Proposal for a phase-space microscope for quantum gases

In an international collaboration with the University of Cambridge, we have studied the possiblity of measuring phase-space observables in synthetic quantum systems of ultracold atoms. The phase space combines position and momentum of particles, which form conjugate variables in quantum mechanics and cannot jointly be sharply measured due to Heisenberg's uncertainty principle. One can however perform positive operator-valued measures in a coherent state basis. We discuss how such a measurement can be implemented in state-of-the art experiments, using access to Fourier space in a matter-wave microscope for mapping momentum space onto an auxiliary dimension or averages of momentum density and its moments to an auxiliary spin degree of freedom, which can then be detected in a spatially resolved manner. These techniques will be important for exploring quantum systems with ultracold atoms and could for example be used to study squeezing in quantum many-body systems.
The preprint is available at Cooper et al.
