Decoherence

Interference needs memory of phase. When a system couples to a large environment—air molecules, phonons, photons, or internal junk—its phase information does not vanish, it spreads into correlations with those extra degrees of freedom. Locally, the system’s interference fades because the “which-way” crumbs are now everywhere. This is decoherence: a dynamical, unitary process that makes classicality emerge from quantum rules without changing them.

For a system \(S\) interacting with an environment \(E\), the joint state \(\rho_{SE}\) evolves unitarily. What we access in the lab is the reduced state \(\rho_S=\mathrm{Tr}_E\,\rho_{SE}\). In a preferred “pointer” basis \(\{|i\rangle\}\) set by the interaction, off-diagonal terms decay as \[ \rho_S(t)_{ij}\approx \rho_S(0)_{ij}\,e^{-t/\tau_\mathrm{dec}} \quad (i\ne j), \] while the diagonals remain approximately fixed on short times. Models (spin-bath, Caldeira–Leggett, collisional decoherence) compute \(\tau_\mathrm{dec}\) and show it can be fantastically small for macroscopic objects.

Decoherence is basis-dependent. The states that resist phase leakage are called pointer states, selected by the interaction Hamiltonian \(H_{SE}\) (“einselection”). For position-coupled noise, localized wavepackets are robust; for photon counting, number states survive; for dephasing qubits, the \(\sigma_z\) eigenstates endure.

Decoherence does not pick one outcome; it explains why alternatives cease to interfere and can be treated as if classical. Interpretations add the final step: Bayesian update (QBism), branching (Many Worlds), objective collapse models, etc. But regardless of metaphysics, experiments agree: off-diagonals become tiny in a preferred basis on breathtakingly short timescales.

Pure dephasing qubit: \(H=\tfrac{\hbar\omega}{2}\sigma_z + \sigma_z\otimes B\). The reduced qubit obeys \(\dot\rho_{01}=-\gamma\,\rho_{01}\) while populations are constant.

Collisional decoherence: A massive particle in a gas: spatial coherences \(\rho(x,x')\) decay as \( \rho(x,x',t)\sim \rho(x,x',0)\exp[-\Lambda t (x-x')^2] \), suppressing long-range superpositions first.

Decoherence time can be orders of magnitude shorter than relaxation time. A dust grain in air decoheres in \(\sim 10^{-31}\,\mathrm{s}\) for micron-separated paths—effectively instantaneous—while energy exchange with the bath is slow. That is why macroscopic objects look classical even though the underlying law is quantum.

Decoherence dissolves much of the mystery around measurement by showing how interference opportunities evaporate. What remains are questions about probability and outcomes—perfect bridges to Wigner’s friend, where different observers assign different quantum states depending on which records they access.