A “Quiet” Measurement of a Quantum Drum

Forrest W. Eagle, Kyser D. Seaney, Michael P. Grubb

Quantum mechanics is a notoriously difficult subject to learn, due to a lack of real-world analogies that might help provide an intuitive grasp of the underlying ideas. Discrete energy levels and absorption and emission wavelengths in atoms are sometimes described as uniquely quantum phenomena, but are actually general to spatially confined waves of any sort. Here, we provide an experiment demonstrating the acoustic spectroscopy of a drum. We show that a struck drum emits sounds of discrete frequencies (tones), and that the lifetime of each emitted tone is directly related by Heisenberg’s uncertainty principle to its line width in the drum’s frequency spectrum. We also show that a still drum absorbs only those same frequencies when exposed to monochromatic sound from an audio speaker. The resonant motion of the drum membrane is too fast to see by eye (>60 Hz), but can be observed with the aid of a strobe light. The observed resonant modes of the drum are the eigenfunctions of a particle trapped in an infinite circular well, and analogous to the shapes of atomic orbitals (1s, 2p, 3d, 2s, etc.). This experiment can be built for under $50, and is an excellent demo or lab exercise for general and physical chemistry courses to provide a visual example of abstract quantum mechanical ideas.

Anonymous

B. Whitten-Wolfe, Gérard G. Emch

Anwesha Chattopadhyay, Bhaskar Mukherjee, K. Sengupta +1 more

We introduce a disorder-free model of S=1/2 S = 1 / 2 spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as "quantum drums". These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasi-one-dimensional drums numerically, dubbed "wire" and a "junction of two wires" respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the one-dimensional PXP chain with open boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model.

David Mason, Massimiliano Rossi, Albert Schließer +1 more

Using a trick inspired by noise-cancellation headphones, we have been able to control the motion of a millimeter-sized drum at the “quantum level”, even though it is big enough to see with our bare eyes. - submission by David Mason, Massimiliano Rossi, Albert Schliesser