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 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 $\mathrm{\Delta }\theta$ within the number of electrons $N$ that does not destroy the specimen. In conventional electron microscopy $\mathrm{\Delta }\theta$ scales as $\sim 1\mathrm{/}{N}^{1\mathrm{/}2}$, which falls short of the Heisenberg limit $\sim 1\mathrm{/}N$. 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.