## Photon Labs

We have used the labs in 3 settings: as a lab for an intro course on quantum physics, as part of a lab for a course on quantum mechanics, and as senior capstone research projects for our students. We list below our instructional materials.

## Quantum Mechanics Labs

- 2018 version (temporarily unavailable- we are about to upgrade the labs):
- Lab 1 Alignment and parametric down conversion. This lab is divided into 3 parts.
- Alignment is a necessary step to get started, because in this lab students do everything. This is mostly a hands-on procedure.
- Parametric down conversion. The objective here is for students to align the apparatus to make photon pairs. It has introductory remarks explaining down-conversion. Students should understand the basics: the process relies on conservation of energy and momentum.
- Hanbury-Brown-Twiss test This lab involves a relatively simple measurement once all is aligned. It proves that photons esist as whole items, and do not split as waves when they reach a beam splitter.

- Lab2 Photon Stern-Gerlachs The objective here is for illustrate how quantum-mechanical operations such as basis rotation or projection are used in an optical setup. Optical elements are represented by unitary operators. It is a great application of ket algebra. This is similar to the operations that appear when spins go through rotated Stern-Gerlach apparatuses, but of course with a much simpler apparatus.
- Lab 3 Single-photon interference:
- Setting the interferometer A first step is to align a Mach-Zehnder interferometer. This is a hands on part.
- Aligning the interferometer This is the conclusion, which involves adjusting the path-length difference to be less that a few micrometers. It is probably the most complex component of these experiments.
- Experiment This is the real thing. The objective is for students to think deeply about what is happening. A photon taking two arms of an interferometer, can be throught to be in a superposition of possibilities. We use quantum algebra to understand this analytically, but it is important that photons are interfering with themselves.
- Lab 4 Quantum Eraser. This experiment addresses a key aspect of quantum interference: distinguishability of possibilities. The quantum eraser uses polarization for this demonstration.
- Alignment A first part involves understanding what needs to be done and to learn a few things about polarization.
- Experiment The theoretical description is not trivial. It involves the tensor product of the momentum and polarization degrees of freedom. More deeply the experiment shows that quantum interference depends on whether the path information is present or not. It does not matter if the path information is available after the light has gone through the interferometer, as counter-intuitive aspect of quantum physics.

- Lab 5 Delayed Choice This is our most recent addition. It involves extending the quantum eraser even further: determine whether the light acts as a wave or a particle after the light has been detected. The experiment exploits the entanglement of energy present in down conversion. It also addresses misconceptions: is the energy of the photon exactly h time the frequency? This is a load-full for students and faculty(!), but its objective is to challenge students to think deeply about quantum measurement.
- Lab 6 Entanglement. This lab is the staple of modern quantum physics. Ironically is one of the easiest experiments to implement.
- Preparing the state There are some subtleties to do with creating an entangled state. In this section students make the necessary alignment to prepare one of the Bell states.
- Bell test This is the ultimate test. The objective is for students to understand its importance: that is implies that nature is nonlocal and non-realistic. The experiment itself is not very revealing the final result is a number. Students should digest on what that number means.

- 2019 version. In this iteration we tried something different. We prepared the photons so that they go in opposite directions. The alignment worked, but the problem was that it was fragile, and required instructor to make sure students were not sloppy and undo the alignment. One difference from the previous 2018 version was that the Hanbury-Brown-Twiss was done in the interference experiment, where the interferometer was the beam splitter. It provide a striking result: the photon interferes like a wave but is detected like a particle. A brief syllabus is shown here.
**Please contact me for copies.**

- Lab 1 Alignment and parametric down conversion. This lab is divided into 3 parts.

## Introductory Physics Lab: The Quantum Eraser

- Introduction
- Quantum mechanics a la Feynman
- Photon Quantum Mechanics for first-year students (taught in our intro course Phys131): Probability amplitudes and the Quantum Eraser.

Entanglement. - A lab on the quantum eraser. and results taken by students.