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Modern Physics

Geometric Phase in an Imaginary Photon Process

元新 乔

Published Jan 1, 2017• 1 citation
Publisher

Abstract

利用Lewis-Riesenfeld不变量理论，研究了推广的含时二能级虚光子过程的 Jaynes-Cummings模型。发现周期情况下的几何相位与光子场的频率、光子和原子之间的耦合系数以及原子跃迁频率无关。 By using the Lewis-Riesenfeld invariant theory, we have studied the geometric phase in a generalized time-dependent Jaynes-Cummings model with imaginary photon process for two-level atoms interacting with light field. It is found that the geometric phase in a cycle case has nothing to do with the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency.

DOI
10.12677/mp.2017.74016

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利用Lewis-Riesenfeld不变量理论，研究了推广的含时二能级虚光子过程的 Jaynes-Cummings模型。发现周期情况下的几何相位与光子场的频率、光子和原子之间的耦合系数以及原子跃迁频率无关。 By using the Lewis-Riesenfeld invariant theory, we have studied the geometric phase in a generalized time-dependent Jaynes-Cummings model with imaginary photon process for two-level atoms interacting with light field. It is found that the geometric phase in a cycle case has nothing to do with the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency.
By using the Lewis Riesenfeld invariant theory,we have studied the dynamical and the geometric phases in a generalized time-dependent Λ-type Jaynes-Cummings model with imaginary photon process.We find that the geometric phases in a cycle case have nothing to do with the frequency of the photon field,the coupling coefficient between photons and atoms,and the atom transition frequency.If we use the more accuracy device,the geometric phase in the imaginary photon process may be observed,and the geometric phases in this process have the observable physical effect.
By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent Λ-type Jaynes–Cummings model. We find that, compared with the dynamical phases, the geometric phases in a cycle case are independent of the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. It is pointed out that the geometric phases in a cycle case can be measured under the case of a stronger time-dependent photon field and a stronger coupling photon-atom system. On the other hand, the geometric phases of the model may be measured in the composition of cold atoms.
通过使用Lewis-Riesenfeld不变理论，已经研究了具有双模运算符和相位运算符的广义Jaynes-Cummings模型中的几何相位。与动力学相位相比，一个周期情况下的几何相位与双光子场的频率无关，光子和原子之间的耦合系数以及原子跃迁频率。显然，几何相具有纯几何和拓扑特征，这意味着几何相位代表了厄米线性束中的和乐。 By using the Lewis-Riesenfeld invariant theory, the geometric phase in a generalized Jaynes-Cummings model with double mode operators and phase operators has been studied. Compared with the dynamical phase, the geometric phase in a cycle case is independent of the frequency of the double photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. It is apparent that the geometric phase has the pure geometric and topological characteristics, which means that the geometric phase represents the holonomy in the Hermitian linear bundles.
An approach to exact quantum solutions of the time-dependent two energy level Jaynes–Cummings model with an imaginary photon process is represented in this work. The Lewis–Riesenfeld invariant treatment and the unitary transformation method are used for this purpose. The original Schrödinger equation is reduced to an equivalent solvable one through unitary transformations by using suitable unitary operators. The reduced equation corresponds to a simpler Hamiltonian which is written as a linear combination of the generators of the reduced-dimensional SU(2) algebra. A Hermitian invariant operator is constructed based on the same algebraic formulation and its instantaneous eigenfunctions are obtained. By utilizing such eigenfunctions, the complete quantum wave functions of the system are evaluated. Such wave functions are necessary when we analyze the quantum characteristics of the system.
通过使用Lewis-Riesenfeld不变量理论，我们研究了超导量子位的量子相干可调耦合中的几何相位。发现几何相位与隧道分裂，直流能量偏置和HF信号等无关。这一结果对量子计算有一定的意义。 By using the Lewis-Riesenfeld invariant theory, we have studied the geometric phase in a quantum coherent tunable coupling of superconducting qubits. The geometric phase has nothing to do with the tunnel splitting, but also the dc energy bias and the HF signal. This result has certain significance to the quantum computation.
通过使用Lewis-Riesenfeld不变量理论，我们研究了大约瑟夫逊结量子比特中拉比振荡的几何相位。发现几何相位与偏置电流的直流和微波脉冲无关，也与微波的转换频率无关。 By using the Lewis–Riesenfeld invariant theory, we have studied the geometric phase of Rabi oscillations in a large Josephson-junction qubit. The geometric phase has nothing to do with the dc and microwave pulses of bias current, and is independent of the transitions frequencies of microwaves.