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数理解析研究所講究録

Jaynes-Cummings modelに対するエントロピー及び相互エントロピーの計算 (量子確率論とエントロピー解析)

茂 古市

Published Oct 1, 1998• 0 citations
OpenAlex

Abstract

は Jaynes-Cummings モデルのハミルトニアンについて簡単に述べ, 第 4 節では そのハミルトニアンからユニタリ作用素を導く.第 $\iota 5$ 節ではこのユニタリ作用 素を使って, 従来, 原子のダイナミックスを調べる尺度となっている, 遷移確 率を計算し, これを用いて Jaynes-Cuumings モデルの物理的性質を論じる

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は Jaynes-Cummings モデルのハミルトニアンについて簡単に述べ, 第 4 節では そのハミルトニアンからユニタリ作用素を導く.第 ι5\iota 5ι5 節ではこのユニタリ作用 素を使って, 従来, 原子のダイナミックスを調べる尺度となっている, 遷移確 率を計算し, これを用いて Jaynes-Cuumings モデルの物理的性質を論じる
Abstract The aim of this work is to show how supersymmetric (SUSY) quantum mechanics can be applied to the Jaynes–Cummings (JC) Hamiltonian of quantum optics. These SUSY transformations connect pairs of Jaynes–Cummings Hamiltonians characterized by different detuning parameters as well as Jaynes–Cummings to anti-Jaynes–Cummings Hamiltonians. Therefore, JC Hamiltonians can be classified in hierarchies or sequences which are connected through SUSY transformations. As a byproduct, the symmetries of JC Hamiltonians are found as well as the special case of a sequence of resonant-like interacting systems having the form of a simple shape invariant JC Hamiltonian hierarchy.
The supersymmetric connection that exists between the Jaynes-Cummings (JC) and anti-Jaynes Cummings (AJC) models in quantum optics is unraveled entirely. A new method is proposed to obtain the temporal evolution of observables in the AJC model using supersymmetric techniques, providing an overview of its dynamics and extending the calculation to full photon counting statistics. The approach is general and can be applied to determine the high-order cumulants given an initial state. The analysis reveals that engineering the collapse-revival behavior and the quantum properties of the interacting field is possible by controlling the initial state of the atomic subsystem and the corresponding atomic frequency in the AJC model. The substantial potential for applications of supersymmetric techniques in the context of photonic quantum technologies is thus demonstrated. Published by the American Physical Society 2024