Subtomographic imaging of a polarisation sensitive phase pattern localised in phase space

A transparent polarisation-sensitive phase pattern changes the phase of transmitted light without absorption, whereas this change of phase depends on the polarisation of incident light. A position-localised polarisation-dependent phase pattern is imprinted onto the phase-space of atoms by using atomic state dependent velocity-selective hole burning. A phase-space localised pattern is a higher dimensional generalisation of patterns localised in the position-space. Such a pattern cannot be imaged with a lens. The imprinted pattern is localised in a unique three-dimensional subspace of the six-dimensional phase-space of atoms. The phase-space localised pattern transforms the polarisation of light transmitting through it. This pattern is tomographically imaged at room temperature by measuring the intensity of the transmitted imaging laser beam of variable frequency with a camera after its polarisation analysis. Two sub-tomographs of the imprinted phase-space localised pattern are constructed. This paper presents a concept and experiment of imprinting and imaging of a polarisation-sensitive phase pattern localised in the phase-space.