Quantum interference effects observed in molecules, analogous to double-slit experiments.Molecular interferometry is the experimental demonstration of quantum wave-like behavior in molecules, extending the classic double-slit experiment to objects composed of hundreds or even thousands of atoms. When a beam of molecules passes through a grating or an interferometer, the molecules interfere with themselves, producing a pattern that reveals their wave nature. This is a direct test of the quantum superposition principle at macroscopic scales, probing the boundary between the classical and quantum worlds. Such experiments also provide a sensitive probe of decoherence—the process by which interactions with the environment destroy quantum coherence—and can be used to measure molecular properties with extreme precision.
The first interference experiments with molecules were performed in the 1990s, with groups led by Anton Zeilinger and others demonstrating diffraction of fullerenes (C60) in 1999. Since then, the mass and complexity of interfering molecules have steadily increased, reaching molecules with over 10,000 atomic mass units by the 2020s.
In a typical setup, a beam of molecules is collimated and directed toward a diffraction grating—often a nanofabricated silicon nitride mask with periodic slits. The molecules are detected downstream, and their arrival positions are recorded. If the molecules behaved classically, they would form a simple shadow pattern, but quantum mechanics predicts an interference pattern of alternating bright and dark fringes. The fringe visibility depends on the molecule's de Broglie wavelength, which is inversely proportional to its momentum. To observe interference, the molecules must be cooled and their internal states controlled to minimize decoherence from thermal radiation or collisions. Advanced setups use Kapitza-Dirac scattering with laser light or Talbot-Lau interferometers with multiple gratings to enhance the effect.
Molecular interferometry is used to measure molecular polarizabilities, magnetic moments, and internal energy levels with high precision, and it informs the design of matter-wave sensors for inertial navigation and gravitational field mapping.
In 2019, researchers interfered molecules made of over 2,000 atoms, each molecule containing more than 100 carbon atoms, and the interference pattern remained visible—demonstrating that quantum superposition survives in objects far larger than single particles.
| U | variable | First unitary matrix — unitary matrix |
| V | variable | Second unitary matrix — unitary matrix |
| N | variable | Dimension of the Hilbert space — dimension |
| Tr | operator | Sum of diagonal elements of a matrix — trace operator |
| † | operator | Conjugate transpose of a matrix — hermitian conjugate |
| | | | operator | Magnitude of a complex number — absolute value |
| c | variable | cross-correlation value — cross correlation |
| v | variable | Doppler shift velocity — velocity metre per second |
| λ | variable | wavelength — wavelength metre |
| S1 | variable | first spectrum — spectrum |
| S2 | variable | second spectrum — spectrum |
| S̄1 | variable | mean of first spectrum over wavelength — mean spectrum |
| S̄2 | variable | mean of second spectrum over wavelength — mean spectrum |
| σ | variable | standard deviation of spectrum — standard deviation |
| ∑ | operator | sum over wavelength bins — summation |
| g^(2) | variable | Second-order correlation function — second order correlation function |
| τ | variable | Time argument — time second |
| Δτ | variable | Time delay — time second |
| â†(τ) | variable | Creation operator at time τ — creation operator |
| â(τ) | variable | Annihilation operator at time τ — annihilation operator |
| ⟨...⟩ | operator | Quantum mechanical expectation value — expectation value |
| F | variable | flux density — spectral flux density joule per second per metre squared per hertz |
| ν | variable | frequency — frequency hertz |
| ν_p | variable | break frequency — frequency hertz |
| F_νp | variable | flux density at break frequency — spectral flux density joule per second per metre squared per hertz |
| β_1 | variable | low-frequency spectral index — dimensionless |
| β_2 | variable | high-frequency spectral index — dimensionless |
| s | variable | smoothness parameter — dimensionless |










