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Journal of the Optical Society of America B

Interaction of two two-level atoms with a single-mode squeezed field

Lei Xu, Zhiming Zhang, Jin-lin Chai

Published May 1, 1991• 16 citations
Publisher

Abstract

The N-photon interaction of two two-level atoms with a single-mode quantized radiation field is studied. The general expression for the state vector of the atom–field system is presented with the probability amplitudes in analytic form. For the initial condition in which the atoms are both at their upper levels and the field is in a squeezed state, we study the time evolution of the atomic population inversions and that of the statistics of the field. We find that the ratio of the two coupling constants, the initial squeezing of the field, and N have significant effects on the features of the atoms and of the field.

DOI
10.1364/josab.8.001157

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The quatum statistical properties of two-photon radiation from two-level atomic system are investigated by using complete set in the nth subspace of generalized Jaynes-Cummings hamiltonian, and the general expression for field variance is obtained. The conditions for optimum squeezing as well as the optimum squeezed quantity are found out for an arbitrary initial state, and the time evolution of the optimum squeezed state is then analysed. As an example, the squeezing in an initial state with bare atomic system in thermal equilibrium is discussed, which demonstrates the dependence of squeezing on several parameters, such as, temperature, detuning, coupling strength. The conditions for squeezing are given analytically and numerically. Finally, the physical picture of the squeezing is pointed out.

Acta Physica Sinica•Jan 1, 1988•2 citations
The N-photon interaction of two two-level atoms with a single-mode quantized radiation field is studied. The general expression for the state vector of the atom–field system is presented with the probability amplitudes in analytic form. For the initial condition in which the atoms are both at their upper levels and the field is in a squeezed state, we study the time evolution of the atomic population inversions and that of the statistics of the field. We find that the ratio of the two coupling constants, the initial squeezing of the field, and N have significant effects on the features of the atoms and of the field.
The interaction between the pair of cold two-level atoms and the single-mode cavity field is investigated. The two-level atoms in the pair are supposed to be indistinguishable. This problem generalizes the two-photon Jaynes-Cummings model of a single two-level atom interacting with the squeezed vacuum. The model of the pair of indistinguishable two-level atoms is equivalent to the problem of the equidistant three-level radiator with equal dipole moment matrix transition elements between the adjacent energy levels. Supposing that at the initial moment the field is in the squeezed vacuum state we obtain the exact analytical solution for the atom-field state-vector. By using this solution the quantum-statistical and squeezing properties of the radiation field are investigated. The obtained results are compared with those for the single two-level atom system. We observe that in the model of the pair of cold two-level atoms the exact periodicity of the squeezing revivals is violated by the analogy with the single two-level atom one.
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.
We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-resonant quantized field. The atomic levels are coupled by the multiphoton transitions and the coupling constants between the field and the atomic levels are supposed to be intensity dependent. We find the exact solution for the state vector describing the dynamics of the atom-plus-field system. As an illustration we use the model for studying (i) the time evolution of the atomic occupation probability with the initially coherent field and (ii) the light squeezing, when the cavity field is initially in the vacuum state and the atom is prepared in the atomic ‘coherent state’ (a superposition of atomic states).
The present study described about the interaction of a two level atom and squeezed field with time varying frequency. By applying a sinusoidal variation\nin the frequency of the field, the randomness in population inversion is reduced and the collapses and periodic revivals are regained. Quantum optics is an emerging field in physics which mainly deals with the interaction of atoms with quantised electromagnetic fields. Jaynes-Cummings Model (JCM) is a key model among them, which describes the interaction between a two level atom and a single mode radiation field. Here the study begins with a brief history of light, atom and their interactions. Also discussed the interaction between atoms and electromagnetic fields. The study suggest a method to manipulate the population inversion due to interaction and control the randomness in it, by applying a time dependence on the frequency of the interacting squeezed field.The change in behaviour of the population inversion due to the presence of a phase factor in the applied frequency variation is explained here.This study also describes the interaction between two level atom and electromagnetic field in nonlinear Kerr medium. It deals with atomic and field state evolution in a coupled cavity system. \nOur results suggest a new method to control and manipulate the population of states in two level atom radiation interaction,which is very essential for quantum information processing.We have also studied the variation of atomic population inversion with time, when a two level atom interacts with light field, where\nthe light field has a sinusoidal frequency variation with a constant phase. In both coherent field and squeezed field cases, the population inversion variation is completely different from the phase zero frequency modulation case. It is observed that in the presence of a non zero phase φ, the population inversion oscillates sinusoidally.Also the collapses and revivals gradually disappears when φ increases\nfrom 0 to π/2. When φ = π/2 the evolution of population inversion is identical to the case when a two level atom interacts with a Fock state. Thus, by applying a phase shifted frequency modulation one can induce sinusoidal oscillations of atomic inversion in linear medium, those normally observed in Kerr medium. \nWe noticed that the entanglement between the atom and field can be controlled by\nvarying the period of the field frequency fluctuations. The system has been solved numerically and the behaviour of it for different initial conditions and different susceptibility values are analysed. It is observed that, for weak cavity coupling the effect of susceptibility is minimal. In cases of strong cavity coupling, susceptibility factor modifies the nature in which the probability oscillates with time. Effect\nof susceptibility on probability of states is closely related to the initial state of the system.
The time-evolution of a single two-level atom in a single-mode high-Q cavity is sensitive to the quantum fluctuations of the cavity radiation field and to its photon statistics: this sensitivity is realizable experimentally in the Rydberg atom micromaser. We study the effects of the interaction of a two-level atom with two new non-classical radiation fields: the squeezed number state and the displaced number state realizable by nonlinear and linear transformations of field number states which have an initially precise occupation number. The time-varying field fluctuations caused by the atomic interaction are described using the Q-function quasi-probability.
The quatum statistical properties of two-photon radiation from two-level atomic system are investigated by using complete set in the nth subspace of generalized Jaynes-Cummings hamiltonian, and the general expression for field variance is obtained. The conditions for optimum squeezing as well as the optimum squeezed quantity are found out for an arbitrary initial state, and the time evolution of the optimum squeezed state is then analysed. As an example, the squeezing in an initial state with bare atomic system in thermal equilibrium is discussed, which demonstrates the dependence of squeezing on several parameters, such as, temperature, detuning, coupling strength. The conditions for squeezing are given analytically and numerically. Finally, the physical picture of the squeezing is pointed out.