Monthly Archives: October 2024

The purpose of this post is to review some basic experimental physics taught as part of the \(2\)nd-year physics course at Cambridge. Digitization & Signal Processing In what follows, it is convenient to think of \(f(t)\in\textbf R\) as a real-valued … Continue reading →

The purpose of this post is to calculate the energy band structure of the famous \(2\)-D material graphene. This of course is a monolayer of carbon \(\text C\) atoms arranged in a hexagonal “honeycomb” lattice. Sheets of graphene stacked on … Continue reading →

The purpose of this post is to quickly explain the basics of what quantum gas microscopy is, how it works, and what it’s good for. Essentially, the steps can be summarized as follows:

Free Electrons Consider the usual cubic box of side lengths \(L\) with nothing inside it (i.e. a vacuous Bravais lattice \(\Lambda=\emptyset\)). Now put an electron \(e^-\) inside this box. Its position space wavefunction will be a free plane wave of … Continue reading →

The purpose of this post is to discuss historically one of the first decision problems for which quantum computing was shown to provide an exponential advantage over classical computing. One of the initially striking discrepancies between classical logic gates such … Continue reading →

A qubit is any quantum system with a two-dimensional state space \(\mathcal H\cong\textbf C^2\). In particular because the state space is two-dimensional \(\dim\textbf C^2=2\), the Gram-Schmidt orthogonalization algorithm guarantees the existence of an orthonormal basis \(|0\rangle,|1\rangle\in\mathcal H\) of state vectors … Continue reading →

The purpose of this post is to quickly review some fundamentals of classical computation in order to better appreciate the distinctions between classical computing and quantum computing. Note that the word computation itself, whether classical or quantum, basically just means … Continue reading →

The purpose of this post is to build up to an explanation of the Mössbauer effect in quantum mechanics. At an intuitive level, the Mössbauer effect simply asserts that when an atom absorbs or emits a \(\gamma\)-ray photon, if it’s … Continue reading →