analysis by calculating the collapses and revivals of the atomic inversion. We discuss the degree of purity of the field (given by the entropy) and its disentanglement from the atomic source. The connection with the evolution of the Q-function is also made. We notice that contrary to the coherent state case, the field turns into a nearly pure (squeezed) state at the revival time as if the field was prepared in a coherent state. The field also becomes a superposition of squeezed states at half of the revival time, and this is confirmed by investigating the photon number distribution. The phase properties of the field are discussed using the Pegg-Barnett formalism.
When the displacement and squeeze parameters for a squeezed coherent state are chosen appropriately, the squeezed state has an oscillatory photon number distribution P(n). Schleich and Wheeler1 have shown that the oscillations arise from the interference between contributions to P(n) from two regions in phase space where an elongated error ellipse, characterizing the squeezed coherent state, overlaps the annuli characterizing the number states. We study the Jaynes-Cummings model for the interaction of a two-level atom with a single mode of the radiation field when the radiation field is initially in such a squeezed coherent state. Revivals of the atomic inversion occur which have a quite different appearance from those produced when the radiation field is initially In a coherent state.2 Each revival is followed by a series of echoes—a phenomenon we call ringing revivals. We discuss the relationship between these echoes and the oscillations in P(n). There is a one-to-one correspondence between echoes and the peaks in P(n); however, interference between the contributions to the inversion from different peaks in P(n) plays an important role in forming the ringing structure of the revivals.
Quantum-statistical properties such as the photon-number probability distribution and sub-Poissonian distribution are studied by considering the resonant interaction of two radiation fields, one of which is in a squeezed state with a cascade-structure three-level atom. It is noteworthy to emphasize that the direction of squeezing, i.e., the angle \ensuremath{\theta}, and the squeezing parameter r as well as the initial atomic state play important roles in the determination of the nonclassical behavior of the radiation field. At the same time we give a possible explanation for the effect of the ratio of the intensity of the two fields on the quantum-statistical properties.