# 物理代写|热力学代写thermodynamics代考|NEM2201

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## 物理代写|热力学代写thermodynamics代考|Photon Interactions with Optical Phonons

The interaction of optical phonons with photons is appreciable when the frequencies and wave vectors of both coincide, which signifies the crossover of the dispersion relation for photons, $\omega=c k$, and the dispersion relation for an optical phonon branch.

This crossover is found by simultaneously solving the Maxwell equations for the electric field of the light and the equations for the medium polarization induced by the lattice displacement (phonon field), which is, in turn, driven by the light field. The resulting solutions express the hybridization of photon and phonon modes, characterized by the polarization dispersion. In particular, in an ionic crystal with two ions per primitive cell, the dispersion relation is
$$\omega^{2}=\frac{\omega_{\mathrm{t}}^{2} \epsilon_{0}+c^{2} k^{2}}{2 \epsilon_{\infty}} \pm\left[\frac{\left(\omega_{\mathrm{t}}^{2} \epsilon_{0}+c^{2} k^{2}\right)^{2}}{4 \epsilon_{\infty}^{2}}-\frac{\omega_{\mathrm{t}}^{2} k^{2} c^{2}}{\epsilon_{\infty}}\right]^{1 / 2}$$
As $k \rightarrow 0$, the polaritonic frequencies reduce to
$$\omega^{2}=\omega_{\mathrm{t}}^{2}\left(\epsilon_{0} / \epsilon_{\infty}\right)=\omega_{1}^{2}$$
and
$$\omega^{2}=\left(c^{2} / \epsilon_{0}\right) k^{2} .$$
Each of these solutions has double degeneracy, associated with two independent directions of the electric field $\boldsymbol{E}$ in the plane normal to $\boldsymbol{k}$. For high $\boldsymbol{k}$, the dispersion has two branches,
$$\omega^{2}=c^{2} k^{2} / \epsilon_{\infty} ; \quad \omega^{2}=\omega_{\mathrm{t}}^{2} .$$

## 物理代写|热力学代写thermodynamics代考|Cold-Atom Optical-Polariton Baths

We consider a medium composed of cold alkali atoms with level configuration as shown in Figure 3.6.

The atoms, taken to be optically pumped to the ground states $|b\rangle$, resonantly interact with a running-wave classical field that drives the atomic transition $|c\rangle \rightarrow|a\rangle$ with the Rabi frequency $\Omega_{\mathrm{d}}$. Near the two-photon (Raman) resonance
$|b\rangle \rightarrow|c\rangle$, the atomic medium then becomes transparent through an effect known as electromagnetically induced transparency (EIT) for a weak (quantum) signal field $\hat{\mathcal{E}}$ that acts on the transition $|b\rangle \rightarrow|a\rangle$.

A classical signal pulse of duration $t_{\mathrm{s}}$ in the atomic medium, under EIT conditions, is slowed down to group velocity $v_{\mathrm{s}}$ and spatially compressed, by a factor of $v_{\mathrm{s}} / c \ll 1$, to the length $z_{\mathrm{loc}} \approx v_{\mathrm{s}} t_{\mathrm{s}}$. In a medium of length $L$, such that $z_{\mathrm{loc}}<L$, the signal pulse is converted into a standing-wave polaritonic excitation (Fig. 3.6), provided the driving field is adiabatically switched off and the signal pulse is stopped in the medium. The atoms then dispersively interact with a standing-wave classical field having the Rabi frequency $\Omega_{\mathrm{s}}(z)=2 \Omega_{\mathrm{s}} \cos \left(k_{\mathrm{s}} z\right)$ and detuning $\delta \gg \Omega_{\mathrm{s}}$ from the atomic transition $|c\rangle \rightarrow|d\rangle$. This field induces a spatially periodic ac Stark shift of level $|c\rangle$ and a corresponding modulation of the refractive index for the signal field,
$$\delta n_{\mathrm{s}}(z)=\frac{c}{v_{\mathrm{s}}} \frac{4 \delta_{\mathrm{s}}}{\omega_{a b}} \cos ^{2}\left(k_{\mathrm{s}} z\right)$$
where $\delta_{\mathrm{s}}=\Omega_{\mathrm{s}}^{2} / \delta$ is the ac Stark-shift amplitude, $v_{\mathrm{s}} \propto\left|\Omega_{\mathrm{d}}\right|^{2}$, and $\omega_{a b}$ is the $|a\rangle \leftrightarrow$ $|b\rangle$ transition frequency.

# 热力学代写

## 物理代写|热力学代写thermodynamics代考|Photon Interactions with Optical Phonons

$$\omega^{2}=\frac{\omega_{\mathrm{t}}^{2} \epsilon_{0}+c^{2} k^{2}}{2 \epsilon_{\infty}} \pm\left[\frac{\left(\omega_{\mathrm{t}}^{2} \epsilon_{0}+c^{2} k^{2}\right)^{2}}{4 \epsilon_{\infty}^{2}}-\frac{\omega_{\mathrm{t}}^{2} k^{2} c^{2}}{\epsilon_{\infty}}\right]^{1 / 2}$$

$$\omega^{2}=\omega_{\mathrm{t}}^{2}\left(\epsilon_{0} / \epsilon_{\infty}\right)=\omega_{1}^{2}$$

$$\omega^{2}=\left(c^{2} / \epsilon_{0}\right) k^{2} .$$

$$\omega^{2}=c^{2} k^{2} / \epsilon_{\infty} ; \quad \omega^{2}=\omega_{t}^{2} .$$

## 物理代写|热力学代写thermodynamics代考|Cold-Atom Optical-Polariton Baths

$|b\rangle \rightarrow|c\rangle$ ，然后原子介质通过称为电磁感应透明 (EIT) 的效应変得透明，用于弱（量子) 信号场 $\hat{\mathcal{E}}$ 作用于过渡 $|b\rangle \rightarrow|a\rangle$.

$\delta \gg \Omega_{\mathrm{s}}$ 从原子跃迁 $|c\rangle \rightarrow|d\rangle$. 该场引起空间周期性的交流斯塔克水平位移 $|c\rangle$ 以及对信号 场的折射率进行相应调制，
$$\delta n_{\mathrm{s}}(z)=\frac{c}{v_{\mathrm{s}}} \frac{4 \delta_{\mathrm{s}}}{\omega_{a b}} \cos ^{2}\left(k_{\mathrm{s}} z\right)$$

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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