Quantum coherence in a specified basis (${\rho }_{jk}\ne 0$, $j\ne k$)

For a chosen orthonormal basis, the off-diagonal entries of a density operator encode quantum coherence between distinct basis states. A diagonal density operator is an incoherent mixture in that basis. This property is basis-dependent: diagonalizing the operator does not imply that it lacked coherence in the measurement or energy basis of interest. Relative phases affect these entries, while a global wavefunction phase cancels from the density operator. Dephasing damps the entries and can spoil stimulated Raman adiabatic passage by removing the ground-state interference that maintains the dark state.

Preservation of relative electronic phase along alternative paths so they can interfere. Loss of coherence suppresses interference structure, but semiclassical magnetic focusing can persist if momentum trajectories remain sufficiently ballistic.