物理代写|ECE5310 Quantum Optics
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ECE5310 Quantum Optics课程简介
This is a graduate level course on quantum optics. Topics covered include density matrices, semi-classical light matter interactions, Rabi oscillations, electromagnetically induced transparency and interference effects, quantization of fields in cavity and free space, properties of photons, field commutation relations, number states, coherent states, quadrature and amplitude-phase squeezed states, vacuum fluctuations, matter-photon interactions, stimulated and spontaneous emission processes, classical/quantum descriptions of photon detection, coherent homodyne and heterodyne detection, coherence functions, cavity quantum optics and microcavity effects in spontaneous emission, cavity quantum optics in strong coupling and weak coupling limits, generation of quantum states of light, phase sensitive and phase insensitive optical amplifiers, parametric amplifiers, fundamental performance limits of optical amplifiers, photon statistics and characteristic functions, laser oscillators, number and phase characteristics of laser light, parametric oscillators and squeezing, quantum opto-mechanics, opto-mechanical cooling and squeezing, noise penalty in simultaneous detection of two non-commuting field quadratures, bit error rates in optical communication systems, classical and quantum information and information carrying capacity of quantum states of light.
PREREQUISITES
This is a graduate level course on quantum optics. Topics covered include density matrices, semi-classical light matter interactions, Rabi oscillations, electromagnetically induced transparency and interference effects, quantization of fields in cavity and free space, properties of photons, field commutation relations, number states, coherent states, quadrature and amplitude-phase squeezed states, vacuum fluctuations, matter-photon interactions, stimulated and spontaneous emission processes, classical/quantum descriptions of photon detection, coherent homodyne and heterodyne detection, coherence functions, cavity quantum optics and microcavity effects in spontaneous emission, cavity quantum optics in strong coupling and weak coupling limits, generation of quantum states of light, phase sensitive and phase insensitive optical amplifiers, parametric amplifiers, fundamental performance limits of optical amplifiers, photon statistics and characteristic functions, laser oscillators, number and phase characteristics of laser light, parametric oscillators and squeezing, quantum opto-mechanics, opto-mechanical cooling and squeezing, noise penalty in simultaneous detection of two non-commuting field quadratures, bit error rates in optical communication systems, classical and quantum information and information carrying capacity of quantum states of light.
ECE5310 Quantum Optics HELP（EXAM HELP， ONLINE TUTOR）
Exercise 4.4 Consider the situation where a laser beam with a power of $100 \mathrm{~mW}$ is focused onto an area of the square wavelength $\lambda^2$.
(a) Estimate the field strength in the focus spot. Use a light wavelength of $500 \mathrm{~nm}$ and assume a homogeneous field distribution.
(b) Estimate the number of photons passing per second through the area $\lambda^2$.
(c) Assume that each photon transfers a momentum $\hbar k$. Estimate the force exerted by the total incoming photon flux.
Exercise 4.6 The polarizability of a small dielectric sphere is given by
$$
\alpha=4 \pi \varepsilon_2\left(\frac{\varepsilon_1-\varepsilon_2}{\varepsilon_1+2 \varepsilon_2}\right) a^3 .
$$
Here $a$ is the sphere radius, and $\varepsilon_1, \varepsilon_2$ are the permittivities inside and outside the sphere. Consider a glass sphere $\left(n_1=1.5\right)$ embedded in water $(n=1.33)$, and a sphere diameter of $100 \mathrm{~nm}$. Use the results of Exercise 4.5 to compute the dipole force of Eq. (4.6) acting on the glass sphere in the focus spot and away from it. Express the forces in $\mathrm{pN}$.
Exercise 4.11 Compute Maxwell’s stress tensor of Eq. (4.33) for a plane wave with arbitrary polarization. Interpret the result in terms of momentum and angular momentum carried by the wave.
Exercise 4.12 Use the polarizability given in Exercise 4.6, and a dielectric particle with a real polarizability $\varepsilon_1=\varepsilon_1^{\prime}$ that is excited by a time-harmonic field $\boldsymbol{E}_0$.
(a) Compute the induced dipole moment of the sphere.
(b) Compute the fields of a dipole using the results of electrostatics. These results are also valid for an oscillating dipole in the nearfield zone.
(c) Compute in the nearfield zone Maxwell’s stress tensor.
Textbooks
• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.
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