Quantum Superposition and Single-Photon Interference: Mach-Zehnder Interferometer Explained

This video delves into quantum superposition using a Mach-Zehnder interferometer setup. It explains how a single photon can travel through two paths at once, producing interference patterns, and how measurement collapses the state into definite outcomes. The talk also connects these ideas to state vectors, amplitudes, and probabilities, emphasizing the postulate of measurement and the reconstruction of quantum states from repeated trials.

Overview of Quantum Superposition

The presenter begins by contrasting classical superposition of electric fields with quantum superposition, where a single photon can occupy two paths simultaneously in an interferometer. The key idea is that interference arises not from photon-photon interactions but from a single photon interfering with itself when it is in a superposition of being in the upper and lower paths.

The Mach-Zehnder Interferometer

In the described device, input light is split by a beam splitter into two paths, reflected by two mirrors, and recombined at a second beam splitter before detectors. By adjusting phase relations, the setup can direct almost all the light to one detector or split it according to designed interference, illustrating the probabilistic yet coherent nature of quantum amplitudes.

Photons, Interference, and Probabilities

The talk emphasizes that photons do not interfere with other photons in this experiment; instead, each photon interferes with itself. When measured, outcomes are discrete: a photon is detected at either detector with probabilities determined by the amplitudes along each path, described by the Born rule.

State Vectors and Superposition

States are treated as vectors that can be added to form superpositions, such as alpha times state A plus beta times state B. Measurement yields state A or state B with probabilities proportional to |alpha|^2 and |beta|^2, respectively. After a measurement, the system collapses to the corresponding eigenstate, and subsequent measurements reflect that state.

Measurement Postulate and State Reconstruction

To determine the coefficients in a superposition, one must prepare many copies of the state and perform measurements repeatedly. The resulting statistics reveal the probabilities and allow reconstruction of the state, illustrating the fundamental difference between quantum and classical predictions.