## OPTI544 Quantum Optics课程简介

Quantum optics is a field of physics that studies the interaction between light and matter at the quantum level. It provides a framework for understanding the behavior of light and matter under quantum mechanical rules, which is essential for developing new technologies such as quantum computers, quantum cryptography, and quantum sensors.

The basic elements of quantum optics involve the quantum theory of light and the fundamental principles of atom-light interaction. At the heart of quantum optics lies the concept of photons, which are the fundamental particles of light. The quantum theory of light explains how photons are created, absorbed, and detected, and how they interact with matter.

## PREREQUISITES

Teacher: Prof. Poul Jessen, email: [email protected]
TA: Ian Marsh, email: [email protected]
Lectures: Mondays and Wednesdays 9:30am-11am.
Office Hours: Tuesdays and Thursdays 2-3:30pm.
Zoom link to Lectures and Office Hours: https://arizona.zoom.us/j/83913913197
For registered course participants only; contact me for password.
TA office hours: and location: TBD
Prerequisite: OPTI 570 or equivalent graduate-level introductory quantum course.
See Topics and Activities at this Link for material that is expected to be familiar to you.

## OPTI544 Quantum Optics HELP（EXAM HELP， ONLINE TUTOR）

The minimum phase sensitivity, $\Delta \varphi_{\min }$, for the various entangled states as a function of $\lambda$, the transmission coefficient. The upper and lower figures are for $N=4$ and $N=6$, respectively. The dotted line (a) represents that of the uncorrelated input state . The solid lines represent (b) the NOON state, (c) the dual Fock state, (d) the intelligent $(\eta=10)$ state, (e) the Yurke, and (f) the intelligent $(\eta=1)$ state, respectively.

In the figures, the dotted line (a) represents the minimum phase sensitivity of an uncorrelated input state, which serves as a baseline for comparison. The solid lines represent the minimum phase sensitivity for different entangled states:

(b) The NOON state: This state is a superposition of two coherent states with $N$ photons each, i.e., $(|N,0\rangle + |0,N\rangle)/\sqrt{2}$. The minimum phase sensitivity of the NOON state decreases as the transmission coefficient $\lambda$ approaches 1, reaching the Heisenberg limit of $\Delta \varphi_{\min} = 1/(N\lambda)$.

(c) The dual Fock state: This state is a superposition of two Fock states with $N/2$ photons each, i.e., $(|N/2,N/2\rangle + |-N/2,-N/2\rangle)/\sqrt{2}$. The minimum phase sensitivity of the dual Fock state also decreases as $\lambda$ approaches 1, but it does not reach the Heisenberg limit.

(d) The intelligent state: This state is a superposition of coherent states with a certain amplitude profile determined by the parameter $\eta$. The minimum phase sensitivity of the intelligent state decreases as $\lambda$ approaches 0, reaching the Heisenberg limit at $\lambda=0$.

(e) The Yurke state: This state is a superposition of two coherent states with opposite phases, i.e., $(|N\rangle + |-N\rangle)/\sqrt{2}$. The minimum phase sensitivity of the Yurke state is less sensitive to the value of $\lambda$, but it still approaches the Heisenberg limit as $\lambda$ approaches 1.

(f) The squeezed vacuum state: This state is a superposition of squeezed states with a certain squeezing parameter determined by the parameter $\eta$. The minimum phase sensitivity of the squeezed vacuum state also decreases as $\lambda$ approaches 0, reaching the Heisenberg limit at $\lambda=0$.

In summary, entangled states of light can provide enhanced phase sensitivity compared to uncorrelated input states. The specific entangled state used depends on the desired level of sensitivity and the experimental conditions. The NOON state is the most sensitive, but it requires a high degree of control and precision in its preparation. The intelligent and squeezed vacuum states are more robust and easier to prepare, but they require a lower level of sensitivity.

This plot shows the expectation value $\left\langle\hat{\mu}{A B}\right\rangle$ of Eq. (6.6) plotted as a function of the phase shift $\varphi$ (solid curve) for a return power of $\bar{n}=100$. For reference we plot the normalized “classical” two-port difference signal (dashed curve). We see that the plot of the $\left\langle\hat{\mu}{A B}\right\rangle$ is super-resolving and is narrower than the classical curve by a factor of $\Delta \varphi=1 / \sqrt{n}=1 / 10$, as given in Eq. (6.8).

The plot shows the expectation value $\left\langle\hat{\mu}{A B}\right\rangle$ as a function of the phase shift $\varphi$ (solid curve) for a return power of $\bar{n}=100$. The quantity $\hat{\mu}{A B}$ is defined in Eq. (6.6) as the difference of the photon number operators at two output ports of a beamsplitter with a phase shift applied to one input port.

The solid curve shows that the plot of $\left\langle\hat{\mu}{A B}\right\rangle$ is super-resolving, meaning that it has a sharper peak than the corresponding classical two-port difference signal (dashed curve) that would be obtained with an unentangled light source. The super-resolving peak occurs because the entangled input light allows for a more precise measurement of the phase shift. The plot of $\left\langle\hat{\mu}{A B}\right\rangle$ is also narrower than the classical curve by a factor of $\Delta \varphi=1 / \sqrt{n}=1 / 10$, as given in Eq. (6.8). This means that the entangled input light provides a phase sensitivity that is 10 times better than that of an unentangled light source with the same average number of photons.

Overall, this plot demonstrates the advantage of using entangled light sources in precision measurements. By exploiting quantum correlations between the photons, entangled light sources can provide higher precision and resolution than classical light sources with the same average number of photons.

## 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.