A Fifth-Coordinate Phase Interferometer: Atom-Optical Readout of Extra-Coordinate Displacement with Computed Resolution

An interferometer whose arms are arranged to cancel ordinary displacement can retain sensitivity to displacement along a compact fifth coordinate, which appears as a residual phase that common-mode rejection does not remove. This paper specifies such an instrument on the platform of a Raman atom interferometer, with a stated extra-coordinate coupling of five per cent of the optical wavevector product. Quantum projection noise and technical phase noise together give a computed extra-coordinate resolution of 3.75e-09 metres per root hertz; the unambiguous range before phase wrapping is 7.80e-06 metres of extra-coordinate displacement; and integration to a resolution of 1e-11 metres requires 39.1 hours at the stated cycle rate. The design includes the vibration-isolation, wavefront, and rotation-compensation provisions needed to keep the ordinary-displacement channel below the residual channel. SIMULATED, NOT MEASURED: the performance figures are computed from stated assumptions and no apparatus has been operated.