| coherence length | |
|---|---|
| Name | Coherence length |
| Unit | metre (m) |
| Dimension | Length |
coherence length
Coherence length is the characteristic distance over which a wave-like quantum system (such as a photon, electron, or matter wave) maintains a well-defined phase relationship. It quantifies the spatial scale of phase correlation and determines whether interference effects persist in experiments and technologies. In Quantum Physics and Optics, coherence length is central to understanding phenomena from interferometry to superconducting circuits.
Coherence length L_c is defined as the maximum separation between two points in space (or events in time, via the speed of propagation) for which the complex coherence function remains appreciable. Physically, it indicates the range over which a quantum state or a classical electromagnetic field can produce stable interference fringes. In practical terms, L_c limits the resolution of instruments such as the Michelson interferometer and sets design constraints for systems like optical fiber networks, Josephson junctions, and electron microscopy.
Because coherence properties influence signal visibility, they bear directly on national infrastructure and technology sectors—telecommunications, precision navigation, and secure communications. Institutions such as Bell Labs and National Institute of Standards and Technology have historically developed measurement standards and instrumentation tied to coherence phenomena.
Mathematically, coherence length is related to the spatial decay of the first-order coherence function g^(1)(r1,r2) = ⟨E*(r1)E(r2)⟩/√(⟨|E(r1)|^2⟩⟨|E(r2)|^2⟩). For stationary fields, the temporal coherence time τ_c is the decay time of g^(1)(τ), and L_c ≈ v_g τ_c, where v_g is the group velocity (e.g., c/n in a medium with refractive index n). For a spectrum S(ω), the Wiener–Khinchin theorem links g^(1)(τ) to S(ω) via the Fourier transform; a narrow linewidth (small Δω) gives long τ_c and thus long L_c. Examples include the Lorentzian lineshape of a homogeneously broadened laser where τ_c ≈ 1/Δω, and Gaussian spectra from classical sources such as thermal blackbody radiation.
Quantitative measures include the full width at half maximum (FWHM) of |g^(1)|, the coherence area for spatial coherence, and higher-order coherence functions g^(n) introduced in Roy J. Glauber’s quantum optical formalism. In solid-state systems, the phase coherence length for electrons L_φ is determined by quantum transport theories, such as those developed by Philip W. Anderson and in the theory of weak localization. L_φ appears in expressions for conductance corrections and universal conductance fluctuations in mesoscopic physics.
Coherence is a property of pure and mixed quantum states and underpins entanglement, superposition, and interference. For photons, coherence properties are studied within quantum optics and described by creation and annihilation operators in the Glauber–Sudarshan P representation. In matter waves, coherence length determines the visibility of interference in experiments like the Davisson–Germer experiment and modern Bose–Einstein condensate interferometry refined at institutions such as MIT and University of Cambridge.
Superconducting qubits and trapped ion systems require phase coherence over times and lengths sufficient for gate operations. Decoherence processes shorten the effective L_c for qubits, limiting quantum error correction rates and scalable quantum computing architectures pursued by organizations like IBM and Google Quantum AI.
Decoherence arises from coupling to environments: phonons, photons, electromagnetic fluctuations, and many-body interactions. In electronic systems, electron–phonon scattering, magnetic impurities, and electron–electron interactions set the phase coherence length L_φ; seminal work by Imry Yoseph and others formalized environment-induced dephasing. In optics, thermal emission, inhomogeneous broadening, and finite emitter lifetimes reduce coherence. Open quantum systems are modeled by master equations (Lindblad form) and decoherence times T_1 and T_2 in magnetic resonance and qubit physics; T_2 relates directly to phase coherence and thus spatial L_c when translated via velocity.
Engineering to preserve coherence involves isolation, cryogenics (e.g., dilution refrigerators used at Stanford University and Yale University), magnetic shielding, and material purification, as employed in particle accelerators and precision measurement facilities like CERN and national metrology laboratories.
Interferometric techniques measure coherence length: Michelson and Mach–Zehnder interferometers map fringe visibility versus path difference. Spectroscopy (heterodyne, Fourier-transform) extracts linewidth Δν and infers τ_c and L_c. Hanbury Brown and Twiss setups probe intensity correlations and higher-order coherence; these were instrumental at Jodrell Bank Observatory and in radio astronomy. In solid-state systems, weak localization magnetoresistance and Aharonov–Bohm oscillations measure electron phase coherence, often in cryogenic transport labs at Bell Labs and leading universities.
Single-photon sources (quantum dots, nitrogen-vacancy centers in diamond), stabilized lasers (e.g., those locked to optical frequency combs), and superconducting circuits use Ramsey and spin-echo sequences to assess coherence. Metrological centers employ standards developed from the work of Theodor W. Hänsch and John L. Hall in frequency stabilization.
Coherence length directly impacts optical coherence tomography (OCT) resolution, fiber-optic communication channel design, and interferometric gravitational wave detectors like LIGO. Long L_c lasers enable precision spectroscopy, atomic clocks (e.g., at NIST and PTB), and coherent lidar. In quantum information, coherence sets gate fidelities in superconducting qubits, coherence times in ion trap systems, and entanglement distribution ranges in quantum networks pursued by national programs and companies such as Xanadu and D-Wave Systems.
Preserving and exploiting coherence supports stable institutions and critical infrastructure by enabling reliable timing, secure communication, and advanced sensing—areas of strategic national importance.
Category:Quantum physics Category:Optics