The set of energy levels that a system can occupy when excited from its ground state.The excitation spectrum of a system is the set of energy levels it can occupy when promoted from its ground state. It's like a fingerprint of the system's internal dynamics, revealing how energy is absorbed or emitted in discrete quanta. For atoms, this spectrum is the familiar series of spectral lines; for more complex systems like quantum gases or crystals, it includes collective excitations such as phonons or magnons.
The concept of discrete excitation spectra dates back to the early 20th century with Bohr's model of the hydrogen atom, later formalized by quantum mechanics.
When a system absorbs energy, it transitions to a higher energy state. The excitation spectrum lists all possible such states, each with a specific energy. The structure of this spectrum is determined by the system's Hamiltonian, which encodes interactions and confinement. Measuring the spectrum—for example, by scattering particles or photons off the system—reveals the allowed energy levels and their lifetimes, providing a direct window into the system's underlying physics.
Excitation spectra are used in spectroscopy to identify materials, in quantum computing to characterize qubit energy levels, and in condensed matter physics to probe exotic phases like superconductors.
The excitation spectrum of a superfluid helium-4 shows a roton minimum, a dip in energy at a specific momentum, which was a major puzzle until Landau explained it as a precursor to turbulence.
