Atom interferometers with weak-measurement path detectors and their quantum mechanical analysis
Li Zhi-Yuan
       

A general scheme of MZI-type WM-AI involving an internal quantum state correlated beam splitter as the WM-PD. The wave nature of the atoms, the interference pattern, is probed via observation of the transverse interference pattern while the particle nature of the atoms, the which-path information, is probed automatically via the PBS. The incident beam is described by a composite wave function ψ 0 e i kx ( φ 1 + φ 2 ) , which involves the usual coherent spatial wave function ψ 0 e i kx but dressed with a coherent superposition of internal quantum state φ 1 and φ 2 . The PBS selectively transmits the beam component with state φ 2 along the path Y, while it reflects the beam component with state φ 1 along the path X, thus automatically offering the which-path information. The transverse interference pattern arising from the two atom beam cross over is recorded by a deliberately designed interference screen that is only sensitive to the atom center-of-mass spatial state ψ 0 , but is insensitive to the internal electronic state φ 1 and φ 2 . This simple scheme of PBS WM-AI can also offer a superior power to simultaneously observe the wave and particle nature of the atoms, and can be applicable to other massive particles.