Delayed-Choice Quantum Eraser: The paradox of time-independent correlated measurements

This thesis on quantum entanglement comes in two parts: one part describes and executes an experiment in quantum optics called a delayed-choice quantum eraser; the other is an exploration of some specific topics in the more general subject of entanglement. Naturally, the thesis process itself has similarly been in two distinct parts. Part of my time has focused on building the experiment in the optics lab in Fisher Science and Academic Center. The other has focused mostly on researching and learning the unique and often confusing properties of entanglement. Quantum entanglement describes a certain connection between two or more particles, such as electrons, photons, or even whole atoms. Although they may be spatially or temporally separated as far as two opposite sides of the Universe, they behave in unison and when observed, the measurement results will be strongly correlated. In short, these entangled particles act as if they are a single, irreducible system instead of multiple smaller ones. Thus, in working with entanglement, it makes no sense to refer to one particle without how it affects its entangled partner. This has some truly counterintuitive consequences. It turns out that one can entangle particles that have never even interacted and can use entanglement to trans- port information in novel ways. The latter, known as quantum teleportation, has some powerful applications in communication and cryptography. Quantum cryptog- raphy promises the unbreakable cybersecurity and up to double the current maximum transmission speed using traditional, or classical, channels. It is perhaps the most famous application of entanglement. At the heart of this thesis is the phenomenon of delayed choice. In the quantum world, measurement has an active role in shaping reality. How we measure a system can cause a serious change in how the system actually behaves, but precisely when we make that measurement is independent of its effect. Therefore, we can actually make the measurement after the relevant event has already happened, but still influence how the system behaved during that event. Yes{a future choice of how we make a measurement can in uence past events. But do not be fooled by this apparent para- dox: we cannot use this to see the future or send information backwards in time. The past event in question is not truly determined until it is observed. This is a funda- mental property of quantum physics, and the delayed choice phenomenon reinforces it in a more dramatic way. The experimental verification of such a phenomenon is presented here using a set up called a quantum eraser. Our quantum eraser involves a Mach-Zehnder interferometer, through which a photon can take two separate paths. Each path is encoded with a dierent po- larization, an example of quantum information. The quantum eraser destroys this information and \causes a single photon to eectively traverse both paths. At the output, we see an array of light and dark stripes instead of a continuous beam, which we call an interference pattern. The shape of the interference pattern depends on its starting polarization. If we entangle this photon with another outside the quantum eraser, we can \choose which polarization the first photon takes on by performing appropriate mea- surements with the partner. This allows us to manipulate the interference pattern at the output of the quantum eraser. In a delayed-choice mode, we can make these \appropriate measurements after we have already observed the interference pattern, showing that an action on an entangled photon can aect its partner\u27s behavior during a past event. We attempt to show this experimentally in the lab