Possible use of a Cooper-pair box for low-dose electron microscopy

A transmission electron microscope that takes advantage of superconducting quantum circuitry is proposed. The microscope is designed to improve the image contrast of radiation-sensitive weak-phase objects, in particular, biological specimens. The objective in this setting is to measure the phase shift of the probe electron wave to a precision Δθ within the number of electrons N that does not destroy the specimen. In conventional electron microscopy Δθ scales as ∼1/N^1/2, which falls short of the Heisenberg limit ∼1/N. To approach the latter by using quantum entanglement, we propose a design that involves a Cooper-pair box placed on the surface of an electrostatic electron mirror in the microscope. Significant improvement could be attained if inelastic scattering processes are sufficiently delocalized.