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arXiv:1512.08607

Photon Emission Dynamics of a Two-Level Atom in a Cavity

Chang Jae Lee

Published Dec 29, 2015• 0 citations
arXivHTMLPDF

Abstract

The collapse and revival of quantum states appear in diverse areas of physics. In quantum optics the occurrence of such a phenomena in the evolution of an atomic state, interacting with a light field initially in a coherent state, was predicted by using the Jaynes-Cummings model (JCM), and subsequently demonstrated experimentally. In this paper we revisit the JCM with the Monte-Carlo wave function approach and investigate the time evolution of the photon emission rate of the atom in a cavity. Analytical and numerical quantum trajectory calculations show that the cavity and the initial field statistics strongly influence the photon emission dynamics. A coherent field indeed gives rise to a collapse and revival behavior that mirrors atomic state evolution. However, there are differences between the two. The emission rate for a field in a Fock number state exhibits a sinusoidal oscillation, and there exists a quiescent period for a thermal field. These properties are quite different from those in free space. It is also shown that the fluctuation in photon emission is much less than that of the atomic population.

DOI
10.48550/arxiv.1512.08607

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The collapse and revival of quantum states appear in diverse areas of physics. In quantum optics the occurrence of such a phenomena in the evolution of an atomic state, interacting with a light field initially in a coherent state, was predicted by using the Jaynes-Cummings model (JCM), and subsequently demonstrated experimentally. In this paper we revisit the JCM with the Monte-Carlo wave function approach and investigate the time evolution of the photon emission rate of the atom in a cavity. Analytical and numerical quantum trajectory calculations show that the cavity and the initial field statistics strongly influence the photon emission dynamics. A coherent field indeed gives rise to a collapse and revival behavior that mirrors atomic state evolution. However, there are differences between the two. The emission rate for a field in a Fock number state exhibits a sinusoidal oscillation, and there exists a quiescent period for a thermal field. These properties are quite different from those in free space. It is also shown that the fluctuation in photon emission is much less than that of the atomic population.
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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.
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The absorption and the emission of photons by an atom involves quantum jumps between states. We investigate the quantum jump statistics for the system of a two-level atom and a single-mode cavity field. We use the Jaynes-Cummings model for this problem, perform Monte Carlo numerical simulations, and give a detailed exact analysis on these simulations. These studies reveal that the waiting-time distribution (WTD) for photon absorptions (emissions) has a unique novel statistic, and that the photon absorption (emission) rate is not uniform, but counter-intuitively depends on the position in the Rabi cycle. The effects of the nonclassical nature of the field on the WTD is discussed.
A two-level system driven by a classical single frequency field in rotating-wave approximation is a basic model for resonance in quantum optics. The probability of making a transition depends sinusoidally on time with a characteristic frequency called the Rabi frequency. The Jaynes-Cummings model (JCM) consists of a two-level atomic system driven by a single quantized electromagnetic field mode. The field entropy in the case of an atom interacting with an initially coherent field is expected to reflect the collapse and revival of Rabi oscillations. The photon statistics of the JCM are examined and the entropy concepts are used to describe the apparently disordered collapses. A density matrix method is used to describe the influence of photon statistics in the JCM. The quantum generalization defines entropy through where the trace is taken over a convenient basis set. The thermal field JCM shows enhanced photon variances as expected for an initially Bose-Einstein field with large fluctuations.