Dark States and De Broglie Wave Optics

The techniques of laser cooling have now become sufficiently developed that the focus has shifted toward interesting applications such as the quantum domain of atomic motion. This topic is characterized by the failure of the classical description in which atoms move as point particles whose trajectories can be known: instead, atomic motion must be described as the optics of de Broglie waves. For example, when the de Broglie wavelength λ$\text{}_{dB}$ exceeds λ$\text{}_{optical}$, then a classical description is insufficient (Bose condensation is done in the dark, and the quantum condition becomes λ$\text{}_{dB}$ > nearest neighbor distance). One of the most fascinating topics of quantized atomic motion in a laser field derives from optical dark states that can even occur in the simplest (two-level) atoms, where there are no magnetic sublevels and the polarization is irrelevant. In spite of the simplicity of this two-level atom case however, the more interesting cases occur in multilevel atoms where the internal magnetic states and external quantum states of atomic motion become truly entangled. Schrödinger called such states "the heart of quantum mechanics" because they led to puzzles such as his famous "cat" and the EPR paradox.