A periodic potential formed by interfering laser beams to trap and control atoms or ions.An optical lattice is a periodic potential energy landscape created by the interference of counter-propagating laser beams. It traps neutral atoms or ions in a grid-like pattern, allowing scientists to study quantum many-body systems with unprecedented control. This 'crystal of light' serves as a versatile platform for simulating condensed matter phenomena, exploring quantum phase transitions, and building quantum computers.
The concept was developed in the late 1980s and early 1990s, with pioneering work by Claude Cohen-Tannoudji, Steven Chu, and others on laser cooling and trapping. The first experiments with atoms in optical lattices were performed in the mid-1990s.
When two or more laser beams overlap, their electric fields interfere, creating a standing wave pattern with regions of high and low intensity. Atoms experience a force proportional to the intensity gradient (dipole force), so they are attracted to the intensity maxima or minima, depending on the laser detuning. By using multiple beams in different directions, a 1D, 2D, or 3D lattice of potential wells is formed. Atoms can be loaded into these wells, and by adjusting the laser intensity and frequency, the lattice depth and spacing can be precisely controlled.
Used in quantum simulation of the Hubbard model, studying Bose-Einstein condensates, and as a basis for neutral-atom quantum computing, where qubits are trapped in individual lattice sites.
Optical lattices can be used to create 'quasicrystals' for atoms, where the potential pattern never repeats exactly, mimicking the structure of quasicrystalline materials.
| H | variable | Hamiltonian matrix in momentum space — hamiltonian joule |
| k | variable | Crystal momentum vector — crystal momentum kilogram metre per second |
| c_α | variable | Coefficient function for each Γ_α term joule |
| Γ_α | variable | Matrix representing hopping and on-site terms |
| ∑ | operator | Sum over all relevant terms α — summation |

